TSTP Solution File: ITP240^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP240^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 03:24:14 EDT 2023
% Result : Theorem 283.60s 283.91s
% Output : Proof 283.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.89/2.89 % Problem : ITP240^3 : TPTP v8.1.2. Released v8.1.0.
% 2.89/2.90 % Command : do_cvc5 %s %d
% 2.93/3.11 % Computer : n015.cluster.edu
% 2.93/3.11 % Model : x86_64 x86_64
% 2.93/3.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.93/3.11 % Memory : 8042.1875MB
% 2.93/3.11 % OS : Linux 3.10.0-693.el7.x86_64
% 2.93/3.11 % CPULimit : 300
% 2.93/3.11 % WCLimit : 300
% 2.93/3.11 % DateTime : Sun Aug 27 12:23:26 EDT 2023
% 2.93/3.11 % CPUTime :
% 5.49/5.83 %----Proving TH0
% 5.49/5.83 %------------------------------------------------------------------------------
% 5.49/5.83 % File : ITP240^3 : TPTP v8.1.2. Released v8.1.0.
% 5.49/5.83 % Domain : Interactive Theorem Proving
% 5.49/5.83 % Problem : Sledgehammer problem VEBT_Pred 00667_037763
% 5.49/5.83 % Version : [Des22] axioms.
% 5.49/5.83 % English :
% 5.49/5.83
% 5.49/5.83 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.49/5.83 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.49/5.83 % Source : [Des22]
% 5.49/5.83 % Names : 0069_VEBT_Pred_00667_037763 [Des22]
% 5.49/5.83
% 5.49/5.83 % Status : Theorem
% 5.49/5.83 % Rating : 1.00 v8.1.0
% 5.49/5.83 % Syntax : Number of formulae : 11327 (5634 unt;1082 typ; 0 def)
% 5.49/5.83 % Number of atoms : 28472 (12077 equ; 0 cnn)
% 5.49/5.83 % Maximal formula atoms : 71 ( 2 avg)
% 5.49/5.83 % Number of connectives : 115947 (2663 ~; 523 |;1755 &;100081 @)
% 5.49/5.83 % ( 0 <=>;10925 =>; 0 <=; 0 <~>)
% 5.49/5.83 % Maximal formula depth : 39 ( 6 avg)
% 5.49/5.83 % Number of types : 99 ( 98 usr)
% 5.49/5.83 % Number of type conns : 5029 (5029 >; 0 *; 0 +; 0 <<)
% 5.49/5.83 % Number of symbols : 987 ( 984 usr; 64 con; 0-8 aty)
% 5.49/5.83 % Number of variables : 26680 (2440 ^;23449 !; 791 ?;26680 :)
% 5.49/5.83 % SPC : TH0_THM_EQU_NAR
% 5.49/5.83
% 5.49/5.83 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.49/5.83 % from the van Emde Boas Trees session in the Archive of Formal
% 5.49/5.83 % proofs -
% 5.49/5.83 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.49/5.83 % 2022-02-17 23:27:20.743
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% 5.49/5.83 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.49/5.83 product_prod_o_int: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.83 set_VEBT_VEBT: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.49/5.83 set_set_nat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 5.49/5.83 set_set_int: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 5.49/5.83 thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
% 5.49/5.83 set_list_o: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.49/5.83 product_prod_o_o: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.83 set_complex: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
% 5.49/5.83 filter_real: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 5.49/5.83 option_num: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
% 5.49/5.83 option_nat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
% 5.49/5.83 filter_nat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 5.49/5.83 set_char: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
% 5.49/5.83 list_real: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 5.49/5.83 set_real: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.83 list_nat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 5.49/5.83 list_int: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
% 5.49/5.83 vEBT_VEBT: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 5.49/5.83 set_rat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
% 5.49/5.83 set_num: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.83 set_nat: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.83 set_int: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Code____Numeral__Ointeger,type,
% 5.49/5.83 code_integer: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Extended____Nat__Oenat,type,
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% 5.49/5.83
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% 5.49/5.83 list_o: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Complex__Ocomplex,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 5.49/5.83 set_o: $tType ).
% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__String__Ochar,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Real__Oreal,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Rat__Orat,type,
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Num__Onum,type,
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% 5.49/5.83
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% 5.49/5.83
% 5.49/5.83 thf(ty_n_t__Int__Oint,type,
% 5.49/5.83 int: $tType ).
% 5.49/5.83
% 5.49/5.83 % Explicit typings (984)
% 5.49/5.83 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
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% 5.49/5.83
% 5.49/5.83 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.49/5.83 archim3151403230148437115or_rat: rat > int ).
% 5.49/5.83
% 5.49/5.83 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 5.49/5.83 archim6058952711729229775r_real: real > int ).
% 5.49/5.83
% 5.49/5.83 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
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% 5.49/5.83
% 5.49/5.83 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 5.49/5.83 archim8280529875227126926d_real: real > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 5.49/5.84 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.49/5.84 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.49/5.84 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.49/5.84 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
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% 5.49/5.84 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,
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% 5.49/5.84 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 ).
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% 5.49/5.84 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 ).
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% 5.49/5.84 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,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Oeucl__rel__int,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
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% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.49/5.84 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.49/5.84 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 5.49/5.84 comm_s2602460028002588243omplex: complex > nat > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.49/5.84 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.49/5.84 semiri2265585572941072030t_real: nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.49/5.84 invers8013647133539491842omplex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.49/5.84 inverse_inverse_rat: rat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.49/5.84 inverse_inverse_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.49/5.84 at_bot_real: filter_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.49/5.84 at_top_nat: filter_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.49/5.84 at_top_real: filter_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.49/5.84 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.49/5.84 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.49/5.84 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.49/5.84 finite_card_o: set_o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.49/5.84 finite_card_complex: set_complex > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.49/5.84 finite_card_int: set_int > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.84 finite_card_list_nat: set_list_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.49/5.84 finite_card_nat: set_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.49/5.84 finite_card_char: set_char > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 5.49/5.84 finite_finite_o: set_o > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.49/5.84 finite3207457112153483333omplex: set_complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.49/5.84 finite_finite_int: set_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 5.49/5.84 finite_finite_list_o: set_list_o > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.49/5.84 finite8712137658972009173omplex: set_list_complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 5.49/5.84 finite3922522038869484883st_int: set_list_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.84 finite8100373058378681591st_nat: set_list_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.49/5.84 finite_finite_nat: set_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 5.49/5.84 finite_finite_num: set_num > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 5.49/5.84 finite_finite_rat: set_rat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 5.49/5.84 finite_finite_real: set_real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.84 finite6551019134538273531omplex: set_set_complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 finite6197958912794628473et_int: set_set_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 finite1152437895449049373et_nat: set_set_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.49/5.84 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.49/5.84 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.49/5.84 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.49/5.84 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.49/5.84 id_o: $o > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.49/5.84 id_nat: nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.49/5.84 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 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 ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 map_fu1532550112467129777l_real: ( real > nat > rat ) > ( ( ( nat > rat ) > nat > rat ) > real > real ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > real > real > real ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 map_fu7146612038024189824t_real: ( real > nat > rat ) > ( ( nat > rat ) > real ) > ( ( nat > rat ) > nat > rat ) > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_GCD_Obezw,type,
% 5.49/5.84 bezw: nat > nat > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_GCD_Obezw__rel,type,
% 5.49/5.84 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
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% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.49/5.84 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.49/5.84 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.49/5.84 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.49/5.84 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.49/5.84 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.49/5.84 nth_real: list_real > nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.49/5.84 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.49/5.84 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.49/5.84 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.49/5.84 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.49/5.84 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.49/5.84 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.49/5.84 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.49/5.84 replicate_o: nat > $o > list_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.49/5.84 replicate_complex: nat > complex > list_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.49/5.84 replicate_int: nat > int > list_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.49/5.84 replicate_nat: nat > nat > list_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.49/5.84 replicate_real: nat > real > list_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.49/5.84 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.49/5.84 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.49/5.84 take_nat: nat > list_nat > list_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oupt,type,
% 5.49/5.84 upt: nat > nat > list_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oupto,type,
% 5.49/5.84 upto: int > int > list_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_List_Oupto__rel,type,
% 5.49/5.84 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_OSuc,type,
% 5.49/5.84 suc: nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.49/5.84 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.49/5.84 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.49/5.84 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Onat_Opred,type,
% 5.49/5.84 pred: nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 semiri4939895301339042750nteger: nat > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.49/5.84 semiri8010041392384452111omplex: nat > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.49/5.84 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.49/5.84 semiri1314217659103216013at_int: nat > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.49/5.84 semiri1316708129612266289at_nat: nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.49/5.84 semiri681578069525770553at_rat: nat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.49/5.84 semiri5074537144036343181t_real: nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.49/5.84 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.49/5.84 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.49/5.84 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.49/5.84 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.49/5.84 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.49/5.84 size_size_list_o: list_o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.49/5.84 size_s3451745648224563538omplex: list_complex > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.49/5.84 size_size_list_int: list_int > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.49/5.84 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.84 size_size_list_nat: list_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.49/5.84 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.49/5.84 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.49/5.84 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.49/5.84 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.49/5.84 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.49/5.84 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.49/5.84 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.49/5.84 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.49/5.84 size_size_list_real: list_real > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.49/5.84 size_size_num: num > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.49/5.84 size_size_option_nat: option_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.49/5.84 size_size_option_num: option_num > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.49/5.84 size_size_char: char > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.49/5.84 nat_list_encode: list_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.49/5.84 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.49/5.84 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.49/5.84 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.49/5.84 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.49/5.84 nat_set_decode: nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.49/5.84 nat_set_encode: set_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.49/5.84 nat_triangle: nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_NthRoot_Oroot,type,
% 5.49/5.84 root: nat > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_NthRoot_Osqrt,type,
% 5.49/5.84 sqrt: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_OBitM,type,
% 5.49/5.84 bitM: num > num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oinc,type,
% 5.49/5.84 inc: num > num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.49/5.84 neg_nu7009210354673126013omplex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.49/5.84 neg_numeral_dbl_int: int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.49/5.84 neg_numeral_dbl_rat: rat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.49/5.84 neg_numeral_dbl_real: real > real ).
% 5.49/5.84
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% 5.49/5.84 produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.49/5.84 produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.49/5.84 produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.49/5.84 produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.49/5.84 produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.49/5.84 produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.49/5.84 produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.49/5.84 produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 5.49/5.84 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 5.49/5.84 product_Pair_o_int: $o > int > product_prod_o_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 5.49/5.84 product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.49/5.84 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 5.49/5.84 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.49/5.84 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.49/5.84 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.49/5.84 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.49/5.84 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Complex__Ocomplex_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.84 produc3790773574474814305omplex: set_complex > set_complex > produc8064648209034914857omplex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 produc6363374080413544029et_int: set_int > set_int > produc2115011035271226405et_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.49/5.84 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.49/5.84 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.49/5.84 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.49/5.84 produc8678311845419106900er_nat: ( code_integer > nat ) > ( code_integer > nat ) > produc8923325533196201883nteger > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 5.49/5.84 produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.84 produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.49/5.84 produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 5.49/5.84 produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 produc8289552606927098482et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc7773217078559923341nt_int > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 5.49/5.84 produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 5.49/5.84 produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.49/5.84 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.49/5.84 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.49/5.84 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.49/5.84 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.84 produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.49/5.84 produc1656060378719767003at_nat: ( int > int > set_Pr1261947904930325089at_nat ) > product_prod_int_int > set_Pr1261947904930325089at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.49/5.84 produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.49/5.84 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.49/5.84 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.49/5.84 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.49/5.84
% 5.49/5.84 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,
% 5.49/5.84 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.49/5.84 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.49/5.84 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.49/5.84 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 product_fst_int_int: product_prod_int_int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 product_snd_int_int: product_prod_int_int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_OAbs__Rat,type,
% 5.49/5.84 abs_Rat: product_prod_int_int > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_OFract,type,
% 5.49/5.84 fract: int > int > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_OFrct,type,
% 5.49/5.84 frct: product_prod_int_int > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_ORep__Rat,type,
% 5.49/5.84 rep_Rat: rat > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.49/5.84 field_5140801741446780682s_real: set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.49/5.84 field_7254667332652039916t_real: rat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Onormalize,type,
% 5.49/5.84 normalize: product_prod_int_int > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Oof__int,type,
% 5.49/5.84 of_int: int > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Opcr__rat,type,
% 5.49/5.84 pcr_rat: product_prod_int_int > rat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Opositive,type,
% 5.49/5.84 positive: rat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Oquotient__of,type,
% 5.49/5.84 quotient_of: rat > product_prod_int_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rat_Oratrel,type,
% 5.49/5.84 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_OReal,type,
% 5.49/5.84 real2: ( nat > rat ) > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Ocauchy,type,
% 5.49/5.84 cauchy: ( nat > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Ocr__real,type,
% 5.49/5.84 cr_real: ( nat > rat ) > real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Opcr__real,type,
% 5.49/5.84 pcr_real: ( nat > rat ) > real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Opositive,type,
% 5.49/5.84 positive2: real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Orealrel,type,
% 5.49/5.84 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Orep__real,type,
% 5.49/5.84 rep_real: real > nat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real_Ovanishes,type,
% 5.49/5.84 vanishes: ( nat > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.49/5.84 real_V2521375963428798218omplex: set_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.49/5.84 real_V1022390504157884413omplex: complex > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.49/5.84 real_V7735802525324610683m_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.49/5.84 real_V4546457046886955230omplex: real > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.49/5.84 real_V2046097035970521341omplex: real > complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.49/5.84 real_V1485227260804924795R_real: real > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.49/5.84 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.49/5.84 divide1717551699836669952omplex: complex > complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.49/5.84 divide_divide_int: int > int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.49/5.84 divide_divide_nat: nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.49/5.84 divide_divide_rat: rat > rat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.49/5.84 divide_divide_real: real > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.49/5.84 dvd_dvd_complex: complex > complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.49/5.84 dvd_dvd_int: int > int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.49/5.84 dvd_dvd_nat: nat > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.49/5.84 dvd_dvd_rat: rat > rat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.49/5.84 dvd_dvd_real: real > real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.49/5.84 modulo_modulo_int: int > int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.49/5.84 modulo_modulo_nat: nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 zero_n356916108424825756nteger: $o > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.49/5.84 zero_n2684676970156552555ol_int: $o > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.49/5.84 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.49/5.84 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.49/5.84 zero_n3304061248610475627l_real: $o > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.49/5.84 suminf_complex: ( nat > complex ) > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.49/5.84 suminf_int: ( nat > int ) > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.49/5.84 suminf_nat: ( nat > nat ) > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.49/5.84 suminf_real: ( nat > real ) > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.49/5.84 summable_complex: ( nat > complex ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.49/5.84 summable_int: ( nat > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.49/5.84 summable_nat: ( nat > nat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.49/5.84 summable_real: ( nat > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.49/5.84 sums_complex: ( nat > complex ) > complex > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.49/5.84 sums_int: ( nat > int ) > int > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.49/5.84 sums_nat: ( nat > nat ) > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.49/5.84 sums_real: ( nat > real ) > real > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001_Eo,type,
% 5.49/5.84 collect_o: ( $o > $o ) > set_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.49/5.84 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.49/5.84 collect_complex: ( complex > $o ) > set_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.49/5.84 collect_int: ( int > $o ) > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.49/5.84 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.49/5.84 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.49/5.84 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.84 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.84 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.49/5.84 collect_nat: ( nat > $o ) > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 5.49/5.84 collect_num: ( num > $o ) > set_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.49/5.84 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 5.49/5.84 collect_rat: ( rat > $o ) > set_rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 5.49/5.84 collect_real: ( real > $o ) > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.49/5.84 collect_set_complex: ( set_complex > $o ) > set_set_complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 collect_set_int: ( set_int > $o ) > set_set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.49/5.84 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_OCollect_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 5.49/5.84 image_int_int: ( int > int ) > set_int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 5.49/5.84 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.49/5.84 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.49/5.84 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.49/5.84 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 image_real_real: ( real > real ) > set_real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.49/5.84 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.49/5.84 insert_int: int > set_int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.49/5.84 insert_nat: nat > set_nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.49/5.84 insert_real: real > set_real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.49/5.84 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.49/5.84 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.49/5.84 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.49/5.84 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.49/5.84 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel_001t__Nat__Onat,type,
% 5.49/5.84 set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.49/5.84 set_or1266510415728281911st_int: int > int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.49/5.84 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.49/5.84 set_or7049704709247886629st_num: num > num > set_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.49/5.84 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.49/5.84 set_or1222579329274155063t_real: real > real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.49/5.84 set_or4662586982721622107an_int: int > int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.49/5.84 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.49/5.84 set_ord_atLeast_nat: nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.49/5.84 set_ord_atLeast_real: real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.49/5.84 set_ord_atMost_int: int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.49/5.84 set_ord_atMost_nat: nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.49/5.84 set_ord_atMost_num: num > set_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 5.49/5.84 set_ord_atMost_rat: rat > set_rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.49/5.84 set_ord_atMost_real: real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 set_or58775011639299419et_int: set_int > set_set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.49/5.84 set_or6656581121297822940st_int: int > int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.49/5.84 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.49/5.84 set_or5832277885323065728an_int: int > int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.49/5.84 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.49/5.84 set_or1633881224788618240n_real: real > real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.49/5.84 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.49/5.84 set_or5849166863359141190n_real: real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.49/5.84 set_ord_lessThan_int: int > set_int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.49/5.84 set_ord_lessThan_nat: nat > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.49/5.84 set_ord_lessThan_num: num > set_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.49/5.84 set_ord_lessThan_rat: rat > set_rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.49/5.84 set_or5984915006950818249n_real: real > set_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_String_Oascii__of,type,
% 5.49/5.84 ascii_of: char > char ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_String_Ochar_OChar,type,
% 5.49/5.84 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.49/5.84 comm_s629917340098488124ar_nat: char > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_String_Ointeger__of__char,type,
% 5.49/5.84 integer_of_char: char > code_integer ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.49/5.84 unique3096191561947761185of_nat: nat > char ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.49/5.84 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.49/5.84 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.49/5.84 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.49/5.84 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.49/5.84 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.49/5.84 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.84 topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.49/5.84 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.49/5.84 topolo2815343760600316023s_real: real > filter_real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.49/5.84 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oarccos,type,
% 5.49/5.84 arccos: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.49/5.84 arcosh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oarcsin,type,
% 5.49/5.84 arcsin: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oarctan,type,
% 5.49/5.84 arctan: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.49/5.84 arsinh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.49/5.84 artanh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.49/5.84 cos_complex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.49/5.84 cos_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.49/5.84 cos_coeff: nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.49/5.84 cosh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.49/5.84 cot_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.49/5.84 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.49/5.84 diffs_int: ( nat > int ) > nat > int ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.49/5.84 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.49/5.84 diffs_real: ( nat > real ) > nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.49/5.84 exp_complex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.49/5.84 exp_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.49/5.84 ln_ln_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Olog,type,
% 5.49/5.84 log: real > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Opi,type,
% 5.49/5.84 pi: real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.49/5.84 powr_real: real > real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.49/5.84 sin_complex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.49/5.84 sin_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.49/5.84 sin_coeff: nat > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.49/5.84 sinh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.49/5.84 tan_complex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.49/5.84 tan_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.49/5.84 tanh_complex: complex > complex ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.49/5.84 tanh_real: real > real ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.49/5.84 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.49/5.84 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.49/5.84 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.49/5.84 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.49/5.84 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.49/5.84 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.49/5.84 vEBT_VEBT_high: nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.49/5.84 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.49/5.84 vEBT_VEBT_low: nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.49/5.84 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.49/5.84 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.49/5.84 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.49/5.84 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.49/5.84 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.49/5.84 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.49/5.84 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.49/5.84 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.49/5.84 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.49/5.84 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.49/5.84 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.49/5.84 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.49/5.84 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.49/5.84 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.49/5.84 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.49/5.84 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.49/5.84 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.49/5.84 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.49/5.84 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.49/5.84 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.49/5.84 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.49/5.84 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.49/5.84 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.49/5.84 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.49/5.84 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.49/5.84 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Nat__Onat,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Num__Onum,type,
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% 5.49/5.84
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.49/5.84 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.49/5.84 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.49/5.84 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.49/5.84 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.49/5.84 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.49/5.84 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
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% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.49/5.84 accp_P6019419558468335806at_nat: ( produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ) > produc4471711990508489141at_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 5.49/5.84 accp_P5496254298877145759on_nat: ( produc8306885398267862888on_nat > produc8306885398267862888on_nat > $o ) > produc8306885398267862888on_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 5.49/5.84 accp_P7605991808943153877on_num: ( produc1193250871479095198on_num > produc1193250871479095198on_num > $o ) > produc1193250871479095198on_num > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.49/5.84 accp_P3267385326087170368at_nat: ( produc5542196010084753463at_nat > produc5542196010084753463at_nat > $o ) > produc5542196010084753463at_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.84 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.49/5.84 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.49/5.84 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.84 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.49/5.84
% 5.49/5.84 thf(sy_c_Wellfounded_Ofinite__psubset_001t__Complex__Ocomplex,type,
% 5.49/5.85 finite8643634255014194347omplex: set_Pr6308028481084910985omplex ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Ofinite__psubset_001t__Int__Oint,type,
% 5.49/5.85 finite_psubset_int: set_Pr2522554150109002629et_int ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Ofinite__psubset_001t__Nat__Onat,type,
% 5.49/5.85 finite_psubset_nat: set_Pr5488025237498180813et_nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Omeasure_001t__Int__Oint,type,
% 5.49/5.85 measure_int: ( int > nat ) > set_Pr958786334691620121nt_int ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
% 5.49/5.85 measure_nat: ( nat > nat ) > set_Pr1261947904930325089at_nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.49/5.85 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.49/5.85 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.49/5.85 fChoice_real: ( real > $o ) > real ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001_Eo,type,
% 5.49/5.85 member_o: $o > set_o > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.49/5.85 member_complex: complex > set_complex > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Int__Oint,type,
% 5.49/5.85 member_int: int > set_int > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.49/5.85 member_list_o: list_o > set_list_o > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.49/5.85 member_list_int: list_int > set_list_int > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.49/5.85 member_list_nat: list_nat > set_list_nat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.49/5.85 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Nat__Onat,type,
% 5.49/5.85 member_nat: nat > set_nat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Num__Onum,type,
% 5.49/5.85 member_num: num > set_num > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
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% 5.49/5.85
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% 5.49/5.85 member7034335876925520548nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > $o ).
% 5.49/5.85
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% 5.49/5.85 member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o ).
% 5.49/5.85
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% 5.49/5.85 member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.49/5.85 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Complex__Ocomplex_J_Mt__Set__Oset_It__Complex__Ocomplex_J_J,type,
% 5.49/5.85 member351165363924911826omplex: produc8064648209034914857omplex > set_Pr6308028481084910985omplex > $o ).
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% 5.49/5.85 member2572552093476627150et_int: produc2115011035271226405et_int > set_Pr2522554150109002629et_int > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 5.49/5.85 member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Rat__Orat,type,
% 5.49/5.85 member_rat: rat > set_rat > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Real__Oreal,type,
% 5.49/5.85 member_real: real > set_real > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.49/5.85 member_set_int: set_int > set_set_int > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.49/5.85 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_deg____,type,
% 5.49/5.85 deg: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_m____,type,
% 5.49/5.85 m: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_ma____,type,
% 5.49/5.85 ma: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_mi____,type,
% 5.49/5.85 mi: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_minilow____,type,
% 5.49/5.85 minilow: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_na____,type,
% 5.49/5.85 na: nat ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_summary____,type,
% 5.49/5.85 summary: vEBT_VEBT ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_treeList____,type,
% 5.49/5.85 treeList: list_VEBT_VEBT ).
% 5.49/5.85
% 5.49/5.85 thf(sy_v_xa____,type,
% 5.49/5.85 xa: nat ).
% 5.49/5.85
% 5.49/5.85 % Relevant facts (10204)
% 5.49/5.85 thf(fact_0__092_060open_062low_Ax_A_Ideg_Adiv_A2_J_A_092_060le_062_Aminilow_092_060close_062,axiom,
% 5.49/5.85 ord_less_eq_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ minilow ).
% 5.49/5.85
% 5.49/5.85 % \<open>low x (deg div 2) \<le> minilow\<close>
% 5.49/5.85 thf(fact_1_bit__split__inv,axiom,
% 5.49/5.85 ! [X: nat,D: nat] :
% 5.49/5.85 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.49/5.85 = X ) ).
% 5.49/5.85
% 5.49/5.85 % bit_split_inv
% 5.49/5.85 thf(fact_2_max__in__set__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_max_in_set
% 5.49/5.85 = ( ^ [Xs: set_nat,X2: nat] :
% 5.49/5.85 ( ( member_nat @ X2 @ Xs )
% 5.49/5.85 & ! [Y: nat] :
% 5.49/5.85 ( ( member_nat @ Y @ Xs )
% 5.49/5.85 => ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % max_in_set_def
% 5.49/5.85 thf(fact_3__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.49/5.85 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.49/5.85
% 5.49/5.85 % \<open>2 \<le> deg\<close>
% 5.49/5.85 thf(fact_4_True,axiom,
% 5.49/5.85 ord_less_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.49/5.85
% 5.49/5.85 % True
% 5.49/5.85 thf(fact_5__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
% 5.49/5.85 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = na ) ).
% 5.49/5.85
% 5.49/5.85 % \<open>deg div 2 = n\<close>
% 5.49/5.85 thf(fact_6_min__in__set__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_min_in_set
% 5.49/5.85 = ( ^ [Xs: set_nat,X2: nat] :
% 5.49/5.85 ( ( member_nat @ X2 @ Xs )
% 5.49/5.85 & ! [Y: nat] :
% 5.49/5.85 ( ( member_nat @ Y @ Xs )
% 5.49/5.85 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % min_in_set_def
% 5.49/5.85 thf(fact_7_False,axiom,
% 5.49/5.85 ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.85 != none_nat ) ).
% 5.49/5.85
% 5.49/5.85 % False
% 5.49/5.85 thf(fact_8_semiring__norm_I85_J,axiom,
% 5.49/5.85 ! [M: num] :
% 5.49/5.85 ( ( bit0 @ M )
% 5.49/5.85 != one ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(85)
% 5.49/5.85 thf(fact_9_semiring__norm_I83_J,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( one
% 5.49/5.85 != ( bit0 @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(83)
% 5.49/5.85 thf(fact_10_numeral__less__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.49/5.85 = ( ord_less_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_less_iff
% 5.49/5.85 thf(fact_11_numeral__less__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.49/5.85 = ( ord_less_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_less_iff
% 5.49/5.85 thf(fact_12_numeral__less__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( ord_less_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_less_iff
% 5.49/5.85 thf(fact_13_numeral__less__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.49/5.85 = ( ord_less_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_less_iff
% 5.49/5.85 thf(fact_14__092_060open_062vebt__mint_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Aminilow_092_060close_062,axiom,
% 5.49/5.85 ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.85 = ( some_nat @ minilow ) ) ).
% 5.49/5.85
% 5.49/5.85 % \<open>vebt_mint (treeList ! high x (deg div 2)) = Some minilow\<close>
% 5.49/5.85 thf(fact_15_numeral__Bit0__div__2,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( numeral_numeral_nat @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0_div_2
% 5.49/5.85 thf(fact_16_numeral__Bit0__div__2,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( numeral_numeral_int @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0_div_2
% 5.49/5.85 thf(fact_17_high__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_high
% 5.49/5.85 = ( ^ [X2: nat,N2: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % high_def
% 5.49/5.85 thf(fact_18_min__Null__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,X: nat] :
% 5.49/5.85 ( ( vEBT_VEBT_minNull @ T )
% 5.49/5.85 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % min_Null_member
% 5.49/5.85 thf(fact_19_divide__numeral__1,axiom,
% 5.49/5.85 ! [A: complex] :
% 5.49/5.85 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % divide_numeral_1
% 5.49/5.85 thf(fact_20_divide__numeral__1,axiom,
% 5.49/5.85 ! [A: real] :
% 5.49/5.85 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % divide_numeral_1
% 5.49/5.85 thf(fact_21_divide__numeral__1,axiom,
% 5.49/5.85 ! [A: rat] :
% 5.49/5.85 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % divide_numeral_1
% 5.49/5.85 thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062minilow_O_Avebt__mint_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Aminilow_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.49/5.85 ~ ! [Minilow: nat] :
% 5.49/5.85 ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.85 != ( some_nat @ Minilow ) ) ).
% 5.49/5.85
% 5.49/5.85 % \<open>\<And>thesis. (\<And>minilow. vebt_mint (treeList ! high x (deg div 2)) = Some minilow \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.49/5.85 thf(fact_23_minNullmin,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT] :
% 5.49/5.85 ( ( vEBT_VEBT_minNull @ T )
% 5.49/5.85 => ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = none_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % minNullmin
% 5.49/5.85 thf(fact_24_minminNull,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT] :
% 5.49/5.85 ( ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = none_nat )
% 5.49/5.85 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.49/5.85
% 5.49/5.85 % minminNull
% 5.49/5.85 thf(fact_25_power__shift,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.85 ( ( ( power_power_nat @ X @ Y2 )
% 5.49/5.85 = Z )
% 5.49/5.85 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 5.49/5.85 = ( some_nat @ Z ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_shift
% 5.49/5.85 thf(fact_26_numeral__eq__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( numera6690914467698888265omplex @ M )
% 5.49/5.85 = ( numera6690914467698888265omplex @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_eq_iff
% 5.49/5.85 thf(fact_27_numeral__eq__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( numeral_numeral_real @ M )
% 5.49/5.85 = ( numeral_numeral_real @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_eq_iff
% 5.49/5.85 thf(fact_28_numeral__eq__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( numeral_numeral_rat @ M )
% 5.49/5.85 = ( numeral_numeral_rat @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_eq_iff
% 5.49/5.85 thf(fact_29_numeral__eq__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( numeral_numeral_nat @ M )
% 5.49/5.85 = ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_eq_iff
% 5.49/5.85 thf(fact_30_numeral__eq__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( numeral_numeral_int @ M )
% 5.49/5.85 = ( numeral_numeral_int @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_eq_iff
% 5.49/5.85 thf(fact_31_semiring__norm_I87_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ( bit0 @ M )
% 5.49/5.85 = ( bit0 @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(87)
% 5.49/5.85 thf(fact_32_numeral__le__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.49/5.85 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_le_iff
% 5.49/5.85 thf(fact_33_numeral__le__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.49/5.85 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_le_iff
% 5.49/5.85 thf(fact_34_numeral__le__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_le_iff
% 5.49/5.85 thf(fact_35_numeral__le__iff,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.49/5.85 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_le_iff
% 5.49/5.85 thf(fact_36_semiring__norm_I78_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.49/5.85 = ( ord_less_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(78)
% 5.49/5.85 thf(fact_37_semiring__norm_I75_J,axiom,
% 5.49/5.85 ! [M: num] :
% 5.49/5.85 ~ ( ord_less_num @ M @ one ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(75)
% 5.49/5.85 thf(fact_38__C5_Ohyps_C_I4_J,axiom,
% 5.49/5.85 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.49/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(4)
% 5.49/5.85 thf(fact_39_semiring__norm_I76_J,axiom,
% 5.49/5.85 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(76)
% 5.49/5.85 thf(fact_40__C5_Ohyps_C_I10_J,axiom,
% 5.49/5.85 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(10)
% 5.49/5.85 thf(fact_41_less__shift,axiom,
% 5.49/5.85 ( ord_less_nat
% 5.49/5.85 = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_shift
% 5.49/5.85 thf(fact_42_lesseq__shift,axiom,
% 5.49/5.85 ( ord_less_eq_nat
% 5.49/5.85 = ( ^ [X2: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % lesseq_shift
% 5.49/5.85 thf(fact_43_div__le__dividend,axiom,
% 5.49/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.49/5.85
% 5.49/5.85 % div_le_dividend
% 5.49/5.85 thf(fact_44_div__le__mono,axiom,
% 5.49/5.85 ! [M: nat,N: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_le_mono
% 5.49/5.85 thf(fact_45_i1,axiom,
% 5.49/5.85 ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.85 = none_nat )
% 5.49/5.85 | ~ ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % i1
% 5.49/5.85 thf(fact_46__092_060open_062high_Ax_An_A_060_A2_A_094_Am_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,axiom,
% 5.49/5.85 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.49/5.85 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % \<open>high x n < 2 ^ m \<and> low x n < 2 ^ n\<close>
% 5.49/5.85 thf(fact_47__092_060open_062invar__vebt_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_An_092_060close_062,axiom,
% 5.49/5.85 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ na ).
% 5.49/5.85
% 5.49/5.85 % \<open>invar_vebt (treeList ! high x (deg div 2)) n\<close>
% 5.49/5.85 thf(fact_48_greater__shift,axiom,
% 5.49/5.85 ( ord_less_nat
% 5.49/5.85 = ( ^ [Y: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % greater_shift
% 5.49/5.85 thf(fact_49_not__None__eq,axiom,
% 5.49/5.85 ! [X: option_nat] :
% 5.49/5.85 ( ( X != none_nat )
% 5.49/5.85 = ( ? [Y: nat] :
% 5.49/5.85 ( X
% 5.49/5.85 = ( some_nat @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_None_eq
% 5.49/5.85 thf(fact_50_not__None__eq,axiom,
% 5.49/5.85 ! [X: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( X != none_P5556105721700978146at_nat )
% 5.49/5.85 = ( ? [Y: product_prod_nat_nat] :
% 5.49/5.85 ( X
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_None_eq
% 5.49/5.85 thf(fact_51_not__None__eq,axiom,
% 5.49/5.85 ! [X: option_num] :
% 5.49/5.85 ( ( X != none_num )
% 5.49/5.85 = ( ? [Y: num] :
% 5.49/5.85 ( X
% 5.49/5.85 = ( some_num @ Y ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_None_eq
% 5.49/5.85 thf(fact_52_not__Some__eq,axiom,
% 5.49/5.85 ! [X: option_nat] :
% 5.49/5.85 ( ( ! [Y: nat] :
% 5.49/5.85 ( X
% 5.49/5.85 != ( some_nat @ Y ) ) )
% 5.49/5.85 = ( X = none_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_Some_eq
% 5.49/5.85 thf(fact_53_not__Some__eq,axiom,
% 5.49/5.85 ! [X: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( ! [Y: product_prod_nat_nat] :
% 5.49/5.85 ( X
% 5.49/5.85 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.49/5.85 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_Some_eq
% 5.49/5.85 thf(fact_54_not__Some__eq,axiom,
% 5.49/5.85 ! [X: option_num] :
% 5.49/5.85 ( ( ! [Y: num] :
% 5.49/5.85 ( X
% 5.49/5.85 != ( some_num @ Y ) ) )
% 5.49/5.85 = ( X = none_num ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_Some_eq
% 5.49/5.85 thf(fact_55_power2__nat__le__imp__le,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_nat_le_imp_le
% 5.49/5.85 thf(fact_56_power2__nat__le__eq__le,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_nat_le_eq_le
% 5.49/5.85 thf(fact_57_self__le__ge2__pow,axiom,
% 5.49/5.85 ! [K: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % self_le_ge2_pow
% 5.49/5.85 thf(fact_58_less__exp,axiom,
% 5.49/5.85 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_exp
% 5.49/5.85 thf(fact_59_enat__ord__number_I2_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.49/5.85 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % enat_ord_number(2)
% 5.49/5.85 thf(fact_60_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.49/5.85 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_61_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: complex,P: complex > $o] :
% 5.49/5.85 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_62_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: real,P: real > $o] :
% 5.49/5.85 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_63_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: list_nat,P: list_nat > $o] :
% 5.49/5.85 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_64_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: nat,P: nat > $o] :
% 5.49/5.85 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_65_mem__Collect__eq,axiom,
% 5.49/5.85 ! [A: int,P: int > $o] :
% 5.49/5.85 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.49/5.85 = ( P @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % mem_Collect_eq
% 5.49/5.85 thf(fact_66_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.49/5.85 ( ( collec3392354462482085612at_nat
% 5.49/5.85 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_67_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_complex] :
% 5.49/5.85 ( ( collect_complex
% 5.49/5.85 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_68_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_real] :
% 5.49/5.85 ( ( collect_real
% 5.49/5.85 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_69_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_list_nat] :
% 5.49/5.85 ( ( collect_list_nat
% 5.49/5.85 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_70_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_nat] :
% 5.49/5.85 ( ( collect_nat
% 5.49/5.85 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_71_Collect__mem__eq,axiom,
% 5.49/5.85 ! [A2: set_int] :
% 5.49/5.85 ( ( collect_int
% 5.49/5.85 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.49/5.85 = A2 ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_mem_eq
% 5.49/5.85 thf(fact_72_Collect__cong,axiom,
% 5.49/5.85 ! [P: complex > $o,Q: complex > $o] :
% 5.49/5.85 ( ! [X3: complex] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 = ( Q @ X3 ) )
% 5.49/5.85 => ( ( collect_complex @ P )
% 5.49/5.85 = ( collect_complex @ Q ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_cong
% 5.49/5.85 thf(fact_73_Collect__cong,axiom,
% 5.49/5.85 ! [P: real > $o,Q: real > $o] :
% 5.49/5.85 ( ! [X3: real] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 = ( Q @ X3 ) )
% 5.49/5.85 => ( ( collect_real @ P )
% 5.49/5.85 = ( collect_real @ Q ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_cong
% 5.49/5.85 thf(fact_74_Collect__cong,axiom,
% 5.49/5.85 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.49/5.85 ( ! [X3: list_nat] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 = ( Q @ X3 ) )
% 5.49/5.85 => ( ( collect_list_nat @ P )
% 5.49/5.85 = ( collect_list_nat @ Q ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_cong
% 5.49/5.85 thf(fact_75_Collect__cong,axiom,
% 5.49/5.85 ! [P: nat > $o,Q: nat > $o] :
% 5.49/5.85 ( ! [X3: nat] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 = ( Q @ X3 ) )
% 5.49/5.85 => ( ( collect_nat @ P )
% 5.49/5.85 = ( collect_nat @ Q ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_cong
% 5.49/5.85 thf(fact_76_Collect__cong,axiom,
% 5.49/5.85 ! [P: int > $o,Q: int > $o] :
% 5.49/5.85 ( ! [X3: int] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 = ( Q @ X3 ) )
% 5.49/5.85 => ( ( collect_int @ P )
% 5.49/5.85 = ( collect_int @ Q ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Collect_cong
% 5.49/5.85 thf(fact_77_high__bound__aux,axiom,
% 5.49/5.85 ! [Ma: nat,N: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.49/5.85 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % high_bound_aux
% 5.49/5.85 thf(fact_78__C5_Ohyps_C_I6_J,axiom,
% 5.49/5.85 ( deg
% 5.49/5.85 = ( plus_plus_nat @ na @ m ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(6)
% 5.49/5.85 thf(fact_79_mint__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = ( some_nat @ Maxi ) )
% 5.49/5.85 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mint_member
% 5.49/5.85 thf(fact_80_option_Oinject,axiom,
% 5.49/5.85 ! [X22: nat,Y22: nat] :
% 5.49/5.85 ( ( ( some_nat @ X22 )
% 5.49/5.85 = ( some_nat @ Y22 ) )
% 5.49/5.85 = ( X22 = Y22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.inject
% 5.49/5.85 thf(fact_81_option_Oinject,axiom,
% 5.49/5.85 ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.49/5.85 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.49/5.85 = ( X22 = Y22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.inject
% 5.49/5.85 thf(fact_82_option_Oinject,axiom,
% 5.49/5.85 ! [X22: num,Y22: num] :
% 5.49/5.85 ( ( ( some_num @ X22 )
% 5.49/5.85 = ( some_num @ Y22 ) )
% 5.49/5.85 = ( X22 = Y22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.inject
% 5.49/5.85 thf(fact_83__092_060open_062x_A_092_060le_062_Ama_092_060close_062,axiom,
% 5.49/5.85 ord_less_eq_nat @ xa @ ma ).
% 5.49/5.85
% 5.49/5.85 % \<open>x \<le> ma\<close>
% 5.49/5.85 thf(fact_84_member__correct,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_vebt_member @ T @ X )
% 5.49/5.85 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % member_correct
% 5.49/5.85 thf(fact_85_mint__corr__help,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = ( some_nat @ Mini ) )
% 5.49/5.85 => ( ( vEBT_vebt_member @ T @ X )
% 5.49/5.85 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mint_corr_help
% 5.49/5.85 thf(fact_86_pow__sum,axiom,
% 5.49/5.85 ! [A: nat,B: nat] :
% 5.49/5.85 ( ( 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 ) )
% 5.49/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % pow_sum
% 5.49/5.85 thf(fact_87__C5_Ohyps_C_I9_J,axiom,
% 5.49/5.85 ord_less_eq_nat @ mi @ ma ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(9)
% 5.49/5.85 thf(fact_88_member__bound,axiom,
% 5.49/5.85 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 5.49/5.85 ( ( vEBT_vebt_member @ Tree @ X )
% 5.49/5.85 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.49/5.85 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % member_bound
% 5.49/5.85 thf(fact_89__C5_Ohyps_C_I2_J,axiom,
% 5.49/5.85 vEBT_invar_vebt @ summary @ m ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(2)
% 5.49/5.85 thf(fact_90_add__numeral__left,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: complex] :
% 5.49/5.85 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.49/5.85 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_numeral_left
% 5.49/5.85 thf(fact_91_add__numeral__left,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: real] :
% 5.49/5.85 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.49/5.85 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_numeral_left
% 5.49/5.85 thf(fact_92_add__numeral__left,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: rat] :
% 5.49/5.85 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.49/5.85 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_numeral_left
% 5.49/5.85 thf(fact_93_add__numeral__left,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.49/5.85 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_numeral_left
% 5.49/5.85 thf(fact_94_add__numeral__left,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: int] :
% 5.49/5.85 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.49/5.85 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_numeral_left
% 5.49/5.85 thf(fact_95_numeral__plus__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.49/5.85 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_plus_numeral
% 5.49/5.85 thf(fact_96_numeral__plus__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.49/5.85 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_plus_numeral
% 5.49/5.85 thf(fact_97_numeral__plus__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.49/5.85 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_plus_numeral
% 5.49/5.85 thf(fact_98_numeral__plus__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_plus_numeral
% 5.49/5.85 thf(fact_99_numeral__plus__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.49/5.85 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_plus_numeral
% 5.49/5.85 thf(fact_100_misiz,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( some_nat @ M )
% 5.49/5.85 = ( vEBT_vebt_mint @ T ) )
% 5.49/5.85 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % misiz
% 5.49/5.85 thf(fact_101_semiring__norm_I71_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.49/5.85 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(71)
% 5.49/5.85 thf(fact_102_semiring__norm_I68_J,axiom,
% 5.49/5.85 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(68)
% 5.49/5.85 thf(fact_103_semiring__norm_I69_J,axiom,
% 5.49/5.85 ! [M: num] :
% 5.49/5.85 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(69)
% 5.49/5.85 thf(fact_104_enat__ord__number_I1_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.49/5.85 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % enat_ord_number(1)
% 5.49/5.85 thf(fact_105__C5_Ohyps_C_I5_J,axiom,
% 5.49/5.85 ( m
% 5.49/5.85 = ( suc @ na ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(5)
% 5.49/5.85 thf(fact_106_add__self__div__2,axiom,
% 5.49/5.85 ! [M: nat] :
% 5.49/5.85 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = M ) ).
% 5.49/5.85
% 5.49/5.85 % add_self_div_2
% 5.49/5.85 thf(fact_107_local_Opower__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_power
% 5.49/5.85 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % local.power_def
% 5.49/5.85 thf(fact_108_is__num__normalize_I1_J,axiom,
% 5.49/5.85 ! [A: real,B: real,C: real] :
% 5.49/5.85 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.85 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % is_num_normalize(1)
% 5.49/5.85 thf(fact_109_is__num__normalize_I1_J,axiom,
% 5.49/5.85 ! [A: rat,B: rat,C: rat] :
% 5.49/5.85 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.85 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % is_num_normalize(1)
% 5.49/5.85 thf(fact_110_is__num__normalize_I1_J,axiom,
% 5.49/5.85 ! [A: int,B: int,C: int] :
% 5.49/5.85 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.85 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % is_num_normalize(1)
% 5.49/5.85 thf(fact_111_enat__less__induct,axiom,
% 5.49/5.85 ! [P: extended_enat > $o,N: extended_enat] :
% 5.49/5.85 ( ! [N3: extended_enat] :
% 5.49/5.85 ( ! [M2: extended_enat] :
% 5.49/5.85 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 5.49/5.85 => ( P @ M2 ) )
% 5.49/5.85 => ( P @ N3 ) )
% 5.49/5.85 => ( P @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % enat_less_induct
% 5.49/5.85 thf(fact_112_le__num__One__iff,axiom,
% 5.49/5.85 ! [X: num] :
% 5.49/5.85 ( ( ord_less_eq_num @ X @ one )
% 5.49/5.85 = ( X = one ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_num_One_iff
% 5.49/5.85 thf(fact_113_numeral__Bit0,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.49/5.85 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0
% 5.49/5.85 thf(fact_114_numeral__Bit0,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.49/5.85 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0
% 5.49/5.85 thf(fact_115_numeral__Bit0,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.49/5.85 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0
% 5.49/5.85 thf(fact_116_numeral__Bit0,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.49/5.85 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0
% 5.49/5.85 thf(fact_117_numeral__Bit0,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.49/5.85 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_Bit0
% 5.49/5.85 thf(fact_118_power__divide,axiom,
% 5.49/5.85 ! [A: complex,B: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.49/5.85 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_divide
% 5.49/5.85 thf(fact_119_power__divide,axiom,
% 5.49/5.85 ! [A: real,B: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.49/5.85 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_divide
% 5.49/5.85 thf(fact_120_power__divide,axiom,
% 5.49/5.85 ! [A: rat,B: rat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.49/5.85 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_divide
% 5.49/5.85 thf(fact_121_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_nat,P: option_nat > option_nat > $o,Y2: option_nat] :
% 5.49/5.85 ( ( ( X = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: nat,B2: nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_122_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( ( X = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: nat,B2: product_prod_nat_nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_123_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_nat,P: option_nat > option_num > $o,Y2: option_num] :
% 5.49/5.85 ( ( ( X = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: nat,B2: num] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_num @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_124_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y2: option_nat] :
% 5.49/5.85 ( ( ( X = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: product_prod_nat_nat,B2: nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_125_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( ( X = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_126_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y2: option_num] :
% 5.49/5.85 ( ( ( X = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: product_prod_nat_nat,B2: num] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_num @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_127_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_num,P: option_num > option_nat > $o,Y2: option_nat] :
% 5.49/5.85 ( ( ( X = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: num,B2: nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_num @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_128_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y2: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( ( X = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_P5556105721700978146at_nat )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: num,B2: product_prod_nat_nat] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_num @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_129_combine__options__cases,axiom,
% 5.49/5.85 ! [X: option_num,P: option_num > option_num > $o,Y2: option_num] :
% 5.49/5.85 ( ( ( X = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ( ( Y2 = none_num )
% 5.49/5.85 => ( P @ X @ Y2 ) )
% 5.49/5.85 => ( ! [A3: num,B2: num] :
% 5.49/5.85 ( ( X
% 5.49/5.85 = ( some_num @ A3 ) )
% 5.49/5.85 => ( ( Y2
% 5.49/5.85 = ( some_num @ B2 ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) )
% 5.49/5.85 => ( P @ X @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % combine_options_cases
% 5.49/5.85 thf(fact_130_split__option__all,axiom,
% 5.49/5.85 ( ( ^ [P2: option_nat > $o] :
% 5.49/5.85 ! [X4: option_nat] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option_nat > $o] :
% 5.49/5.85 ( ( P3 @ none_nat )
% 5.49/5.85 & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_all
% 5.49/5.85 thf(fact_131_split__option__all,axiom,
% 5.49/5.85 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.49/5.85 ! [X4: option4927543243414619207at_nat] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.49/5.85 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.49/5.85 & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_all
% 5.49/5.85 thf(fact_132_split__option__all,axiom,
% 5.49/5.85 ( ( ^ [P2: option_num > $o] :
% 5.49/5.85 ! [X4: option_num] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option_num > $o] :
% 5.49/5.85 ( ( P3 @ none_num )
% 5.49/5.85 & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_all
% 5.49/5.85 thf(fact_133_split__option__ex,axiom,
% 5.49/5.85 ( ( ^ [P2: option_nat > $o] :
% 5.49/5.85 ? [X4: option_nat] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option_nat > $o] :
% 5.49/5.85 ( ( P3 @ none_nat )
% 5.49/5.85 | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_ex
% 5.49/5.85 thf(fact_134_split__option__ex,axiom,
% 5.49/5.85 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.49/5.85 ? [X4: option4927543243414619207at_nat] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.49/5.85 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.49/5.85 | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_ex
% 5.49/5.85 thf(fact_135_split__option__ex,axiom,
% 5.49/5.85 ( ( ^ [P2: option_num > $o] :
% 5.49/5.85 ? [X4: option_num] : ( P2 @ X4 ) )
% 5.49/5.85 = ( ^ [P3: option_num > $o] :
% 5.49/5.85 ( ( P3 @ none_num )
% 5.49/5.85 | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % split_option_ex
% 5.49/5.85 thf(fact_136_option_Oexhaust,axiom,
% 5.49/5.85 ! [Y2: option_nat] :
% 5.49/5.85 ( ( Y2 != none_nat )
% 5.49/5.85 => ~ ! [X23: nat] :
% 5.49/5.85 ( Y2
% 5.49/5.85 != ( some_nat @ X23 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.exhaust
% 5.49/5.85 thf(fact_137_option_Oexhaust,axiom,
% 5.49/5.85 ! [Y2: option4927543243414619207at_nat] :
% 5.49/5.85 ( ( Y2 != none_P5556105721700978146at_nat )
% 5.49/5.85 => ~ ! [X23: product_prod_nat_nat] :
% 5.49/5.85 ( Y2
% 5.49/5.85 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.exhaust
% 5.49/5.85 thf(fact_138_option_Oexhaust,axiom,
% 5.49/5.85 ! [Y2: option_num] :
% 5.49/5.85 ( ( Y2 != none_num )
% 5.49/5.85 => ~ ! [X23: num] :
% 5.49/5.85 ( Y2
% 5.49/5.85 != ( some_num @ X23 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.exhaust
% 5.49/5.85 thf(fact_139_option_OdiscI,axiom,
% 5.49/5.85 ! [Option: option_nat,X22: nat] :
% 5.49/5.85 ( ( Option
% 5.49/5.85 = ( some_nat @ X22 ) )
% 5.49/5.85 => ( Option != none_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.discI
% 5.49/5.85 thf(fact_140_option_OdiscI,axiom,
% 5.49/5.85 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.49/5.85 ( ( Option
% 5.49/5.85 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.49/5.85 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.discI
% 5.49/5.85 thf(fact_141_option_OdiscI,axiom,
% 5.49/5.85 ! [Option: option_num,X22: num] :
% 5.49/5.85 ( ( Option
% 5.49/5.85 = ( some_num @ X22 ) )
% 5.49/5.85 => ( Option != none_num ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.discI
% 5.49/5.85 thf(fact_142_option_Odistinct_I1_J,axiom,
% 5.49/5.85 ! [X22: nat] :
% 5.49/5.85 ( none_nat
% 5.49/5.85 != ( some_nat @ X22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.distinct(1)
% 5.49/5.85 thf(fact_143_option_Odistinct_I1_J,axiom,
% 5.49/5.85 ! [X22: product_prod_nat_nat] :
% 5.49/5.85 ( none_P5556105721700978146at_nat
% 5.49/5.85 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.distinct(1)
% 5.49/5.85 thf(fact_144_option_Odistinct_I1_J,axiom,
% 5.49/5.85 ! [X22: num] :
% 5.49/5.85 ( none_num
% 5.49/5.85 != ( some_num @ X22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % option.distinct(1)
% 5.49/5.85 thf(fact_145_mint__sound,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.49/5.85 => ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = ( some_nat @ X ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mint_sound
% 5.49/5.85 thf(fact_146_mint__corr,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_mint @ T )
% 5.49/5.85 = ( some_nat @ X ) )
% 5.49/5.85 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mint_corr
% 5.49/5.85 thf(fact_147_post__member__pre__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y2 )
% 5.49/5.85 => ( ( vEBT_vebt_member @ T @ Y2 )
% 5.49/5.85 | ( X = Y2 ) ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % post_member_pre_member
% 5.49/5.85 thf(fact_148_add__shift,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.85 ( ( ( plus_plus_nat @ X @ Y2 )
% 5.49/5.85 = Z )
% 5.49/5.85 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 5.49/5.85 = ( some_nat @ Z ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_shift
% 5.49/5.85 thf(fact_149_maxt__corr__help,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_maxt @ T )
% 5.49/5.85 = ( some_nat @ Maxi ) )
% 5.49/5.85 => ( ( vEBT_vebt_member @ T @ X )
% 5.49/5.85 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % maxt_corr_help
% 5.49/5.85 thf(fact_150__092_060open_062length_AtreeList_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_Am_092_060close_062,axiom,
% 5.49/5.85 ( ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.49/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.49/5.85 & ( vEBT_invar_vebt @ summary @ m ) ) ).
% 5.49/5.85
% 5.49/5.85 % \<open>length treeList = 2 ^ m \<and> invar_vebt summary m\<close>
% 5.49/5.85 thf(fact_151_maxt__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_maxt @ T )
% 5.49/5.85 = ( some_nat @ Maxi ) )
% 5.49/5.85 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % maxt_member
% 5.49/5.85 thf(fact_152__C5_Ohyps_C_I11_J,axiom,
% 5.49/5.85 ( ( mi != ma )
% 5.49/5.85 => ! [I: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.49/5.85 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.49/5.85 = I )
% 5.49/5.85 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.49/5.85 & ! [X5: nat] :
% 5.49/5.85 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 5.49/5.85 = I )
% 5.49/5.85 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 5.49/5.85 => ( ( ord_less_nat @ mi @ X5 )
% 5.49/5.85 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(11)
% 5.49/5.85 thf(fact_153_div__exp__eq,axiom,
% 5.49/5.85 ! [A: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( 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 ) )
% 5.49/5.85 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_exp_eq
% 5.49/5.85 thf(fact_154_div__exp__eq,axiom,
% 5.49/5.85 ! [A: int,M: nat,N: nat] :
% 5.49/5.85 ( ( 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 ) )
% 5.49/5.85 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_exp_eq
% 5.49/5.85 thf(fact_155_field__less__half__sum,axiom,
% 5.49/5.85 ! [X: real,Y2: real] :
% 5.49/5.85 ( ( ord_less_real @ X @ Y2 )
% 5.49/5.85 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % field_less_half_sum
% 5.49/5.85 thf(fact_156_field__less__half__sum,axiom,
% 5.49/5.85 ! [X: rat,Y2: rat] :
% 5.49/5.85 ( ( ord_less_rat @ X @ Y2 )
% 5.49/5.85 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % field_less_half_sum
% 5.49/5.85 thf(fact_157_bit__concat__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_bit_concat
% 5.49/5.85 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % bit_concat_def
% 5.49/5.85 thf(fact_158_low__inv,axiom,
% 5.49/5.85 ! [X: nat,N: nat,Y2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.49/5.85 = X ) ) ).
% 5.49/5.85
% 5.49/5.85 % low_inv
% 5.49/5.85 thf(fact_159_even__odd__cases,axiom,
% 5.49/5.85 ! [X: nat] :
% 5.49/5.85 ( ! [N3: nat] :
% 5.49/5.85 ( X
% 5.49/5.85 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.49/5.85 => ~ ! [N3: nat] :
% 5.49/5.85 ( X
% 5.49/5.85 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % even_odd_cases
% 5.49/5.85 thf(fact_160_not__min__Null__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT] :
% 5.49/5.85 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.49/5.85 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_min_Null_member
% 5.49/5.85 thf(fact_161_valid__member__both__member__options,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.49/5.85 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % valid_member_both_member_options
% 5.49/5.85 thf(fact_162_both__member__options__equiv__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.49/5.85 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % both_member_options_equiv_member
% 5.49/5.85 thf(fact_163_maxbmo,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,X: nat] :
% 5.49/5.85 ( ( ( vEBT_vebt_maxt @ T )
% 5.49/5.85 = ( some_nat @ X ) )
% 5.49/5.85 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % maxbmo
% 5.49/5.85 thf(fact_164_add__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_add
% 5.49/5.85 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_def
% 5.49/5.85 thf(fact_165_set__vebt__set__vebt_H__valid,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_set_vebt @ T )
% 5.49/5.85 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % set_vebt_set_vebt'_valid
% 5.49/5.85 thf(fact_166_maxt__corr,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ( vEBT_vebt_maxt @ T )
% 5.49/5.85 = ( some_nat @ X ) )
% 5.49/5.85 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % maxt_corr
% 5.49/5.85 thf(fact_167_maxt__sound,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.49/5.85 => ( ( vEBT_vebt_maxt @ T )
% 5.49/5.85 = ( some_nat @ X ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % maxt_sound
% 5.49/5.85 thf(fact_168_numeral__times__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.49/5.85 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_times_numeral
% 5.49/5.85 thf(fact_169_numeral__times__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.49/5.85 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_times_numeral
% 5.49/5.85 thf(fact_170_numeral__times__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.49/5.85 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_times_numeral
% 5.49/5.85 thf(fact_171_numeral__times__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_times_numeral
% 5.49/5.85 thf(fact_172_numeral__times__numeral,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.49/5.85 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % numeral_times_numeral
% 5.49/5.85 thf(fact_173_mult__numeral__left__semiring__numeral,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: complex] :
% 5.49/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.49/5.85 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_left_semiring_numeral
% 5.49/5.85 thf(fact_174_mult__numeral__left__semiring__numeral,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: real] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.49/5.85 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_left_semiring_numeral
% 5.49/5.85 thf(fact_175_mult__numeral__left__semiring__numeral,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: rat] :
% 5.49/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.49/5.85 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_left_semiring_numeral
% 5.49/5.85 thf(fact_176_mult__numeral__left__semiring__numeral,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.49/5.85 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_left_semiring_numeral
% 5.49/5.85 thf(fact_177_mult__numeral__left__semiring__numeral,axiom,
% 5.49/5.85 ! [V: num,W: num,Z: int] :
% 5.49/5.85 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.49/5.85 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_left_semiring_numeral
% 5.49/5.85 thf(fact_178_high__inv,axiom,
% 5.49/5.85 ! [X: nat,N: nat,Y2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.49/5.85 = Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % high_inv
% 5.49/5.85 thf(fact_179_valid__insert__both__member__options__pres,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.49/5.85 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % valid_insert_both_member_options_pres
% 5.49/5.85 thf(fact_180_valid__insert__both__member__options__add,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.85 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % valid_insert_both_member_options_add
% 5.49/5.85 thf(fact_181_semiring__norm_I6_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.49/5.85 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(6)
% 5.49/5.85 thf(fact_182_distrib__left__numeral,axiom,
% 5.49/5.85 ! [V: num,B: complex,C: complex] :
% 5.49/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.49/5.85 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_left_numeral
% 5.49/5.85 thf(fact_183_distrib__left__numeral,axiom,
% 5.49/5.85 ! [V: num,B: real,C: real] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.85 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_left_numeral
% 5.49/5.85 thf(fact_184_distrib__left__numeral,axiom,
% 5.49/5.85 ! [V: num,B: rat,C: rat] :
% 5.49/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.85 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_left_numeral
% 5.49/5.85 thf(fact_185_distrib__left__numeral,axiom,
% 5.49/5.85 ! [V: num,B: nat,C: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_left_numeral
% 5.49/5.85 thf(fact_186_distrib__left__numeral,axiom,
% 5.49/5.85 ! [V: num,B: int,C: int] :
% 5.49/5.85 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.85 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_left_numeral
% 5.49/5.85 thf(fact_187_distrib__right__numeral,axiom,
% 5.49/5.85 ! [A: complex,B: complex,V: num] :
% 5.49/5.85 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.49/5.85 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_right_numeral
% 5.49/5.85 thf(fact_188_distrib__right__numeral,axiom,
% 5.49/5.85 ! [A: real,B: real,V: num] :
% 5.49/5.85 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.85 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_right_numeral
% 5.49/5.85 thf(fact_189_distrib__right__numeral,axiom,
% 5.49/5.85 ! [A: rat,B: rat,V: num] :
% 5.49/5.85 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.85 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_right_numeral
% 5.49/5.85 thf(fact_190_distrib__right__numeral,axiom,
% 5.49/5.85 ! [A: nat,B: nat,V: num] :
% 5.49/5.85 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.49/5.85 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_right_numeral
% 5.49/5.85 thf(fact_191_distrib__right__numeral,axiom,
% 5.49/5.85 ! [A: int,B: int,V: num] :
% 5.49/5.85 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.85 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % distrib_right_numeral
% 5.49/5.85 thf(fact_192_semiring__norm_I2_J,axiom,
% 5.49/5.85 ( ( plus_plus_num @ one @ one )
% 5.49/5.85 = ( bit0 @ one ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(2)
% 5.49/5.85 thf(fact_193_le__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [A: real,B: real,W: num] :
% 5.49/5.85 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.49/5.85 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_divide_eq_numeral1(1)
% 5.49/5.85 thf(fact_194_le__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [A: rat,B: rat,W: num] :
% 5.49/5.85 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.49/5.85 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_divide_eq_numeral1(1)
% 5.49/5.85 thf(fact_195_divide__le__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [B: real,W: num,A: real] :
% 5.49/5.85 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.49/5.85 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % divide_le_eq_numeral1(1)
% 5.49/5.85 thf(fact_196_divide__le__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [B: rat,W: num,A: rat] :
% 5.49/5.85 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.49/5.85 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % divide_le_eq_numeral1(1)
% 5.49/5.85 thf(fact_197_less__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [A: real,B: real,W: num] :
% 5.49/5.85 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.49/5.85 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_divide_eq_numeral1(1)
% 5.49/5.85 thf(fact_198_less__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [A: rat,B: rat,W: num] :
% 5.49/5.85 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.49/5.85 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_divide_eq_numeral1(1)
% 5.49/5.85 thf(fact_199_divide__less__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [B: real,W: num,A: real] :
% 5.49/5.85 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.49/5.85 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % divide_less_eq_numeral1(1)
% 5.49/5.85 thf(fact_200_divide__less__eq__numeral1_I1_J,axiom,
% 5.49/5.85 ! [B: rat,W: num,A: rat] :
% 5.49/5.85 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.49/5.85 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % divide_less_eq_numeral1(1)
% 5.49/5.85 thf(fact_201_power__add__numeral,axiom,
% 5.49/5.85 ! [A: complex,M: num,N: num] :
% 5.49/5.85 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.49/5.85 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral
% 5.49/5.85 thf(fact_202_power__add__numeral,axiom,
% 5.49/5.85 ! [A: real,M: num,N: num] :
% 5.49/5.85 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.49/5.85 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral
% 5.49/5.85 thf(fact_203_power__add__numeral,axiom,
% 5.49/5.85 ! [A: rat,M: num,N: num] :
% 5.49/5.85 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.49/5.85 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral
% 5.49/5.85 thf(fact_204_power__add__numeral,axiom,
% 5.49/5.85 ! [A: nat,M: num,N: num] :
% 5.49/5.85 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.49/5.85 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral
% 5.49/5.85 thf(fact_205_power__add__numeral,axiom,
% 5.49/5.85 ! [A: int,M: num,N: num] :
% 5.49/5.85 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.49/5.85 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral
% 5.49/5.85 thf(fact_206_power__add__numeral2,axiom,
% 5.49/5.85 ! [A: complex,M: num,N: num,B: complex] :
% 5.49/5.85 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.49/5.85 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral2
% 5.49/5.85 thf(fact_207_power__add__numeral2,axiom,
% 5.49/5.85 ! [A: real,M: num,N: num,B: real] :
% 5.49/5.85 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.49/5.85 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral2
% 5.49/5.85 thf(fact_208_power__add__numeral2,axiom,
% 5.49/5.85 ! [A: rat,M: num,N: num,B: rat] :
% 5.49/5.85 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.49/5.85 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral2
% 5.49/5.85 thf(fact_209_power__add__numeral2,axiom,
% 5.49/5.85 ! [A: nat,M: num,N: num,B: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.49/5.85 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral2
% 5.49/5.85 thf(fact_210_power__add__numeral2,axiom,
% 5.49/5.85 ! [A: int,M: num,N: num,B: int] :
% 5.49/5.85 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.49/5.85 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add_numeral2
% 5.49/5.85 thf(fact_211_Suc__numeral,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_numeral
% 5.49/5.85 thf(fact_212_add__2__eq__Suc_H,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( suc @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_2_eq_Suc'
% 5.49/5.85 thf(fact_213_add__2__eq__Suc,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.49/5.85 = ( suc @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_2_eq_Suc
% 5.49/5.85 thf(fact_214_div2__Suc__Suc,axiom,
% 5.49/5.85 ! [M: nat] :
% 5.49/5.85 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div2_Suc_Suc
% 5.49/5.85 thf(fact_215_pred__member,axiom,
% 5.49/5.85 ! [T: vEBT_VEBT,X: nat,Y2: nat] :
% 5.49/5.85 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y2 )
% 5.49/5.85 = ( ( vEBT_vebt_member @ T @ Y2 )
% 5.49/5.85 & ( ord_less_nat @ Y2 @ X )
% 5.49/5.85 & ! [Z2: nat] :
% 5.49/5.85 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.49/5.85 & ( ord_less_nat @ Z2 @ X ) )
% 5.49/5.85 => ( ord_less_eq_nat @ Z2 @ Y2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % pred_member
% 5.49/5.85 thf(fact_216__C5_Ohyps_C_I7_J,axiom,
% 5.49/5.85 ! [I: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.49/5.85 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X6 ) )
% 5.49/5.85 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(7)
% 5.49/5.85 thf(fact_217_power__Suc2,axiom,
% 5.49/5.85 ! [A: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc2
% 5.49/5.85 thf(fact_218_power__Suc2,axiom,
% 5.49/5.85 ! [A: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc2
% 5.49/5.85 thf(fact_219_power__Suc2,axiom,
% 5.49/5.85 ! [A: rat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc2
% 5.49/5.85 thf(fact_220_power__Suc2,axiom,
% 5.49/5.85 ! [A: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc2
% 5.49/5.85 thf(fact_221_power__Suc2,axiom,
% 5.49/5.85 ! [A: int,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc2
% 5.49/5.85 thf(fact_222_power__Suc,axiom,
% 5.49/5.85 ! [A: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc
% 5.49/5.85 thf(fact_223_power__Suc,axiom,
% 5.49/5.85 ! [A: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc
% 5.49/5.85 thf(fact_224_power__Suc,axiom,
% 5.49/5.85 ! [A: rat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc
% 5.49/5.85 thf(fact_225_power__Suc,axiom,
% 5.49/5.85 ! [A: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc
% 5.49/5.85 thf(fact_226_power__Suc,axiom,
% 5.49/5.85 ! [A: int,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.49/5.85 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_Suc
% 5.49/5.85 thf(fact_227_add__One__commute,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( plus_plus_num @ one @ N )
% 5.49/5.85 = ( plus_plus_num @ N @ one ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_One_commute
% 5.49/5.85 thf(fact_228_power__commutes,axiom,
% 5.49/5.85 ! [A: complex,N: nat] :
% 5.49/5.85 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.49/5.85 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commutes
% 5.49/5.85 thf(fact_229_power__commutes,axiom,
% 5.49/5.85 ! [A: real,N: nat] :
% 5.49/5.85 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.49/5.85 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commutes
% 5.49/5.85 thf(fact_230_power__commutes,axiom,
% 5.49/5.85 ! [A: rat,N: nat] :
% 5.49/5.85 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.49/5.85 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commutes
% 5.49/5.85 thf(fact_231_power__commutes,axiom,
% 5.49/5.85 ! [A: nat,N: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.49/5.85 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commutes
% 5.49/5.85 thf(fact_232_power__commutes,axiom,
% 5.49/5.85 ! [A: int,N: nat] :
% 5.49/5.85 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.49/5.85 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commutes
% 5.49/5.85 thf(fact_233_power__mult__distrib,axiom,
% 5.49/5.85 ! [A: complex,B: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.49/5.85 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_distrib
% 5.49/5.85 thf(fact_234_power__mult__distrib,axiom,
% 5.49/5.85 ! [A: real,B: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.49/5.85 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_distrib
% 5.49/5.85 thf(fact_235_power__mult__distrib,axiom,
% 5.49/5.85 ! [A: rat,B: rat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.49/5.85 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_distrib
% 5.49/5.85 thf(fact_236_power__mult__distrib,axiom,
% 5.49/5.85 ! [A: nat,B: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.49/5.85 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_distrib
% 5.49/5.85 thf(fact_237_power__mult__distrib,axiom,
% 5.49/5.85 ! [A: int,B: int,N: nat] :
% 5.49/5.85 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.49/5.85 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_distrib
% 5.49/5.85 thf(fact_238_power__commuting__commutes,axiom,
% 5.49/5.85 ! [X: complex,Y2: complex,N: nat] :
% 5.49/5.85 ( ( ( times_times_complex @ X @ Y2 )
% 5.49/5.85 = ( times_times_complex @ Y2 @ X ) )
% 5.49/5.85 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y2 )
% 5.49/5.85 = ( times_times_complex @ Y2 @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commuting_commutes
% 5.49/5.85 thf(fact_239_power__commuting__commutes,axiom,
% 5.49/5.85 ! [X: real,Y2: real,N: nat] :
% 5.49/5.85 ( ( ( times_times_real @ X @ Y2 )
% 5.49/5.85 = ( times_times_real @ Y2 @ X ) )
% 5.49/5.85 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y2 )
% 5.49/5.85 = ( times_times_real @ Y2 @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commuting_commutes
% 5.49/5.85 thf(fact_240_power__commuting__commutes,axiom,
% 5.49/5.85 ! [X: rat,Y2: rat,N: nat] :
% 5.49/5.85 ( ( ( times_times_rat @ X @ Y2 )
% 5.49/5.85 = ( times_times_rat @ Y2 @ X ) )
% 5.49/5.85 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y2 )
% 5.49/5.85 = ( times_times_rat @ Y2 @ ( power_power_rat @ X @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commuting_commutes
% 5.49/5.85 thf(fact_241_power__commuting__commutes,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat,N: nat] :
% 5.49/5.85 ( ( ( times_times_nat @ X @ Y2 )
% 5.49/5.85 = ( times_times_nat @ Y2 @ X ) )
% 5.49/5.85 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y2 )
% 5.49/5.85 = ( times_times_nat @ Y2 @ ( power_power_nat @ X @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commuting_commutes
% 5.49/5.85 thf(fact_242_power__commuting__commutes,axiom,
% 5.49/5.85 ! [X: int,Y2: int,N: nat] :
% 5.49/5.85 ( ( ( times_times_int @ X @ Y2 )
% 5.49/5.85 = ( times_times_int @ Y2 @ X ) )
% 5.49/5.85 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y2 )
% 5.49/5.85 = ( times_times_int @ Y2 @ ( power_power_int @ X @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_commuting_commutes
% 5.49/5.85 thf(fact_243_power__mult,axiom,
% 5.49/5.85 ! [A: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.49/5.85 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult
% 5.49/5.85 thf(fact_244_power__mult,axiom,
% 5.49/5.85 ! [A: real,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.49/5.85 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult
% 5.49/5.85 thf(fact_245_power__mult,axiom,
% 5.49/5.85 ! [A: int,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.49/5.85 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult
% 5.49/5.85 thf(fact_246_power__mult,axiom,
% 5.49/5.85 ! [A: complex,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.49/5.85 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult
% 5.49/5.85 thf(fact_247_left__add__mult__distrib,axiom,
% 5.49/5.85 ! [I2: nat,U: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.49/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_mult_distrib
% 5.49/5.85 thf(fact_248_div__mult2__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.85 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.49/5.85 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_mult2_eq
% 5.49/5.85 thf(fact_249_power__odd__eq,axiom,
% 5.49/5.85 ! [A: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.49/5.85 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_odd_eq
% 5.49/5.85 thf(fact_250_power__odd__eq,axiom,
% 5.49/5.85 ! [A: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.49/5.85 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_odd_eq
% 5.49/5.85 thf(fact_251_power__odd__eq,axiom,
% 5.49/5.85 ! [A: rat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.49/5.85 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_odd_eq
% 5.49/5.85 thf(fact_252_power__odd__eq,axiom,
% 5.49/5.85 ! [A: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.49/5.85 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_odd_eq
% 5.49/5.85 thf(fact_253_power__odd__eq,axiom,
% 5.49/5.85 ! [A: int,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.49/5.85 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_odd_eq
% 5.49/5.85 thf(fact_254_Suc__nat__number__of__add,axiom,
% 5.49/5.85 ! [V: num,N: nat] :
% 5.49/5.85 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.49/5.85 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_nat_number_of_add
% 5.49/5.85 thf(fact_255_div__nat__eqI,axiom,
% 5.49/5.85 ! [N: nat,Q2: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.49/5.85 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.49/5.85 => ( ( divide_divide_nat @ M @ N )
% 5.49/5.85 = Q2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_nat_eqI
% 5.49/5.85 thf(fact_256_mult__numeral__1__right,axiom,
% 5.49/5.85 ! [A: complex] :
% 5.49/5.85 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1_right
% 5.49/5.85 thf(fact_257_mult__numeral__1__right,axiom,
% 5.49/5.85 ! [A: real] :
% 5.49/5.85 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1_right
% 5.49/5.85 thf(fact_258_mult__numeral__1__right,axiom,
% 5.49/5.85 ! [A: rat] :
% 5.49/5.85 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1_right
% 5.49/5.85 thf(fact_259_mult__numeral__1__right,axiom,
% 5.49/5.85 ! [A: nat] :
% 5.49/5.85 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1_right
% 5.49/5.85 thf(fact_260_mult__numeral__1__right,axiom,
% 5.49/5.85 ! [A: int] :
% 5.49/5.85 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1_right
% 5.49/5.85 thf(fact_261_mult__numeral__1,axiom,
% 5.49/5.85 ! [A: complex] :
% 5.49/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1
% 5.49/5.85 thf(fact_262_mult__numeral__1,axiom,
% 5.49/5.85 ! [A: real] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1
% 5.49/5.85 thf(fact_263_mult__numeral__1,axiom,
% 5.49/5.85 ! [A: rat] :
% 5.49/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1
% 5.49/5.85 thf(fact_264_mult__numeral__1,axiom,
% 5.49/5.85 ! [A: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1
% 5.49/5.85 thf(fact_265_mult__numeral__1,axiom,
% 5.49/5.85 ! [A: int] :
% 5.49/5.85 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.49/5.85 = A ) ).
% 5.49/5.85
% 5.49/5.85 % mult_numeral_1
% 5.49/5.85 thf(fact_266_power__add,axiom,
% 5.49/5.85 ! [A: complex,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.85 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add
% 5.49/5.85 thf(fact_267_power__add,axiom,
% 5.49/5.85 ! [A: real,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.85 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add
% 5.49/5.85 thf(fact_268_power__add,axiom,
% 5.49/5.85 ! [A: rat,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.85 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add
% 5.49/5.85 thf(fact_269_power__add,axiom,
% 5.49/5.85 ! [A: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.85 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add
% 5.49/5.85 thf(fact_270_power__add,axiom,
% 5.49/5.85 ! [A: int,M: nat,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.85 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_add
% 5.49/5.85 thf(fact_271_Suc__div__le__mono,axiom,
% 5.49/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_div_le_mono
% 5.49/5.85 thf(fact_272_less__mult__imp__div__less,axiom,
% 5.49/5.85 ! [M: nat,I2: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 5.49/5.85 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_mult_imp_div_less
% 5.49/5.85 thf(fact_273_times__div__less__eq__dividend,axiom,
% 5.49/5.85 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.49/5.85
% 5.49/5.85 % times_div_less_eq_dividend
% 5.49/5.85 thf(fact_274_div__times__less__eq__dividend,axiom,
% 5.49/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.49/5.85
% 5.49/5.85 % div_times_less_eq_dividend
% 5.49/5.85 thf(fact_275_left__add__twice,axiom,
% 5.49/5.85 ! [A: complex,B: complex] :
% 5.49/5.85 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.49/5.85 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_twice
% 5.49/5.85 thf(fact_276_left__add__twice,axiom,
% 5.49/5.85 ! [A: real,B: real] :
% 5.49/5.85 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.49/5.85 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_twice
% 5.49/5.85 thf(fact_277_left__add__twice,axiom,
% 5.49/5.85 ! [A: rat,B: rat] :
% 5.49/5.85 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.49/5.85 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_twice
% 5.49/5.85 thf(fact_278_left__add__twice,axiom,
% 5.49/5.85 ! [A: nat,B: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.49/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_twice
% 5.49/5.85 thf(fact_279_left__add__twice,axiom,
% 5.49/5.85 ! [A: int,B: int] :
% 5.49/5.85 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.49/5.85 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.49/5.85
% 5.49/5.85 % left_add_twice
% 5.49/5.85 thf(fact_280_mult__2__right,axiom,
% 5.49/5.85 ! [Z: complex] :
% 5.49/5.85 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2_right
% 5.49/5.85 thf(fact_281_mult__2__right,axiom,
% 5.49/5.85 ! [Z: real] :
% 5.49/5.85 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2_right
% 5.49/5.85 thf(fact_282_mult__2__right,axiom,
% 5.49/5.85 ! [Z: rat] :
% 5.49/5.85 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2_right
% 5.49/5.85 thf(fact_283_mult__2__right,axiom,
% 5.49/5.85 ! [Z: nat] :
% 5.49/5.85 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2_right
% 5.49/5.85 thf(fact_284_mult__2__right,axiom,
% 5.49/5.85 ! [Z: int] :
% 5.49/5.85 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2_right
% 5.49/5.85 thf(fact_285_mult__2,axiom,
% 5.49/5.85 ! [Z: complex] :
% 5.49/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.49/5.85 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2
% 5.49/5.85 thf(fact_286_mult__2,axiom,
% 5.49/5.85 ! [Z: real] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.49/5.85 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2
% 5.49/5.85 thf(fact_287_mult__2,axiom,
% 5.49/5.85 ! [Z: rat] :
% 5.49/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.49/5.85 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2
% 5.49/5.85 thf(fact_288_mult__2,axiom,
% 5.49/5.85 ! [Z: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.49/5.85 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2
% 5.49/5.85 thf(fact_289_mult__2,axiom,
% 5.49/5.85 ! [Z: int] :
% 5.49/5.85 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.49/5.85 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_2
% 5.49/5.85 thf(fact_290_power2__eq__square,axiom,
% 5.49/5.85 ! [A: complex] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( times_times_complex @ A @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_eq_square
% 5.49/5.85 thf(fact_291_power2__eq__square,axiom,
% 5.49/5.85 ! [A: real] :
% 5.49/5.85 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( times_times_real @ A @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_eq_square
% 5.49/5.85 thf(fact_292_power2__eq__square,axiom,
% 5.49/5.85 ! [A: rat] :
% 5.49/5.85 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( times_times_rat @ A @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_eq_square
% 5.49/5.85 thf(fact_293_power2__eq__square,axiom,
% 5.49/5.85 ! [A: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( times_times_nat @ A @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_eq_square
% 5.49/5.85 thf(fact_294_power2__eq__square,axiom,
% 5.49/5.85 ! [A: int] :
% 5.49/5.85 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( times_times_int @ A @ A ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_eq_square
% 5.49/5.85 thf(fact_295_power4__eq__xxxx,axiom,
% 5.49/5.85 ! [X: complex] :
% 5.49/5.85 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % power4_eq_xxxx
% 5.49/5.85 thf(fact_296_power4__eq__xxxx,axiom,
% 5.49/5.85 ! [X: real] :
% 5.49/5.85 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % power4_eq_xxxx
% 5.49/5.85 thf(fact_297_power4__eq__xxxx,axiom,
% 5.49/5.85 ! [X: rat] :
% 5.49/5.85 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % power4_eq_xxxx
% 5.49/5.85 thf(fact_298_power4__eq__xxxx,axiom,
% 5.49/5.85 ! [X: nat] :
% 5.49/5.85 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % power4_eq_xxxx
% 5.49/5.85 thf(fact_299_power4__eq__xxxx,axiom,
% 5.49/5.85 ! [X: int] :
% 5.49/5.85 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.49/5.85
% 5.49/5.85 % power4_eq_xxxx
% 5.49/5.85 thf(fact_300_power__even__eq,axiom,
% 5.49/5.85 ! [A: nat,N: nat] :
% 5.49/5.85 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_even_eq
% 5.49/5.85 thf(fact_301_power__even__eq,axiom,
% 5.49/5.85 ! [A: real,N: nat] :
% 5.49/5.85 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_even_eq
% 5.49/5.85 thf(fact_302_power__even__eq,axiom,
% 5.49/5.85 ! [A: int,N: nat] :
% 5.49/5.85 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_even_eq
% 5.49/5.85 thf(fact_303_power__even__eq,axiom,
% 5.49/5.85 ! [A: complex,N: nat] :
% 5.49/5.85 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.85 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_even_eq
% 5.49/5.85 thf(fact_304_power2__sum,axiom,
% 5.49/5.85 ! [X: complex,Y2: complex] :
% 5.49/5.85 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_sum
% 5.49/5.85 thf(fact_305_power2__sum,axiom,
% 5.49/5.85 ! [X: real,Y2: real] :
% 5.49/5.85 ( ( power_power_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_sum
% 5.49/5.85 thf(fact_306_power2__sum,axiom,
% 5.49/5.85 ! [X: rat,Y2: rat] :
% 5.49/5.85 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_sum
% 5.49/5.85 thf(fact_307_power2__sum,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat] :
% 5.49/5.85 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_sum
% 5.49/5.85 thf(fact_308_power2__sum,axiom,
% 5.49/5.85 ! [X: int,Y2: int] :
% 5.49/5.85 ( ( power_power_int @ ( plus_plus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.85 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power2_sum
% 5.49/5.85 thf(fact_309_field__sum__of__halves,axiom,
% 5.49/5.85 ! [X: real] :
% 5.49/5.85 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = X ) ).
% 5.49/5.85
% 5.49/5.85 % field_sum_of_halves
% 5.49/5.85 thf(fact_310_field__sum__of__halves,axiom,
% 5.49/5.85 ! [X: rat] :
% 5.49/5.85 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = X ) ).
% 5.49/5.85
% 5.49/5.85 % field_sum_of_halves
% 5.49/5.85 thf(fact_311_in__children__def,axiom,
% 5.49/5.85 ( vEBT_V5917875025757280293ildren
% 5.49/5.85 = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N2 ) ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % in_children_def
% 5.49/5.85 thf(fact_312_mul__def,axiom,
% 5.49/5.85 ( vEBT_VEBT_mul
% 5.49/5.85 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.49/5.85
% 5.49/5.85 % mul_def
% 5.49/5.85 thf(fact_313_mul__shift,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.85 ( ( ( times_times_nat @ X @ Y2 )
% 5.49/5.85 = Z )
% 5.49/5.85 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y2 ) )
% 5.49/5.85 = ( some_nat @ Z ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mul_shift
% 5.49/5.85 thf(fact_314_sum__squares__bound,axiom,
% 5.49/5.85 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % sum_squares_bound
% 5.49/5.85 thf(fact_315_sum__squares__bound,axiom,
% 5.49/5.85 ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % sum_squares_bound
% 5.49/5.85 thf(fact_316_both__member__options__ding,axiom,
% 5.49/5.85 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.49/5.85 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.49/5.85 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.49/5.85 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % both_member_options_ding
% 5.49/5.85 thf(fact_317_mult__Suc__right,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.49/5.85 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % mult_Suc_right
% 5.49/5.85 thf(fact_318_nat__add__left__cancel__le,axiom,
% 5.49/5.85 ! [K: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.49/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_add_left_cancel_le
% 5.49/5.85 thf(fact_319_nat__add__left__cancel__less,axiom,
% 5.49/5.85 ! [K: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.49/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_add_left_cancel_less
% 5.49/5.85 thf(fact_320_add__Suc__right,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.49/5.85 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_Suc_right
% 5.49/5.85 thf(fact_321_Suc__le__mono,axiom,
% 5.49/5.85 ! [N: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.49/5.85 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_le_mono
% 5.49/5.85 thf(fact_322_double__not__eq__Suc__double,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.49/5.85 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % double_not_eq_Suc_double
% 5.49/5.85 thf(fact_323_Suc__double__not__eq__double,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.85 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_double_not_eq_double
% 5.49/5.85 thf(fact_324_deg__deg__n,axiom,
% 5.49/5.85 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.49/5.85 => ( Deg = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % deg_deg_n
% 5.49/5.85 thf(fact_325_deg__SUcn__Node,axiom,
% 5.49/5.85 ! [Tree: vEBT_VEBT,N: nat] :
% 5.49/5.85 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.49/5.85 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.85 ( Tree
% 5.49/5.85 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % deg_SUcn_Node
% 5.49/5.85 thf(fact_326_old_Onat_Oinject,axiom,
% 5.49/5.85 ! [Nat: nat,Nat2: nat] :
% 5.49/5.85 ( ( ( suc @ Nat )
% 5.49/5.85 = ( suc @ Nat2 ) )
% 5.49/5.85 = ( Nat = Nat2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % old.nat.inject
% 5.49/5.85 thf(fact_327_nat_Oinject,axiom,
% 5.49/5.85 ! [X22: nat,Y22: nat] :
% 5.49/5.85 ( ( ( suc @ X22 )
% 5.49/5.85 = ( suc @ Y22 ) )
% 5.49/5.85 = ( X22 = Y22 ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat.inject
% 5.49/5.85 thf(fact_328_lessI,axiom,
% 5.49/5.85 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % lessI
% 5.49/5.85 thf(fact_329_Suc__mono,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ N )
% 5.49/5.85 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_mono
% 5.49/5.85 thf(fact_330_Suc__less__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.49/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_less_eq
% 5.49/5.85 thf(fact_331_semiring__norm_I13_J,axiom,
% 5.49/5.85 ! [M: num,N: num] :
% 5.49/5.85 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.49/5.85 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(13)
% 5.49/5.85 thf(fact_332_semiring__norm_I12_J,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( times_times_num @ one @ N )
% 5.49/5.85 = N ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(12)
% 5.49/5.85 thf(fact_333_semiring__norm_I11_J,axiom,
% 5.49/5.85 ! [M: num] :
% 5.49/5.85 ( ( times_times_num @ M @ one )
% 5.49/5.85 = M ) ).
% 5.49/5.85
% 5.49/5.85 % semiring_norm(11)
% 5.49/5.85 thf(fact_334_num__double,axiom,
% 5.49/5.85 ! [N: num] :
% 5.49/5.85 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.49/5.85 = ( bit0 @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % num_double
% 5.49/5.85 thf(fact_335_power__mult__numeral,axiom,
% 5.49/5.85 ! [A: nat,M: num,N: num] :
% 5.49/5.85 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_numeral
% 5.49/5.85 thf(fact_336_power__mult__numeral,axiom,
% 5.49/5.85 ! [A: real,M: num,N: num] :
% 5.49/5.85 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_numeral
% 5.49/5.85 thf(fact_337_power__mult__numeral,axiom,
% 5.49/5.85 ! [A: int,M: num,N: num] :
% 5.49/5.85 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_numeral
% 5.49/5.85 thf(fact_338_power__mult__numeral,axiom,
% 5.49/5.85 ! [A: complex,M: num,N: num] :
% 5.49/5.85 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.49/5.85 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % power_mult_numeral
% 5.49/5.85 thf(fact_339__C5_Ohyps_C_I8_J,axiom,
% 5.49/5.85 ( ( mi = ma )
% 5.49/5.85 => ! [X5: vEBT_VEBT] :
% 5.49/5.85 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.49/5.85 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % "5.hyps"(8)
% 5.49/5.85 thf(fact_340_four__x__squared,axiom,
% 5.49/5.85 ! [X: real] :
% 5.49/5.85 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.85 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % four_x_squared
% 5.49/5.85 thf(fact_341_L2__set__mult__ineq__lemma,axiom,
% 5.49/5.85 ! [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 ) ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % L2_set_mult_ineq_lemma
% 5.49/5.85 thf(fact_342_div__mult2__numeral__eq,axiom,
% 5.49/5.85 ! [A: nat,K: num,L2: num] :
% 5.49/5.85 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.49/5.85 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_mult2_numeral_eq
% 5.49/5.85 thf(fact_343_div__mult2__numeral__eq,axiom,
% 5.49/5.85 ! [A: int,K: num,L2: num] :
% 5.49/5.85 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.49/5.85 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % div_mult2_numeral_eq
% 5.49/5.85 thf(fact_344_n__not__Suc__n,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ( N
% 5.49/5.85 != ( suc @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % n_not_Suc_n
% 5.49/5.85 thf(fact_345_Suc__inject,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat] :
% 5.49/5.85 ( ( ( suc @ X )
% 5.49/5.85 = ( suc @ Y2 ) )
% 5.49/5.85 => ( X = Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_inject
% 5.49/5.85 thf(fact_346_nat__neq__iff,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( M != N )
% 5.49/5.85 = ( ( ord_less_nat @ M @ N )
% 5.49/5.85 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_neq_iff
% 5.49/5.85 thf(fact_347_less__not__refl,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ~ ( ord_less_nat @ N @ N ) ).
% 5.49/5.85
% 5.49/5.85 % less_not_refl
% 5.49/5.85 thf(fact_348_less__not__refl2,axiom,
% 5.49/5.85 ! [N: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_nat @ N @ M )
% 5.49/5.85 => ( M != N ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_not_refl2
% 5.49/5.85 thf(fact_349_less__not__refl3,axiom,
% 5.49/5.85 ! [S2: nat,T: nat] :
% 5.49/5.85 ( ( ord_less_nat @ S2 @ T )
% 5.49/5.85 => ( S2 != T ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_not_refl3
% 5.49/5.85 thf(fact_350_less__irrefl__nat,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ~ ( ord_less_nat @ N @ N ) ).
% 5.49/5.85
% 5.49/5.85 % less_irrefl_nat
% 5.49/5.85 thf(fact_351_nat__less__induct,axiom,
% 5.49/5.85 ! [P: nat > $o,N: nat] :
% 5.49/5.85 ( ! [N3: nat] :
% 5.49/5.85 ( ! [M2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M2 @ N3 )
% 5.49/5.85 => ( P @ M2 ) )
% 5.49/5.85 => ( P @ N3 ) )
% 5.49/5.85 => ( P @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_less_induct
% 5.49/5.85 thf(fact_352_infinite__descent,axiom,
% 5.49/5.85 ! [P: nat > $o,N: nat] :
% 5.49/5.85 ( ! [N3: nat] :
% 5.49/5.85 ( ~ ( P @ N3 )
% 5.49/5.85 => ? [M2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M2 @ N3 )
% 5.49/5.85 & ~ ( P @ M2 ) ) )
% 5.49/5.85 => ( P @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % infinite_descent
% 5.49/5.85 thf(fact_353_linorder__neqE__nat,axiom,
% 5.49/5.85 ! [X: nat,Y2: nat] :
% 5.49/5.85 ( ( X != Y2 )
% 5.49/5.85 => ( ~ ( ord_less_nat @ X @ Y2 )
% 5.49/5.85 => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % linorder_neqE_nat
% 5.49/5.85 thf(fact_354_Nat_Oex__has__greatest__nat,axiom,
% 5.49/5.85 ! [P: nat > $o,K: nat,B: nat] :
% 5.49/5.85 ( ( P @ K )
% 5.49/5.85 => ( ! [Y3: nat] :
% 5.49/5.85 ( ( P @ Y3 )
% 5.49/5.85 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.49/5.85 => ? [X3: nat] :
% 5.49/5.85 ( ( P @ X3 )
% 5.49/5.85 & ! [Y4: nat] :
% 5.49/5.85 ( ( P @ Y4 )
% 5.49/5.85 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Nat.ex_has_greatest_nat
% 5.49/5.85 thf(fact_355_nat__le__linear,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_le_linear
% 5.49/5.85 thf(fact_356_le__antisym,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.85 => ( M = N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_antisym
% 5.49/5.85 thf(fact_357_eq__imp__le,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( M = N )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % eq_imp_le
% 5.49/5.85 thf(fact_358_le__trans,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ( ord_less_eq_nat @ J @ K )
% 5.49/5.85 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_trans
% 5.49/5.85 thf(fact_359_le__refl,axiom,
% 5.49/5.85 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.49/5.85
% 5.49/5.85 % le_refl
% 5.49/5.85 thf(fact_360_size__neq__size__imp__neq,axiom,
% 5.49/5.85 ! [X: list_VEBT_VEBT,Y2: list_VEBT_VEBT] :
% 5.49/5.85 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.49/5.85 != ( size_s6755466524823107622T_VEBT @ Y2 ) )
% 5.49/5.85 => ( X != Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % size_neq_size_imp_neq
% 5.49/5.85 thf(fact_361_size__neq__size__imp__neq,axiom,
% 5.49/5.85 ! [X: list_o,Y2: list_o] :
% 5.49/5.85 ( ( ( size_size_list_o @ X )
% 5.49/5.85 != ( size_size_list_o @ Y2 ) )
% 5.49/5.85 => ( X != Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % size_neq_size_imp_neq
% 5.49/5.85 thf(fact_362_size__neq__size__imp__neq,axiom,
% 5.49/5.85 ! [X: list_nat,Y2: list_nat] :
% 5.49/5.85 ( ( ( size_size_list_nat @ X )
% 5.49/5.85 != ( size_size_list_nat @ Y2 ) )
% 5.49/5.85 => ( X != Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % size_neq_size_imp_neq
% 5.49/5.85 thf(fact_363_size__neq__size__imp__neq,axiom,
% 5.49/5.85 ! [X: list_int,Y2: list_int] :
% 5.49/5.85 ( ( ( size_size_list_int @ X )
% 5.49/5.85 != ( size_size_list_int @ Y2 ) )
% 5.49/5.85 => ( X != Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % size_neq_size_imp_neq
% 5.49/5.85 thf(fact_364_size__neq__size__imp__neq,axiom,
% 5.49/5.85 ! [X: num,Y2: num] :
% 5.49/5.85 ( ( ( size_size_num @ X )
% 5.49/5.85 != ( size_size_num @ Y2 ) )
% 5.49/5.85 => ( X != Y2 ) ) ).
% 5.49/5.85
% 5.49/5.85 % size_neq_size_imp_neq
% 5.49/5.85 thf(fact_365_is__pred__in__set__def,axiom,
% 5.49/5.85 ( vEBT_is_pred_in_set
% 5.49/5.85 = ( ^ [Xs: set_nat,X2: nat,Y: nat] :
% 5.49/5.85 ( ( member_nat @ Y @ Xs )
% 5.49/5.85 & ( ord_less_nat @ Y @ X2 )
% 5.49/5.85 & ! [Z2: nat] :
% 5.49/5.85 ( ( member_nat @ Z2 @ Xs )
% 5.49/5.85 => ( ( ord_less_nat @ Z2 @ X2 )
% 5.49/5.85 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % is_pred_in_set_def
% 5.49/5.85 thf(fact_366_Nat_OlessE,axiom,
% 5.49/5.85 ! [I2: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ K )
% 5.49/5.85 => ( ( K
% 5.49/5.85 != ( suc @ I2 ) )
% 5.49/5.85 => ~ ! [J2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J2 )
% 5.49/5.85 => ( K
% 5.49/5.85 != ( suc @ J2 ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Nat.lessE
% 5.49/5.85 thf(fact_367_Suc__lessD,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.49/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_lessD
% 5.49/5.85 thf(fact_368_Suc__lessE,axiom,
% 5.49/5.85 ! [I2: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.49/5.85 => ~ ! [J2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J2 )
% 5.49/5.85 => ( K
% 5.49/5.85 != ( suc @ J2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_lessE
% 5.49/5.85 thf(fact_369_Suc__lessI,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ N )
% 5.49/5.85 => ( ( ( suc @ M )
% 5.49/5.85 != N )
% 5.49/5.85 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_lessI
% 5.49/5.85 thf(fact_370_less__SucE,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.49/5.85 => ( ~ ( ord_less_nat @ M @ N )
% 5.49/5.85 => ( M = N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_SucE
% 5.49/5.85 thf(fact_371_less__SucI,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ N )
% 5.49/5.85 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_SucI
% 5.49/5.85 thf(fact_372_Ex__less__Suc,axiom,
% 5.49/5.85 ! [N: nat,P: nat > $o] :
% 5.49/5.85 ( ( ? [I3: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.49/5.85 & ( P @ I3 ) ) )
% 5.49/5.85 = ( ( P @ N )
% 5.49/5.85 | ? [I3: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I3 @ N )
% 5.49/5.85 & ( P @ I3 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Ex_less_Suc
% 5.49/5.85 thf(fact_373_less__Suc__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.49/5.85 = ( ( ord_less_nat @ M @ N )
% 5.49/5.85 | ( M = N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_Suc_eq
% 5.49/5.85 thf(fact_374_not__less__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.49/5.85 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_less_eq
% 5.49/5.85 thf(fact_375_All__less__Suc,axiom,
% 5.49/5.85 ! [N: nat,P: nat > $o] :
% 5.49/5.85 ( ( ! [I3: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.49/5.85 => ( P @ I3 ) ) )
% 5.49/5.85 = ( ( P @ N )
% 5.49/5.85 & ! [I3: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I3 @ N )
% 5.49/5.85 => ( P @ I3 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % All_less_Suc
% 5.49/5.85 thf(fact_376_Suc__less__eq2,axiom,
% 5.49/5.85 ! [N: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.49/5.85 = ( ? [M3: nat] :
% 5.49/5.85 ( ( M
% 5.49/5.85 = ( suc @ M3 ) )
% 5.49/5.85 & ( ord_less_nat @ N @ M3 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_less_eq2
% 5.49/5.85 thf(fact_377_less__antisym,axiom,
% 5.49/5.85 ! [N: nat,M: nat] :
% 5.49/5.85 ( ~ ( ord_less_nat @ N @ M )
% 5.49/5.85 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.49/5.85 => ( M = N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_antisym
% 5.49/5.85 thf(fact_378_Suc__less__SucD,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.49/5.85 => ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_less_SucD
% 5.49/5.85 thf(fact_379_less__trans__Suc,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ( ord_less_nat @ J @ K )
% 5.49/5.85 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_trans_Suc
% 5.49/5.85 thf(fact_380_less__Suc__induct,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 5.49/5.85 => ( ! [I4: nat,J2: nat,K2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I4 @ J2 )
% 5.49/5.85 => ( ( ord_less_nat @ J2 @ K2 )
% 5.49/5.85 => ( ( P @ I4 @ J2 )
% 5.49/5.85 => ( ( P @ J2 @ K2 )
% 5.49/5.85 => ( P @ I4 @ K2 ) ) ) ) )
% 5.49/5.85 => ( P @ I2 @ J ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_Suc_induct
% 5.49/5.85 thf(fact_381_strict__inc__induct,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,P: nat > $o] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ! [I4: nat] :
% 5.49/5.85 ( ( J
% 5.49/5.85 = ( suc @ I4 ) )
% 5.49/5.85 => ( P @ I4 ) )
% 5.49/5.85 => ( ! [I4: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I4 @ J )
% 5.49/5.85 => ( ( P @ ( suc @ I4 ) )
% 5.49/5.85 => ( P @ I4 ) ) )
% 5.49/5.85 => ( P @ I2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % strict_inc_induct
% 5.49/5.85 thf(fact_382_not__less__less__Suc__eq,axiom,
% 5.49/5.85 ! [N: nat,M: nat] :
% 5.49/5.85 ( ~ ( ord_less_nat @ N @ M )
% 5.49/5.85 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.49/5.85 = ( N = M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_less_less_Suc_eq
% 5.49/5.85 thf(fact_383_transitive__stepwise__le,axiom,
% 5.49/5.85 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.49/5.85 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 5.49/5.85 ( ( R @ X3 @ Y3 )
% 5.49/5.85 => ( ( R @ Y3 @ Z3 )
% 5.49/5.85 => ( R @ X3 @ Z3 ) ) )
% 5.49/5.85 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.49/5.85 => ( R @ M @ N ) ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % transitive_stepwise_le
% 5.49/5.85 thf(fact_384_nat__induct__at__least,axiom,
% 5.49/5.85 ! [M: nat,N: nat,P: nat > $o] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ( P @ M )
% 5.49/5.85 => ( ! [N3: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N3 )
% 5.49/5.85 => ( ( P @ N3 )
% 5.49/5.85 => ( P @ ( suc @ N3 ) ) ) )
% 5.49/5.85 => ( P @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_induct_at_least
% 5.49/5.85 thf(fact_385_full__nat__induct,axiom,
% 5.49/5.85 ! [P: nat > $o,N: nat] :
% 5.49/5.85 ( ! [N3: nat] :
% 5.49/5.85 ( ! [M2: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 5.49/5.85 => ( P @ M2 ) )
% 5.49/5.85 => ( P @ N3 ) )
% 5.49/5.85 => ( P @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % full_nat_induct
% 5.49/5.85 thf(fact_386_not__less__eq__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.49/5.85 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.49/5.85
% 5.49/5.85 % not_less_eq_eq
% 5.49/5.85 thf(fact_387_Suc__n__not__le__n,axiom,
% 5.49/5.85 ! [N: nat] :
% 5.49/5.85 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_n_not_le_n
% 5.49/5.85 thf(fact_388_le__Suc__eq,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.49/5.85 = ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 | ( M
% 5.49/5.85 = ( suc @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_Suc_eq
% 5.49/5.85 thf(fact_389_Suc__le__D,axiom,
% 5.49/5.85 ! [N: nat,M4: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 5.49/5.85 => ? [M5: nat] :
% 5.49/5.85 ( M4
% 5.49/5.85 = ( suc @ M5 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_le_D
% 5.49/5.85 thf(fact_390_le__SucI,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_SucI
% 5.49/5.85 thf(fact_391_le__SucE,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.49/5.85 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( M
% 5.49/5.85 = ( suc @ N ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_SucE
% 5.49/5.85 thf(fact_392_Suc__leD,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_leD
% 5.49/5.85 thf(fact_393_add__Suc__shift,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.49/5.85 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_Suc_shift
% 5.49/5.85 thf(fact_394_add__Suc,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.49/5.85 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_Suc
% 5.49/5.85 thf(fact_395_nat__arith_Osuc1,axiom,
% 5.49/5.85 ! [A2: nat,K: nat,A: nat] :
% 5.49/5.85 ( ( A2
% 5.49/5.85 = ( plus_plus_nat @ K @ A ) )
% 5.49/5.85 => ( ( suc @ A2 )
% 5.49/5.85 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_arith.suc1
% 5.49/5.85 thf(fact_396_nat__less__le,axiom,
% 5.49/5.85 ( ord_less_nat
% 5.49/5.85 = ( ^ [M6: nat,N2: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.49/5.85 & ( M6 != N2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_less_le
% 5.49/5.85 thf(fact_397_less__imp__le__nat,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_imp_le_nat
% 5.49/5.85 thf(fact_398_le__eq__less__or__eq,axiom,
% 5.49/5.85 ( ord_less_eq_nat
% 5.49/5.85 = ( ^ [M6: nat,N2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ M6 @ N2 )
% 5.49/5.85 | ( M6 = N2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_eq_less_or_eq
% 5.49/5.85 thf(fact_399_less__or__eq__imp__le,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ( ord_less_nat @ M @ N )
% 5.49/5.85 | ( M = N ) )
% 5.49/5.85 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_or_eq_imp_le
% 5.49/5.85 thf(fact_400_le__neq__implies__less,axiom,
% 5.49/5.85 ! [M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.85 => ( ( M != N )
% 5.49/5.85 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_neq_implies_less
% 5.49/5.85 thf(fact_401_less__mono__imp__le__mono,axiom,
% 5.49/5.85 ! [F: nat > nat,I2: nat,J: nat] :
% 5.49/5.85 ( ! [I4: nat,J2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I4 @ J2 )
% 5.49/5.85 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 5.49/5.85 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_mono_imp_le_mono
% 5.49/5.85 thf(fact_402_add__lessD1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.49/5.85 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_lessD1
% 5.49/5.85 thf(fact_403_add__less__mono,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ( ord_less_nat @ K @ L2 )
% 5.49/5.85 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_less_mono
% 5.49/5.85 thf(fact_404_not__add__less1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat] :
% 5.49/5.85 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.49/5.85
% 5.49/5.85 % not_add_less1
% 5.49/5.85 thf(fact_405_not__add__less2,axiom,
% 5.49/5.85 ! [J: nat,I2: nat] :
% 5.49/5.85 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.49/5.85
% 5.49/5.85 % not_add_less2
% 5.49/5.85 thf(fact_406_add__less__mono1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_less_mono1
% 5.49/5.85 thf(fact_407_trans__less__add1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % trans_less_add1
% 5.49/5.85 thf(fact_408_trans__less__add2,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % trans_less_add2
% 5.49/5.85 thf(fact_409_less__add__eq__less,axiom,
% 5.49/5.85 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_nat @ K @ L2 )
% 5.49/5.85 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.49/5.85 = ( plus_plus_nat @ K @ N ) )
% 5.49/5.85 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % less_add_eq_less
% 5.49/5.85 thf(fact_410_Suc__mult__cancel1,axiom,
% 5.49/5.85 ! [K: nat,M: nat,N: nat] :
% 5.49/5.85 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.49/5.85 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.49/5.85 = ( M = N ) ) ).
% 5.49/5.85
% 5.49/5.85 % Suc_mult_cancel1
% 5.49/5.85 thf(fact_411_nat__le__iff__add,axiom,
% 5.49/5.85 ( ord_less_eq_nat
% 5.49/5.85 = ( ^ [M6: nat,N2: nat] :
% 5.49/5.85 ? [K3: nat] :
% 5.49/5.85 ( N2
% 5.49/5.85 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % nat_le_iff_add
% 5.49/5.85 thf(fact_412_trans__le__add2,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % trans_le_add2
% 5.49/5.85 thf(fact_413_trans__le__add1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,M: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % trans_le_add1
% 5.49/5.85 thf(fact_414_add__le__mono1,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_le_mono1
% 5.49/5.85 thf(fact_415_add__le__mono,axiom,
% 5.49/5.85 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.85 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.49/5.85 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % add_le_mono
% 5.49/5.85 thf(fact_416_le__Suc__ex,axiom,
% 5.49/5.85 ! [K: nat,L2: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ K @ L2 )
% 5.49/5.85 => ? [N3: nat] :
% 5.49/5.85 ( L2
% 5.49/5.85 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.49/5.85
% 5.49/5.85 % le_Suc_ex
% 5.49/5.85 thf(fact_417_add__leD2,axiom,
% 5.49/5.85 ! [M: nat,K: nat,N: nat] :
% 5.49/5.85 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.49/5.85 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_leD2
% 5.49/5.86 thf(fact_418_add__leD1,axiom,
% 5.49/5.86 ! [M: nat,K: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.49/5.86 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_leD1
% 5.49/5.86 thf(fact_419_le__add2,axiom,
% 5.49/5.86 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_add2
% 5.49/5.86 thf(fact_420_le__add1,axiom,
% 5.49/5.86 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_add1
% 5.49/5.86 thf(fact_421_add__leE,axiom,
% 5.49/5.86 ! [M: nat,K: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.49/5.86 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.86 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_leE
% 5.49/5.86 thf(fact_422_mult__le__mono2,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult_le_mono2
% 5.49/5.86 thf(fact_423_mult__le__mono1,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult_le_mono1
% 5.49/5.86 thf(fact_424_mult__le__mono,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.49/5.86 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult_le_mono
% 5.49/5.86 thf(fact_425_le__square,axiom,
% 5.49/5.86 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_square
% 5.49/5.86 thf(fact_426_le__cube,axiom,
% 5.49/5.86 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_cube
% 5.49/5.86 thf(fact_427_add__mult__distrib2,axiom,
% 5.49/5.86 ! [K: nat,M: nat,N: nat] :
% 5.49/5.86 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.86 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mult_distrib2
% 5.49/5.86 thf(fact_428_add__mult__distrib,axiom,
% 5.49/5.86 ! [M: nat,N: nat,K: nat] :
% 5.49/5.86 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.49/5.86 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mult_distrib
% 5.49/5.86 thf(fact_429_lift__Suc__mono__less,axiom,
% 5.49/5.86 ! [F: nat > real,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_real @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less
% 5.49/5.86 thf(fact_430_lift__Suc__mono__less,axiom,
% 5.49/5.86 ! [F: nat > rat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less
% 5.49/5.86 thf(fact_431_lift__Suc__mono__less,axiom,
% 5.49/5.86 ! [F: nat > num,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less
% 5.49/5.86 thf(fact_432_lift__Suc__mono__less,axiom,
% 5.49/5.86 ! [F: nat > nat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less
% 5.49/5.86 thf(fact_433_lift__Suc__mono__less,axiom,
% 5.49/5.86 ! [F: nat > int,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less
% 5.49/5.86 thf(fact_434_lift__Suc__mono__less__iff,axiom,
% 5.49/5.86 ! [F: nat > real,N: nat,M: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.49/5.86 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less_iff
% 5.49/5.86 thf(fact_435_lift__Suc__mono__less__iff,axiom,
% 5.49/5.86 ! [F: nat > rat,N: nat,M: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.49/5.86 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less_iff
% 5.49/5.86 thf(fact_436_lift__Suc__mono__less__iff,axiom,
% 5.49/5.86 ! [F: nat > num,N: nat,M: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.49/5.86 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less_iff
% 5.49/5.86 thf(fact_437_lift__Suc__mono__less__iff,axiom,
% 5.49/5.86 ! [F: nat > nat,N: nat,M: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.49/5.86 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less_iff
% 5.49/5.86 thf(fact_438_lift__Suc__mono__less__iff,axiom,
% 5.49/5.86 ! [F: nat > int,N: nat,M: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.49/5.86 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_less_iff
% 5.49/5.86 thf(fact_439_lift__Suc__antimono__le,axiom,
% 5.49/5.86 ! [F: nat > set_int,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_set_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_antimono_le
% 5.49/5.86 thf(fact_440_lift__Suc__antimono__le,axiom,
% 5.49/5.86 ! [F: nat > rat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_rat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_antimono_le
% 5.49/5.86 thf(fact_441_lift__Suc__antimono__le,axiom,
% 5.49/5.86 ! [F: nat > num,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_antimono_le
% 5.49/5.86 thf(fact_442_lift__Suc__antimono__le,axiom,
% 5.49/5.86 ! [F: nat > nat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_antimono_le
% 5.49/5.86 thf(fact_443_lift__Suc__antimono__le,axiom,
% 5.49/5.86 ! [F: nat > int,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_antimono_le
% 5.49/5.86 thf(fact_444_lift__Suc__mono__le,axiom,
% 5.49/5.86 ! [F: nat > set_int,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_le
% 5.49/5.86 thf(fact_445_lift__Suc__mono__le,axiom,
% 5.49/5.86 ! [F: nat > rat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_le
% 5.49/5.86 thf(fact_446_lift__Suc__mono__le,axiom,
% 5.49/5.86 ! [F: nat > num,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_le
% 5.49/5.86 thf(fact_447_lift__Suc__mono__le,axiom,
% 5.49/5.86 ! [F: nat > nat,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_le
% 5.49/5.86 thf(fact_448_lift__Suc__mono__le,axiom,
% 5.49/5.86 ! [F: nat > int,N: nat,N4: nat] :
% 5.49/5.86 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.49/5.86 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % lift_Suc_mono_le
% 5.49/5.86 thf(fact_449_Suc__leI,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ M @ N )
% 5.49/5.86 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_leI
% 5.49/5.86 thf(fact_450_Suc__le__eq,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.49/5.86 = ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_le_eq
% 5.49/5.86 thf(fact_451_dec__induct,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,P: nat > $o] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 => ( ( P @ I2 )
% 5.49/5.86 => ( ! [N3: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.49/5.86 => ( ( ord_less_nat @ N3 @ J )
% 5.49/5.86 => ( ( P @ N3 )
% 5.49/5.86 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.49/5.86 => ( P @ J ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % dec_induct
% 5.49/5.86 thf(fact_452_inc__induct,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,P: nat > $o] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 => ( ( P @ J )
% 5.49/5.86 => ( ! [N3: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.49/5.86 => ( ( ord_less_nat @ N3 @ J )
% 5.49/5.86 => ( ( P @ ( suc @ N3 ) )
% 5.49/5.86 => ( P @ N3 ) ) ) )
% 5.49/5.86 => ( P @ I2 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inc_induct
% 5.49/5.86 thf(fact_453_Suc__le__lessD,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.49/5.86 => ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_le_lessD
% 5.49/5.86 thf(fact_454_le__less__Suc__eq,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.49/5.86 = ( N = M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_less_Suc_eq
% 5.49/5.86 thf(fact_455_less__Suc__eq__le,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.49/5.86 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_Suc_eq_le
% 5.49/5.86 thf(fact_456_less__eq__Suc__le,axiom,
% 5.49/5.86 ( ord_less_nat
% 5.49/5.86 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_eq_Suc_le
% 5.49/5.86 thf(fact_457_le__imp__less__Suc,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.86 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_imp_less_Suc
% 5.49/5.86 thf(fact_458_less__natE,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ M @ N )
% 5.49/5.86 => ~ ! [Q3: nat] :
% 5.49/5.86 ( N
% 5.49/5.86 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_natE
% 5.49/5.86 thf(fact_459_less__add__Suc1,axiom,
% 5.49/5.86 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_add_Suc1
% 5.49/5.86 thf(fact_460_less__add__Suc2,axiom,
% 5.49/5.86 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_add_Suc2
% 5.49/5.86 thf(fact_461_less__iff__Suc__add,axiom,
% 5.49/5.86 ( ord_less_nat
% 5.49/5.86 = ( ^ [M6: nat,N2: nat] :
% 5.49/5.86 ? [K3: nat] :
% 5.49/5.86 ( N2
% 5.49/5.86 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_iff_Suc_add
% 5.49/5.86 thf(fact_462_less__imp__Suc__add,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ M @ N )
% 5.49/5.86 => ? [K2: nat] :
% 5.49/5.86 ( N
% 5.49/5.86 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_imp_Suc_add
% 5.49/5.86 thf(fact_463_Suc__mult__less__cancel1,axiom,
% 5.49/5.86 ! [K: nat,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.49/5.86 = ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_mult_less_cancel1
% 5.49/5.86 thf(fact_464_mono__nat__linear__lb,axiom,
% 5.49/5.86 ! [F: nat > nat,M: nat,K: nat] :
% 5.49/5.86 ( ! [M5: nat,N3: nat] :
% 5.49/5.86 ( ( ord_less_nat @ M5 @ N3 )
% 5.49/5.86 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mono_nat_linear_lb
% 5.49/5.86 thf(fact_465_Suc__mult__le__cancel1,axiom,
% 5.49/5.86 ! [K: nat,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.49/5.86 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_mult_le_cancel1
% 5.49/5.86 thf(fact_466_mult__Suc,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.49/5.86 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult_Suc
% 5.49/5.86 thf(fact_467_member__inv,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.49/5.86 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.86 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.86 & ( ( X = Mi )
% 5.49/5.86 | ( X = Ma )
% 5.49/5.86 | ( ( ord_less_nat @ X @ Ma )
% 5.49/5.86 & ( ord_less_nat @ Mi @ X )
% 5.49/5.86 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.86 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % member_inv
% 5.49/5.86 thf(fact_468_thisvalid,axiom,
% 5.49/5.86 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 5.49/5.86
% 5.49/5.86 % thisvalid
% 5.49/5.86 thf(fact_469__C5_Ohyps_C_I3_J,axiom,
% 5.49/5.86 ! [X: nat,Px: nat] :
% 5.49/5.86 ( ( ( vEBT_vebt_pred @ summary @ X )
% 5.49/5.86 = ( some_nat @ Px ) )
% 5.49/5.86 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ X @ Px ) ) ).
% 5.49/5.86
% 5.49/5.86 % "5.hyps"(3)
% 5.49/5.86 thf(fact_470_mi__ma__2__deg,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.49/5.86 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.49/5.86 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.49/5.86 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mi_ma_2_deg
% 5.49/5.86 thf(fact_471_times__divide__eq__left,axiom,
% 5.49/5.86 ! [B: complex,C: complex,A: complex] :
% 5.49/5.86 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.49/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_left
% 5.49/5.86 thf(fact_472_times__divide__eq__left,axiom,
% 5.49/5.86 ! [B: real,C: real,A: real] :
% 5.49/5.86 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.86 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_left
% 5.49/5.86 thf(fact_473_times__divide__eq__left,axiom,
% 5.49/5.86 ! [B: rat,C: rat,A: rat] :
% 5.49/5.86 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.86 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_left
% 5.49/5.86 thf(fact_474_divide__divide__eq__left,axiom,
% 5.49/5.86 ! [A: complex,B: complex,C: complex] :
% 5.49/5.86 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.49/5.86 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left
% 5.49/5.86 thf(fact_475_divide__divide__eq__left,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.49/5.86 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left
% 5.49/5.86 thf(fact_476_divide__divide__eq__left,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.49/5.86 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left
% 5.49/5.86 thf(fact_477_divide__divide__eq__right,axiom,
% 5.49/5.86 ! [A: complex,B: complex,C: complex] :
% 5.49/5.86 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_right
% 5.49/5.86 thf(fact_478_divide__divide__eq__right,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.86 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_right
% 5.49/5.86 thf(fact_479_divide__divide__eq__right,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.86 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_right
% 5.49/5.86 thf(fact_480_times__divide__eq__right,axiom,
% 5.49/5.86 ! [A: complex,B: complex,C: complex] :
% 5.49/5.86 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_right
% 5.49/5.86 thf(fact_481_times__divide__eq__right,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.86 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_right
% 5.49/5.86 thf(fact_482_times__divide__eq__right,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.86 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_eq_right
% 5.49/5.86 thf(fact_483_add__less__cancel__left,axiom,
% 5.49/5.86 ! [C: real,A: real,B: real] :
% 5.49/5.86 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.49/5.86 = ( ord_less_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_left
% 5.49/5.86 thf(fact_484_add__less__cancel__left,axiom,
% 5.49/5.86 ! [C: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.49/5.86 = ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_left
% 5.49/5.86 thf(fact_485_add__less__cancel__left,axiom,
% 5.49/5.86 ! [C: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.49/5.86 = ( ord_less_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_left
% 5.49/5.86 thf(fact_486_add__less__cancel__left,axiom,
% 5.49/5.86 ! [C: int,A: int,B: int] :
% 5.49/5.86 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.49/5.86 = ( ord_less_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_left
% 5.49/5.86 thf(fact_487_add__less__cancel__right,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.86 = ( ord_less_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_right
% 5.49/5.86 thf(fact_488_add__less__cancel__right,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.86 = ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_right
% 5.49/5.86 thf(fact_489_add__less__cancel__right,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.86 = ( ord_less_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_right
% 5.49/5.86 thf(fact_490_add__less__cancel__right,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.86 = ( ord_less_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_cancel_right
% 5.49/5.86 thf(fact_491_add__le__cancel__right,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.86 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_right
% 5.49/5.86 thf(fact_492_add__le__cancel__right,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.86 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_right
% 5.49/5.86 thf(fact_493_add__le__cancel__right,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.86 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_right
% 5.49/5.86 thf(fact_494_add__le__cancel__right,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.86 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_right
% 5.49/5.86 thf(fact_495_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.49/5.86 ( ! [X3: real] :
% 5.49/5.86 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_496_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 5.49/5.86 ( ! [X3: complex] :
% 5.49/5.86 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_497_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 5.49/5.86 ( ! [X3: product_prod_nat_nat] :
% 5.49/5.86 ( ( member8440522571783428010at_nat @ X3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_498_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_499_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.49/5.86 ( ! [X3: $o] :
% 5.49/5.86 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_500_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.49/5.86 ( ! [X3: nat] :
% 5.49/5.86 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_501_inthall,axiom,
% 5.49/5.86 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.49/5.86 ( ! [X3: int] :
% 5.49/5.86 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.49/5.86 => ( P @ X3 ) )
% 5.49/5.86 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.86 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % inthall
% 5.49/5.86 thf(fact_502_add__left__cancel,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ A @ B )
% 5.49/5.86 = ( plus_plus_real @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_cancel
% 5.49/5.86 thf(fact_503_add__left__cancel,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ A @ B )
% 5.49/5.86 = ( plus_plus_rat @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_cancel
% 5.49/5.86 thf(fact_504_add__left__cancel,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ( plus_plus_nat @ A @ B )
% 5.49/5.86 = ( plus_plus_nat @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_cancel
% 5.49/5.86 thf(fact_505_add__left__cancel,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ A @ B )
% 5.49/5.86 = ( plus_plus_int @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_cancel
% 5.49/5.86 thf(fact_506_add__right__cancel,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ B @ A )
% 5.49/5.86 = ( plus_plus_real @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_cancel
% 5.49/5.86 thf(fact_507_add__right__cancel,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ B @ A )
% 5.49/5.86 = ( plus_plus_rat @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_cancel
% 5.49/5.86 thf(fact_508_add__right__cancel,axiom,
% 5.49/5.86 ! [B: nat,A: nat,C: nat] :
% 5.49/5.86 ( ( ( plus_plus_nat @ B @ A )
% 5.49/5.86 = ( plus_plus_nat @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_cancel
% 5.49/5.86 thf(fact_509_add__right__cancel,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ B @ A )
% 5.49/5.86 = ( plus_plus_int @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_cancel
% 5.49/5.86 thf(fact_510_real__divide__square__eq,axiom,
% 5.49/5.86 ! [R2: real,A: real] :
% 5.49/5.86 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.49/5.86 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.49/5.86
% 5.49/5.86 % real_divide_square_eq
% 5.49/5.86 thf(fact_511__C5_Ohyps_C_I1_J,axiom,
% 5.49/5.86 ! [X5: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.49/5.86 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.49/5.86 & ! [Xa: nat,Xb: nat] :
% 5.49/5.86 ( ( ( vEBT_vebt_pred @ X5 @ Xa )
% 5.49/5.86 = ( some_nat @ Xb ) )
% 5.49/5.86 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ X5 ) @ Xa @ Xb ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % "5.hyps"(1)
% 5.49/5.86 thf(fact_512_mi__eq__ma__no__ch,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.49/5.86 => ( ( Mi = Ma )
% 5.49/5.86 => ( ! [X5: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.49/5.86 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mi_eq_ma_no_ch
% 5.49/5.86 thf(fact_513_add__le__cancel__left,axiom,
% 5.49/5.86 ! [C: real,A: real,B: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.49/5.86 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_left
% 5.49/5.86 thf(fact_514_add__le__cancel__left,axiom,
% 5.49/5.86 ! [C: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.49/5.86 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_left
% 5.49/5.86 thf(fact_515_add__le__cancel__left,axiom,
% 5.49/5.86 ! [C: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.49/5.86 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_left
% 5.49/5.86 thf(fact_516_add__le__cancel__left,axiom,
% 5.49/5.86 ! [C: int,A: int,B: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.49/5.86 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_cancel_left
% 5.49/5.86 thf(fact_517_insert__simp__mima,axiom,
% 5.49/5.86 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( ( X = Mi )
% 5.49/5.86 | ( X = Ma ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.86 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % insert_simp_mima
% 5.49/5.86 thf(fact_518_pred__max,axiom,
% 5.49/5.86 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.86 => ( ( ord_less_nat @ Ma @ X )
% 5.49/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.86 = ( some_nat @ Ma ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % pred_max
% 5.49/5.86 thf(fact_519_pred__list__to__short,axiom,
% 5.49/5.86 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.86 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.49/5.86 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.86 = none_nat ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % pred_list_to_short
% 5.49/5.86 thf(fact_520_less__eq__real__def,axiom,
% 5.49/5.86 ( ord_less_eq_real
% 5.49/5.86 = ( ^ [X2: real,Y: real] :
% 5.49/5.86 ( ( ord_less_real @ X2 @ Y )
% 5.49/5.86 | ( X2 = Y ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_eq_real_def
% 5.49/5.86 thf(fact_521_complete__real,axiom,
% 5.49/5.86 ! [S3: set_real] :
% 5.49/5.86 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 5.49/5.86 => ( ? [Z4: real] :
% 5.49/5.86 ! [X3: real] :
% 5.49/5.86 ( ( member_real @ X3 @ S3 )
% 5.49/5.86 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 5.49/5.86 => ? [Y3: real] :
% 5.49/5.86 ( ! [X5: real] :
% 5.49/5.86 ( ( member_real @ X5 @ S3 )
% 5.49/5.86 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 5.49/5.86 & ! [Z4: real] :
% 5.49/5.86 ( ! [X3: real] :
% 5.49/5.86 ( ( member_real @ X3 @ S3 )
% 5.49/5.86 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 5.49/5.86 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % complete_real
% 5.49/5.86 thf(fact_522_vebt__pred_Osimps_I4_J,axiom,
% 5.49/5.86 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.49/5.86 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.49/5.86 = none_nat ) ).
% 5.49/5.86
% 5.49/5.86 % vebt_pred.simps(4)
% 5.49/5.86 thf(fact_523_linordered__field__no__ub,axiom,
% 5.49/5.86 ! [X5: real] :
% 5.49/5.86 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.49/5.86
% 5.49/5.86 % linordered_field_no_ub
% 5.49/5.86 thf(fact_524_linordered__field__no__ub,axiom,
% 5.49/5.86 ! [X5: rat] :
% 5.49/5.86 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.49/5.86
% 5.49/5.86 % linordered_field_no_ub
% 5.49/5.86 thf(fact_525_linordered__field__no__lb,axiom,
% 5.49/5.86 ! [X5: real] :
% 5.49/5.86 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 5.49/5.86
% 5.49/5.86 % linordered_field_no_lb
% 5.49/5.86 thf(fact_526_linordered__field__no__lb,axiom,
% 5.49/5.86 ! [X5: rat] :
% 5.49/5.86 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 5.49/5.86
% 5.49/5.86 % linordered_field_no_lb
% 5.49/5.86 thf(fact_527_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_mult_class.mult_ac(1)
% 5.49/5.86 thf(fact_528_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_mult_class.mult_ac(1)
% 5.49/5.86 thf(fact_529_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_mult_class.mult_ac(1)
% 5.49/5.86 thf(fact_530_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_mult_class.mult_ac(1)
% 5.49/5.86 thf(fact_531_mult_Oassoc,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.assoc
% 5.49/5.86 thf(fact_532_mult_Oassoc,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.assoc
% 5.49/5.86 thf(fact_533_mult_Oassoc,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.assoc
% 5.49/5.86 thf(fact_534_mult_Oassoc,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.49/5.86 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.assoc
% 5.49/5.86 thf(fact_535_mult_Ocommute,axiom,
% 5.49/5.86 ( times_times_real
% 5.49/5.86 = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.commute
% 5.49/5.86 thf(fact_536_mult_Ocommute,axiom,
% 5.49/5.86 ( times_times_rat
% 5.49/5.86 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.commute
% 5.49/5.86 thf(fact_537_mult_Ocommute,axiom,
% 5.49/5.86 ( times_times_nat
% 5.49/5.86 = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.commute
% 5.49/5.86 thf(fact_538_mult_Ocommute,axiom,
% 5.49/5.86 ( times_times_int
% 5.49/5.86 = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.commute
% 5.49/5.86 thf(fact_539_mult_Oleft__commute,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.49/5.86 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.left_commute
% 5.49/5.86 thf(fact_540_mult_Oleft__commute,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.49/5.86 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.left_commute
% 5.49/5.86 thf(fact_541_mult_Oleft__commute,axiom,
% 5.49/5.86 ! [B: nat,A: nat,C: nat] :
% 5.49/5.86 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.49/5.86 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.left_commute
% 5.49/5.86 thf(fact_542_mult_Oleft__commute,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.49/5.86 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mult.left_commute
% 5.49/5.86 thf(fact_543_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_add_class.add_ac(1)
% 5.49/5.86 thf(fact_544_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_add_class.add_ac(1)
% 5.49/5.86 thf(fact_545_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_add_class.add_ac(1)
% 5.49/5.86 thf(fact_546_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % ab_semigroup_add_class.add_ac(1)
% 5.49/5.86 thf(fact_547_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ( plus_plus_real @ I2 @ K )
% 5.49/5.86 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(4)
% 5.49/5.86 thf(fact_548_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ( plus_plus_rat @ I2 @ K )
% 5.49/5.86 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(4)
% 5.49/5.86 thf(fact_549_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ( plus_plus_nat @ I2 @ K )
% 5.49/5.86 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(4)
% 5.49/5.86 thf(fact_550_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ( plus_plus_int @ I2 @ K )
% 5.49/5.86 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(4)
% 5.49/5.86 thf(fact_551_group__cancel_Oadd1,axiom,
% 5.49/5.86 ! [A2: real,K: real,A: real,B: real] :
% 5.49/5.86 ( ( A2
% 5.49/5.86 = ( plus_plus_real @ K @ A ) )
% 5.49/5.86 => ( ( plus_plus_real @ A2 @ B )
% 5.49/5.86 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add1
% 5.49/5.86 thf(fact_552_group__cancel_Oadd1,axiom,
% 5.49/5.86 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( A2
% 5.49/5.86 = ( plus_plus_rat @ K @ A ) )
% 5.49/5.86 => ( ( plus_plus_rat @ A2 @ B )
% 5.49/5.86 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add1
% 5.49/5.86 thf(fact_553_group__cancel_Oadd1,axiom,
% 5.49/5.86 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( A2
% 5.49/5.86 = ( plus_plus_nat @ K @ A ) )
% 5.49/5.86 => ( ( plus_plus_nat @ A2 @ B )
% 5.49/5.86 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add1
% 5.49/5.86 thf(fact_554_group__cancel_Oadd1,axiom,
% 5.49/5.86 ! [A2: int,K: int,A: int,B: int] :
% 5.49/5.86 ( ( A2
% 5.49/5.86 = ( plus_plus_int @ K @ A ) )
% 5.49/5.86 => ( ( plus_plus_int @ A2 @ B )
% 5.49/5.86 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add1
% 5.49/5.86 thf(fact_555_group__cancel_Oadd2,axiom,
% 5.49/5.86 ! [B4: real,K: real,B: real,A: real] :
% 5.49/5.86 ( ( B4
% 5.49/5.86 = ( plus_plus_real @ K @ B ) )
% 5.49/5.86 => ( ( plus_plus_real @ A @ B4 )
% 5.49/5.86 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add2
% 5.49/5.86 thf(fact_556_group__cancel_Oadd2,axiom,
% 5.49/5.86 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.49/5.86 ( ( B4
% 5.49/5.86 = ( plus_plus_rat @ K @ B ) )
% 5.49/5.86 => ( ( plus_plus_rat @ A @ B4 )
% 5.49/5.86 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add2
% 5.49/5.86 thf(fact_557_group__cancel_Oadd2,axiom,
% 5.49/5.86 ! [B4: nat,K: nat,B: nat,A: nat] :
% 5.49/5.86 ( ( B4
% 5.49/5.86 = ( plus_plus_nat @ K @ B ) )
% 5.49/5.86 => ( ( plus_plus_nat @ A @ B4 )
% 5.49/5.86 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add2
% 5.49/5.86 thf(fact_558_group__cancel_Oadd2,axiom,
% 5.49/5.86 ! [B4: int,K: int,B: int,A: int] :
% 5.49/5.86 ( ( B4
% 5.49/5.86 = ( plus_plus_int @ K @ B ) )
% 5.49/5.86 => ( ( plus_plus_int @ A @ B4 )
% 5.49/5.86 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % group_cancel.add2
% 5.49/5.86 thf(fact_559_add_Oassoc,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.assoc
% 5.49/5.86 thf(fact_560_add_Oassoc,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.assoc
% 5.49/5.86 thf(fact_561_add_Oassoc,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.assoc
% 5.49/5.86 thf(fact_562_add_Oassoc,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.assoc
% 5.49/5.86 thf(fact_563_add_Oleft__cancel,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ A @ B )
% 5.49/5.86 = ( plus_plus_real @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_cancel
% 5.49/5.86 thf(fact_564_add_Oleft__cancel,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ A @ B )
% 5.49/5.86 = ( plus_plus_rat @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_cancel
% 5.49/5.86 thf(fact_565_add_Oleft__cancel,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ A @ B )
% 5.49/5.86 = ( plus_plus_int @ A @ C ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_cancel
% 5.49/5.86 thf(fact_566_add_Oright__cancel,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ B @ A )
% 5.49/5.86 = ( plus_plus_real @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.right_cancel
% 5.49/5.86 thf(fact_567_add_Oright__cancel,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ B @ A )
% 5.49/5.86 = ( plus_plus_rat @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.right_cancel
% 5.49/5.86 thf(fact_568_add_Oright__cancel,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ B @ A )
% 5.49/5.86 = ( plus_plus_int @ C @ A ) )
% 5.49/5.86 = ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.right_cancel
% 5.49/5.86 thf(fact_569_add_Ocommute,axiom,
% 5.49/5.86 ( plus_plus_real
% 5.49/5.86 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.commute
% 5.49/5.86 thf(fact_570_add_Ocommute,axiom,
% 5.49/5.86 ( plus_plus_rat
% 5.49/5.86 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.commute
% 5.49/5.86 thf(fact_571_add_Ocommute,axiom,
% 5.49/5.86 ( plus_plus_nat
% 5.49/5.86 = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.commute
% 5.49/5.86 thf(fact_572_add_Ocommute,axiom,
% 5.49/5.86 ( plus_plus_int
% 5.49/5.86 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.commute
% 5.49/5.86 thf(fact_573_add_Oleft__commute,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.49/5.86 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_commute
% 5.49/5.86 thf(fact_574_add_Oleft__commute,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.49/5.86 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_commute
% 5.49/5.86 thf(fact_575_add_Oleft__commute,axiom,
% 5.49/5.86 ! [B: nat,A: nat,C: nat] :
% 5.49/5.86 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.49/5.86 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_commute
% 5.49/5.86 thf(fact_576_add_Oleft__commute,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.49/5.86 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add.left_commute
% 5.49/5.86 thf(fact_577_add__left__imp__eq,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ A @ B )
% 5.49/5.86 = ( plus_plus_real @ A @ C ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_imp_eq
% 5.49/5.86 thf(fact_578_add__left__imp__eq,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ A @ B )
% 5.49/5.86 = ( plus_plus_rat @ A @ C ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_imp_eq
% 5.49/5.86 thf(fact_579_add__left__imp__eq,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ( plus_plus_nat @ A @ B )
% 5.49/5.86 = ( plus_plus_nat @ A @ C ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_imp_eq
% 5.49/5.86 thf(fact_580_add__left__imp__eq,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ A @ B )
% 5.49/5.86 = ( plus_plus_int @ A @ C ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_imp_eq
% 5.49/5.86 thf(fact_581_add__right__imp__eq,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( ( plus_plus_real @ B @ A )
% 5.49/5.86 = ( plus_plus_real @ C @ A ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_imp_eq
% 5.49/5.86 thf(fact_582_add__right__imp__eq,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( ( plus_plus_rat @ B @ A )
% 5.49/5.86 = ( plus_plus_rat @ C @ A ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_imp_eq
% 5.49/5.86 thf(fact_583_add__right__imp__eq,axiom,
% 5.49/5.86 ! [B: nat,A: nat,C: nat] :
% 5.49/5.86 ( ( ( plus_plus_nat @ B @ A )
% 5.49/5.86 = ( plus_plus_nat @ C @ A ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_imp_eq
% 5.49/5.86 thf(fact_584_add__right__imp__eq,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( ( plus_plus_int @ B @ A )
% 5.49/5.86 = ( plus_plus_int @ C @ A ) )
% 5.49/5.86 => ( B = C ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_imp_eq
% 5.49/5.86 thf(fact_585_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(3)
% 5.49/5.86 thf(fact_586_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(3)
% 5.49/5.86 thf(fact_587_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(3)
% 5.49/5.86 thf(fact_588_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(3)
% 5.49/5.86 thf(fact_589_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_eq_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(2)
% 5.49/5.86 thf(fact_590_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(2)
% 5.49/5.86 thf(fact_591_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(2)
% 5.49/5.86 thf(fact_592_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_eq_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(2)
% 5.49/5.86 thf(fact_593_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(1)
% 5.49/5.86 thf(fact_594_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(1)
% 5.49/5.86 thf(fact_595_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(1)
% 5.49/5.86 thf(fact_596_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_semiring(1)
% 5.49/5.86 thf(fact_597_add__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_real @ C @ D )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono
% 5.49/5.86 thf(fact_598_add__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_rat @ C @ D )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono
% 5.49/5.86 thf(fact_599_add__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_nat @ C @ D )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono
% 5.49/5.86 thf(fact_600_add__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_int @ C @ D )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono
% 5.49/5.86 thf(fact_601_add__left__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_mono
% 5.49/5.86 thf(fact_602_add__left__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_mono
% 5.49/5.86 thf(fact_603_add__left__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_mono
% 5.49/5.86 thf(fact_604_add__left__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_left_mono
% 5.49/5.86 thf(fact_605_less__eqE,axiom,
% 5.49/5.86 ! [A: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.86 => ~ ! [C2: nat] :
% 5.49/5.86 ( B
% 5.49/5.86 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % less_eqE
% 5.49/5.86 thf(fact_606_add__right__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_mono
% 5.49/5.86 thf(fact_607_add__right__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_mono
% 5.49/5.86 thf(fact_608_add__right__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.86 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_mono
% 5.49/5.86 thf(fact_609_add__right__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_right_mono
% 5.49/5.86 thf(fact_610_le__iff__add,axiom,
% 5.49/5.86 ( ord_less_eq_nat
% 5.49/5.86 = ( ^ [A4: nat,B3: nat] :
% 5.49/5.86 ? [C3: nat] :
% 5.49/5.86 ( B3
% 5.49/5.86 = ( plus_plus_nat @ A4 @ C3 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % le_iff_add
% 5.49/5.86 thf(fact_611_add__le__imp__le__left,axiom,
% 5.49/5.86 ! [C: real,A: real,B: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.49/5.86 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_left
% 5.49/5.86 thf(fact_612_add__le__imp__le__left,axiom,
% 5.49/5.86 ! [C: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.49/5.86 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_left
% 5.49/5.86 thf(fact_613_add__le__imp__le__left,axiom,
% 5.49/5.86 ! [C: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.49/5.86 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_left
% 5.49/5.86 thf(fact_614_add__le__imp__le__left,axiom,
% 5.49/5.86 ! [C: int,A: int,B: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.49/5.86 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_left
% 5.49/5.86 thf(fact_615_add__le__imp__le__right,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.86 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_right
% 5.49/5.86 thf(fact_616_add__le__imp__le__right,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.86 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_right
% 5.49/5.86 thf(fact_617_add__le__imp__le__right,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.86 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_right
% 5.49/5.86 thf(fact_618_add__le__imp__le__right,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.86 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_imp_le_right
% 5.49/5.86 thf(fact_619_add__less__imp__less__right,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.86 => ( ord_less_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_right
% 5.49/5.86 thf(fact_620_add__less__imp__less__right,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.86 => ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_right
% 5.49/5.86 thf(fact_621_add__less__imp__less__right,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.86 => ( ord_less_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_right
% 5.49/5.86 thf(fact_622_add__less__imp__less__right,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.86 => ( ord_less_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_right
% 5.49/5.86 thf(fact_623_add__less__imp__less__left,axiom,
% 5.49/5.86 ! [C: real,A: real,B: real] :
% 5.49/5.86 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.49/5.86 => ( ord_less_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_left
% 5.49/5.86 thf(fact_624_add__less__imp__less__left,axiom,
% 5.49/5.86 ! [C: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.49/5.86 => ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_left
% 5.49/5.86 thf(fact_625_add__less__imp__less__left,axiom,
% 5.49/5.86 ! [C: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.49/5.86 => ( ord_less_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_left
% 5.49/5.86 thf(fact_626_add__less__imp__less__left,axiom,
% 5.49/5.86 ! [C: int,A: int,B: int] :
% 5.49/5.86 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.49/5.86 => ( ord_less_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_imp_less_left
% 5.49/5.86 thf(fact_627_add__strict__right__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ord_less_real @ A @ B )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_right_mono
% 5.49/5.86 thf(fact_628_add__strict__right__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_rat @ A @ B )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_right_mono
% 5.49/5.86 thf(fact_629_add__strict__right__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ord_less_nat @ A @ B )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_right_mono
% 5.49/5.86 thf(fact_630_add__strict__right__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ord_less_int @ A @ B )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_right_mono
% 5.49/5.86 thf(fact_631_add__strict__left__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ord_less_real @ A @ B )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_left_mono
% 5.49/5.86 thf(fact_632_add__strict__left__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_rat @ A @ B )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_left_mono
% 5.49/5.86 thf(fact_633_add__strict__left__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat] :
% 5.49/5.86 ( ( ord_less_nat @ A @ B )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_left_mono
% 5.49/5.86 thf(fact_634_add__strict__left__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ord_less_int @ A @ B )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_left_mono
% 5.49/5.86 thf(fact_635_add__strict__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ord_less_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_real @ C @ D )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_mono
% 5.49/5.86 thf(fact_636_add__strict__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ord_less_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_rat @ C @ D )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_mono
% 5.49/5.86 thf(fact_637_add__strict__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.86 ( ( ord_less_nat @ A @ B )
% 5.49/5.86 => ( ( ord_less_nat @ C @ D )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_mono
% 5.49/5.86 thf(fact_638_add__strict__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ord_less_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_int @ C @ D )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_strict_mono
% 5.49/5.86 thf(fact_639_add__mono__thms__linordered__field_I1_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_real @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(1)
% 5.49/5.86 thf(fact_640_add__mono__thms__linordered__field_I1_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_rat @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(1)
% 5.49/5.86 thf(fact_641_add__mono__thms__linordered__field_I1_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_nat @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(1)
% 5.49/5.86 thf(fact_642_add__mono__thms__linordered__field_I1_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_int @ I2 @ J )
% 5.49/5.86 & ( K = L2 ) )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(1)
% 5.49/5.86 thf(fact_643_add__mono__thms__linordered__field_I2_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(2)
% 5.49/5.86 thf(fact_644_add__mono__thms__linordered__field_I2_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(2)
% 5.49/5.86 thf(fact_645_add__mono__thms__linordered__field_I2_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(2)
% 5.49/5.86 thf(fact_646_add__mono__thms__linordered__field_I2_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( I2 = J )
% 5.49/5.86 & ( ord_less_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(2)
% 5.49/5.86 thf(fact_647_add__mono__thms__linordered__field_I5_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_real @ I2 @ J )
% 5.49/5.86 & ( ord_less_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(5)
% 5.49/5.86 thf(fact_648_add__mono__thms__linordered__field_I5_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_rat @ I2 @ J )
% 5.49/5.86 & ( ord_less_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(5)
% 5.49/5.86 thf(fact_649_add__mono__thms__linordered__field_I5_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_nat @ I2 @ J )
% 5.49/5.86 & ( ord_less_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(5)
% 5.49/5.86 thf(fact_650_add__mono__thms__linordered__field_I5_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_int @ I2 @ J )
% 5.49/5.86 & ( ord_less_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(5)
% 5.49/5.86 thf(fact_651_divide__divide__eq__left_H,axiom,
% 5.49/5.86 ! [A: complex,B: complex,C: complex] :
% 5.49/5.86 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.49/5.86 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left'
% 5.49/5.86 thf(fact_652_divide__divide__eq__left_H,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.49/5.86 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left'
% 5.49/5.86 thf(fact_653_divide__divide__eq__left_H,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.49/5.86 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_eq_left'
% 5.49/5.86 thf(fact_654_divide__divide__times__eq,axiom,
% 5.49/5.86 ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 5.49/5.86 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.49/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y2 @ Z ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_times_eq
% 5.49/5.86 thf(fact_655_divide__divide__times__eq,axiom,
% 5.49/5.86 ! [X: real,Y2: real,Z: real,W: real] :
% 5.49/5.86 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.49/5.86 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y2 @ Z ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_times_eq
% 5.49/5.86 thf(fact_656_divide__divide__times__eq,axiom,
% 5.49/5.86 ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 5.49/5.86 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.49/5.86 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y2 @ Z ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % divide_divide_times_eq
% 5.49/5.86 thf(fact_657_times__divide__times__eq,axiom,
% 5.49/5.86 ! [X: complex,Y2: complex,Z: complex,W: complex] :
% 5.49/5.86 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.49/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y2 @ W ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_times_eq
% 5.49/5.86 thf(fact_658_times__divide__times__eq,axiom,
% 5.49/5.86 ! [X: real,Y2: real,Z: real,W: real] :
% 5.49/5.86 ( ( times_times_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ Z @ W ) )
% 5.49/5.86 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ W ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_times_eq
% 5.49/5.86 thf(fact_659_times__divide__times__eq,axiom,
% 5.49/5.86 ! [X: rat,Y2: rat,Z: rat,W: rat] :
% 5.49/5.86 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.49/5.86 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ W ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % times_divide_times_eq
% 5.49/5.86 thf(fact_660_add__divide__distrib,axiom,
% 5.49/5.86 ! [A: complex,B: complex,C: complex] :
% 5.49/5.86 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_divide_distrib
% 5.49/5.86 thf(fact_661_add__divide__distrib,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_divide_distrib
% 5.49/5.86 thf(fact_662_add__divide__distrib,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.86 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_divide_distrib
% 5.49/5.86 thf(fact_663_add__less__le__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ord_less_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_real @ C @ D )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_le_mono
% 5.49/5.86 thf(fact_664_add__less__le__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ord_less_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_rat @ C @ D )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_le_mono
% 5.49/5.86 thf(fact_665_add__less__le__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.86 ( ( ord_less_nat @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_nat @ C @ D )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_le_mono
% 5.49/5.86 thf(fact_666_add__less__le__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ord_less_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_int @ C @ D )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_less_le_mono
% 5.49/5.86 thf(fact_667_add__le__less__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_real @ C @ D )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_less_mono
% 5.49/5.86 thf(fact_668_add__le__less__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_rat @ C @ D )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_less_mono
% 5.49/5.86 thf(fact_669_add__le__less__mono,axiom,
% 5.49/5.86 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.86 => ( ( ord_less_nat @ C @ D )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_less_mono
% 5.49/5.86 thf(fact_670_add__le__less__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_int @ C @ D )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_le_less_mono
% 5.49/5.86 thf(fact_671_add__mono__thms__linordered__field_I3_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_real @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(3)
% 5.49/5.86 thf(fact_672_add__mono__thms__linordered__field_I3_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_rat @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(3)
% 5.49/5.86 thf(fact_673_add__mono__thms__linordered__field_I3_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_nat @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(3)
% 5.49/5.86 thf(fact_674_add__mono__thms__linordered__field_I3_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_int @ I2 @ J )
% 5.49/5.86 & ( ord_less_eq_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(3)
% 5.49/5.86 thf(fact_675_add__mono__thms__linordered__field_I4_J,axiom,
% 5.49/5.86 ! [I2: real,J: real,K: real,L2: real] :
% 5.49/5.86 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.49/5.86 & ( ord_less_real @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(4)
% 5.49/5.86 thf(fact_676_add__mono__thms__linordered__field_I4_J,axiom,
% 5.49/5.86 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.49/5.86 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.49/5.86 & ( ord_less_rat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(4)
% 5.49/5.86 thf(fact_677_add__mono__thms__linordered__field_I4_J,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.49/5.86 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.86 & ( ord_less_nat @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(4)
% 5.49/5.86 thf(fact_678_add__mono__thms__linordered__field_I4_J,axiom,
% 5.49/5.86 ! [I2: int,J: int,K: int,L2: int] :
% 5.49/5.86 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.86 & ( ord_less_int @ K @ L2 ) )
% 5.49/5.86 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_mono_thms_linordered_field(4)
% 5.49/5.86 thf(fact_679__C2_C,axiom,
% 5.49/5.86 ( ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.86 = none_nat )
% 5.49/5.86 => ( ( ( ord_less_nat @ mi @ xa )
% 5.49/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.49/5.86 = ( some_nat @ mi ) ) )
% 5.49/5.86 & ( ~ ( ord_less_nat @ mi @ xa )
% 5.49/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.49/5.86 = none_nat ) ) ) )
% 5.49/5.86 & ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.86 != none_nat )
% 5.49/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.49/5.86 = ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % "2"
% 5.49/5.86 thf(fact_680_invar__vebt_Ointros_I5_J,axiom,
% 5.49/5.86 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.49/5.86 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.49/5.86 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.49/5.86 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( M
% 5.49/5.86 = ( suc @ N ) )
% 5.49/5.86 => ( ( Deg
% 5.49/5.86 = ( plus_plus_nat @ N @ M ) )
% 5.49/5.86 => ( ! [I4: nat] :
% 5.49/5.86 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X6 ) )
% 5.49/5.86 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.49/5.86 => ( ( ( Mi = Ma )
% 5.49/5.86 => ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.49/5.86 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.49/5.86 => ( ( ( Mi != Ma )
% 5.49/5.86 => ! [I4: nat] :
% 5.49/5.86 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.49/5.86 = I4 )
% 5.49/5.86 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.49/5.86 & ! [X3: nat] :
% 5.49/5.86 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.49/5.86 = I4 )
% 5.49/5.86 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ Mi @ X3 )
% 5.49/5.86 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % invar_vebt.intros(5)
% 5.49/5.86 thf(fact_681_invar__vebt_Ointros_I4_J,axiom,
% 5.49/5.86 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.49/5.86 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.49/5.86 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.49/5.86 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( M = N )
% 5.49/5.86 => ( ( Deg
% 5.49/5.86 = ( plus_plus_nat @ N @ M ) )
% 5.49/5.86 => ( ! [I4: nat] :
% 5.49/5.86 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X6 ) )
% 5.49/5.86 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.49/5.86 => ( ( ( Mi = Ma )
% 5.49/5.86 => ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.49/5.86 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.49/5.86 => ( ( ( Mi != Ma )
% 5.49/5.86 => ! [I4: nat] :
% 5.49/5.86 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.49/5.86 = I4 )
% 5.49/5.86 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.49/5.86 & ! [X3: nat] :
% 5.49/5.86 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.49/5.86 = I4 )
% 5.49/5.86 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.49/5.86 => ( ( ord_less_nat @ Mi @ X3 )
% 5.49/5.86 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % invar_vebt.intros(4)
% 5.49/5.86 thf(fact_682_nested__mint,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.49/5.86 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.49/5.86 => ( ( N
% 5.49/5.86 = ( suc @ ( suc @ Va ) ) )
% 5.49/5.86 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.49/5.86 => ( ( Ma != Mi )
% 5.49/5.86 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % nested_mint
% 5.49/5.86 thf(fact_683_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.49/5.86 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.86 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.49/5.86 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.49/5.86 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % both_member_options_from_chilf_to_complete_tree
% 5.49/5.86 thf(fact_684_invar__vebt_Ointros_I3_J,axiom,
% 5.49/5.86 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.49/5.86 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.49/5.86 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.49/5.86 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( M
% 5.49/5.86 = ( suc @ N ) )
% 5.49/5.86 => ( ( Deg
% 5.49/5.86 = ( plus_plus_nat @ N @ M ) )
% 5.49/5.86 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.49/5.86 => ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % invar_vebt.intros(3)
% 5.49/5.86 thf(fact_685_both__member__options__from__complete__tree__to__child,axiom,
% 5.49/5.86 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.49/5.86 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.86 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 5.49/5.86 | ( X = Mi )
% 5.49/5.86 | ( X = Ma ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % both_member_options_from_complete_tree_to_child
% 5.49/5.86 thf(fact_686_invar__vebt_Ointros_I2_J,axiom,
% 5.49/5.86 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.49/5.86 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.49/5.86 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.49/5.86 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ( M = N )
% 5.49/5.86 => ( ( Deg
% 5.49/5.86 = ( plus_plus_nat @ N @ M ) )
% 5.49/5.86 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.49/5.86 => ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % invar_vebt.intros(2)
% 5.49/5.86 thf(fact_687_mintlistlength,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.49/5.86 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.49/5.86 => ( ( Mi != Ma )
% 5.49/5.86 => ( ( ord_less_nat @ Mi @ Ma )
% 5.49/5.86 & ? [M5: nat] :
% 5.49/5.86 ( ( ( some_nat @ M5 )
% 5.49/5.86 = ( vEBT_vebt_mint @ Summary ) )
% 5.49/5.86 & ( ord_less_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % mintlistlength
% 5.49/5.86 thf(fact_688_summaxma,axiom,
% 5.49/5.86 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.86 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.49/5.86 => ( ( Mi != Ma )
% 5.49/5.86 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.49/5.86 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % summaxma
% 5.49/5.86 thf(fact_689_set__n__deg__not__0,axiom,
% 5.49/5.86 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 5.49/5.86 ( ! [X3: vEBT_VEBT] :
% 5.49/5.86 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.49/5.86 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.49/5.86 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.49/5.86 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.86 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % set_n_deg_not_0
% 5.49/5.86 thf(fact_690__092_060open_0621_A_092_060le_062_An_092_060close_062,axiom,
% 5.49/5.86 ord_less_eq_nat @ one_one_nat @ na ).
% 5.49/5.86
% 5.49/5.86 % \<open>1 \<le> n\<close>
% 5.49/5.86 thf(fact_691_VEBT_Oinject_I1_J,axiom,
% 5.49/5.86 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.49/5.86 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.49/5.86 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.49/5.86 = ( ( X11 = Y11 )
% 5.49/5.86 & ( X12 = Y12 )
% 5.49/5.86 & ( X13 = Y13 )
% 5.49/5.86 & ( X14 = Y14 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % VEBT.inject(1)
% 5.49/5.86 thf(fact_692_power__minus__is__div,axiom,
% 5.49/5.86 ! [B: nat,A: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.86 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.49/5.86 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_minus_is_div
% 5.49/5.86 thf(fact_693_mult__1,axiom,
% 5.49/5.86 ! [A: complex] :
% 5.49/5.86 ( ( times_times_complex @ one_one_complex @ A )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult_1
% 5.49/5.86 thf(fact_694_mult__1,axiom,
% 5.49/5.86 ! [A: real] :
% 5.49/5.86 ( ( times_times_real @ one_one_real @ A )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult_1
% 5.49/5.86 thf(fact_695_mult__1,axiom,
% 5.49/5.86 ! [A: rat] :
% 5.49/5.86 ( ( times_times_rat @ one_one_rat @ A )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult_1
% 5.49/5.86 thf(fact_696_mult__1,axiom,
% 5.49/5.86 ! [A: nat] :
% 5.49/5.86 ( ( times_times_nat @ one_one_nat @ A )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult_1
% 5.49/5.86 thf(fact_697_mult__1,axiom,
% 5.49/5.86 ! [A: int] :
% 5.49/5.86 ( ( times_times_int @ one_one_int @ A )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult_1
% 5.49/5.86 thf(fact_698_mult_Oright__neutral,axiom,
% 5.49/5.86 ! [A: complex] :
% 5.49/5.86 ( ( times_times_complex @ A @ one_one_complex )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult.right_neutral
% 5.49/5.86 thf(fact_699_mult_Oright__neutral,axiom,
% 5.49/5.86 ! [A: real] :
% 5.49/5.86 ( ( times_times_real @ A @ one_one_real )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult.right_neutral
% 5.49/5.86 thf(fact_700_mult_Oright__neutral,axiom,
% 5.49/5.86 ! [A: rat] :
% 5.49/5.86 ( ( times_times_rat @ A @ one_one_rat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult.right_neutral
% 5.49/5.86 thf(fact_701_mult_Oright__neutral,axiom,
% 5.49/5.86 ! [A: nat] :
% 5.49/5.86 ( ( times_times_nat @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult.right_neutral
% 5.49/5.86 thf(fact_702_mult_Oright__neutral,axiom,
% 5.49/5.86 ! [A: int] :
% 5.49/5.86 ( ( times_times_int @ A @ one_one_int )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % mult.right_neutral
% 5.49/5.86 thf(fact_703_add__diff__cancel__right_H,axiom,
% 5.49/5.86 ! [A: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right'
% 5.49/5.86 thf(fact_704_add__diff__cancel__right_H,axiom,
% 5.49/5.86 ! [A: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right'
% 5.49/5.86 thf(fact_705_add__diff__cancel__right_H,axiom,
% 5.49/5.86 ! [A: nat,B: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right'
% 5.49/5.86 thf(fact_706_add__diff__cancel__right_H,axiom,
% 5.49/5.86 ! [A: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right'
% 5.49/5.86 thf(fact_707_add__diff__cancel__right,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.49/5.86 = ( minus_minus_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right
% 5.49/5.86 thf(fact_708_add__diff__cancel__right,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.86 = ( minus_minus_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right
% 5.49/5.86 thf(fact_709_add__diff__cancel__right,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.86 = ( minus_minus_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right
% 5.49/5.86 thf(fact_710_add__diff__cancel__right,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.49/5.86 = ( minus_minus_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_right
% 5.49/5.86 thf(fact_711_add__diff__cancel__left_H,axiom,
% 5.49/5.86 ! [A: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.49/5.86 = B ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left'
% 5.49/5.86 thf(fact_712_add__diff__cancel__left_H,axiom,
% 5.49/5.86 ! [A: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.49/5.86 = B ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left'
% 5.49/5.86 thf(fact_713_add__diff__cancel__left_H,axiom,
% 5.49/5.86 ! [A: nat,B: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.49/5.86 = B ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left'
% 5.49/5.86 thf(fact_714_add__diff__cancel__left_H,axiom,
% 5.49/5.86 ! [A: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.49/5.86 = B ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left'
% 5.49/5.86 thf(fact_715_add__diff__cancel__left,axiom,
% 5.49/5.86 ! [C: real,A: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.49/5.86 = ( minus_minus_real @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left
% 5.49/5.86 thf(fact_716_add__diff__cancel__left,axiom,
% 5.49/5.86 ! [C: rat,A: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.49/5.86 = ( minus_minus_rat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left
% 5.49/5.86 thf(fact_717_add__diff__cancel__left,axiom,
% 5.49/5.86 ! [C: nat,A: nat,B: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.49/5.86 = ( minus_minus_nat @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left
% 5.49/5.86 thf(fact_718_add__diff__cancel__left,axiom,
% 5.49/5.86 ! [C: int,A: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.49/5.86 = ( minus_minus_int @ A @ B ) ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel_left
% 5.49/5.86 thf(fact_719_diff__add__cancel,axiom,
% 5.49/5.86 ! [A: real,B: real] :
% 5.49/5.86 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % diff_add_cancel
% 5.49/5.86 thf(fact_720_diff__add__cancel,axiom,
% 5.49/5.86 ! [A: rat,B: rat] :
% 5.49/5.86 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % diff_add_cancel
% 5.49/5.86 thf(fact_721_diff__add__cancel,axiom,
% 5.49/5.86 ! [A: int,B: int] :
% 5.49/5.86 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % diff_add_cancel
% 5.49/5.86 thf(fact_722_add__diff__cancel,axiom,
% 5.49/5.86 ! [A: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel
% 5.49/5.86 thf(fact_723_add__diff__cancel,axiom,
% 5.49/5.86 ! [A: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel
% 5.49/5.86 thf(fact_724_add__diff__cancel,axiom,
% 5.49/5.86 ! [A: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % add_diff_cancel
% 5.49/5.86 thf(fact_725_bits__div__by__1,axiom,
% 5.49/5.86 ! [A: nat] :
% 5.49/5.86 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % bits_div_by_1
% 5.49/5.86 thf(fact_726_bits__div__by__1,axiom,
% 5.49/5.86 ! [A: int] :
% 5.49/5.86 ( ( divide_divide_int @ A @ one_one_int )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % bits_div_by_1
% 5.49/5.86 thf(fact_727_power__one,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( power_power_rat @ one_one_rat @ N )
% 5.49/5.86 = one_one_rat ) ).
% 5.49/5.86
% 5.49/5.86 % power_one
% 5.49/5.86 thf(fact_728_power__one,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( power_power_nat @ one_one_nat @ N )
% 5.49/5.86 = one_one_nat ) ).
% 5.49/5.86
% 5.49/5.86 % power_one
% 5.49/5.86 thf(fact_729_power__one,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( power_power_real @ one_one_real @ N )
% 5.49/5.86 = one_one_real ) ).
% 5.49/5.86
% 5.49/5.86 % power_one
% 5.49/5.86 thf(fact_730_power__one,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( power_power_int @ one_one_int @ N )
% 5.49/5.86 = one_one_int ) ).
% 5.49/5.86
% 5.49/5.86 % power_one
% 5.49/5.86 thf(fact_731_power__one,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( power_power_complex @ one_one_complex @ N )
% 5.49/5.86 = one_one_complex ) ).
% 5.49/5.86
% 5.49/5.86 % power_one
% 5.49/5.86 thf(fact_732_Suc__diff__diff,axiom,
% 5.49/5.86 ! [M: nat,N: nat,K: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.49/5.86 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_diff_diff
% 5.49/5.86 thf(fact_733_diff__Suc__Suc,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.49/5.86 = ( minus_minus_nat @ M @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_Suc_Suc
% 5.49/5.86 thf(fact_734_power__one__right,axiom,
% 5.49/5.86 ! [A: nat] :
% 5.49/5.86 ( ( power_power_nat @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % power_one_right
% 5.49/5.86 thf(fact_735_power__one__right,axiom,
% 5.49/5.86 ! [A: real] :
% 5.49/5.86 ( ( power_power_real @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % power_one_right
% 5.49/5.86 thf(fact_736_power__one__right,axiom,
% 5.49/5.86 ! [A: int] :
% 5.49/5.86 ( ( power_power_int @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % power_one_right
% 5.49/5.86 thf(fact_737_power__one__right,axiom,
% 5.49/5.86 ! [A: complex] :
% 5.49/5.86 ( ( power_power_complex @ A @ one_one_nat )
% 5.49/5.86 = A ) ).
% 5.49/5.86
% 5.49/5.86 % power_one_right
% 5.49/5.86 thf(fact_738_diff__diff__cancel,axiom,
% 5.49/5.86 ! [I2: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ I2 @ N )
% 5.49/5.86 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 5.49/5.86 = I2 ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_diff_cancel
% 5.49/5.86 thf(fact_739_diff__diff__left,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.49/5.86 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_diff_left
% 5.49/5.86 thf(fact_740_nat__mult__eq__1__iff,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( ( times_times_nat @ M @ N )
% 5.49/5.86 = one_one_nat )
% 5.49/5.86 = ( ( M = one_one_nat )
% 5.49/5.86 & ( N = one_one_nat ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % nat_mult_eq_1_iff
% 5.49/5.86 thf(fact_741_nat__1__eq__mult__iff,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( one_one_nat
% 5.49/5.86 = ( times_times_nat @ M @ N ) )
% 5.49/5.86 = ( ( M = one_one_nat )
% 5.49/5.86 & ( N = one_one_nat ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % nat_1_eq_mult_iff
% 5.49/5.86 thf(fact_742_right__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [V: num,B: complex,C: complex] :
% 5.49/5.86 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.49/5.86 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % right_diff_distrib_numeral
% 5.49/5.86 thf(fact_743_right__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [V: num,B: real,C: real] :
% 5.49/5.86 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.49/5.86 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % right_diff_distrib_numeral
% 5.49/5.86 thf(fact_744_right__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [V: num,B: rat,C: rat] :
% 5.49/5.86 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.49/5.86 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % right_diff_distrib_numeral
% 5.49/5.86 thf(fact_745_right__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [V: num,B: int,C: int] :
% 5.49/5.86 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.49/5.86 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % right_diff_distrib_numeral
% 5.49/5.86 thf(fact_746_left__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [A: complex,B: complex,V: num] :
% 5.49/5.86 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.49/5.86 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % left_diff_distrib_numeral
% 5.49/5.86 thf(fact_747_left__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [A: real,B: real,V: num] :
% 5.49/5.86 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.86 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % left_diff_distrib_numeral
% 5.49/5.86 thf(fact_748_left__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [A: rat,B: rat,V: num] :
% 5.49/5.86 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.86 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % left_diff_distrib_numeral
% 5.49/5.86 thf(fact_749_left__diff__distrib__numeral,axiom,
% 5.49/5.86 ! [A: int,B: int,V: num] :
% 5.49/5.86 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.86 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % left_diff_distrib_numeral
% 5.49/5.86 thf(fact_750_numeral__eq__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ( numera6690914467698888265omplex @ N )
% 5.49/5.86 = one_one_complex )
% 5.49/5.86 = ( N = one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_eq_one_iff
% 5.49/5.86 thf(fact_751_numeral__eq__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ( numeral_numeral_real @ N )
% 5.49/5.86 = one_one_real )
% 5.49/5.86 = ( N = one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_eq_one_iff
% 5.49/5.86 thf(fact_752_numeral__eq__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ( numeral_numeral_rat @ N )
% 5.49/5.86 = one_one_rat )
% 5.49/5.86 = ( N = one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_eq_one_iff
% 5.49/5.86 thf(fact_753_numeral__eq__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ( numeral_numeral_nat @ N )
% 5.49/5.86 = one_one_nat )
% 5.49/5.86 = ( N = one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_eq_one_iff
% 5.49/5.86 thf(fact_754_numeral__eq__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ( numeral_numeral_int @ N )
% 5.49/5.86 = one_one_int )
% 5.49/5.86 = ( N = one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_eq_one_iff
% 5.49/5.86 thf(fact_755_one__eq__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( one_one_complex
% 5.49/5.86 = ( numera6690914467698888265omplex @ N ) )
% 5.49/5.86 = ( one = N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_eq_numeral_iff
% 5.49/5.86 thf(fact_756_one__eq__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( one_one_real
% 5.49/5.86 = ( numeral_numeral_real @ N ) )
% 5.49/5.86 = ( one = N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_eq_numeral_iff
% 5.49/5.86 thf(fact_757_one__eq__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( one_one_rat
% 5.49/5.86 = ( numeral_numeral_rat @ N ) )
% 5.49/5.86 = ( one = N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_eq_numeral_iff
% 5.49/5.86 thf(fact_758_one__eq__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( one_one_nat
% 5.49/5.86 = ( numeral_numeral_nat @ N ) )
% 5.49/5.86 = ( one = N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_eq_numeral_iff
% 5.49/5.86 thf(fact_759_one__eq__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( one_one_int
% 5.49/5.86 = ( numeral_numeral_int @ N ) )
% 5.49/5.86 = ( one = N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_eq_numeral_iff
% 5.49/5.86 thf(fact_760_power__inject__exp,axiom,
% 5.49/5.86 ! [A: real,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.86 => ( ( ( power_power_real @ A @ M )
% 5.49/5.86 = ( power_power_real @ A @ N ) )
% 5.49/5.86 = ( M = N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_inject_exp
% 5.49/5.86 thf(fact_761_power__inject__exp,axiom,
% 5.49/5.86 ! [A: rat,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.86 => ( ( ( power_power_rat @ A @ M )
% 5.49/5.86 = ( power_power_rat @ A @ N ) )
% 5.49/5.86 = ( M = N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_inject_exp
% 5.49/5.86 thf(fact_762_power__inject__exp,axiom,
% 5.49/5.86 ! [A: nat,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.86 => ( ( ( power_power_nat @ A @ M )
% 5.49/5.86 = ( power_power_nat @ A @ N ) )
% 5.49/5.86 = ( M = N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_inject_exp
% 5.49/5.86 thf(fact_763_power__inject__exp,axiom,
% 5.49/5.86 ! [A: int,M: nat,N: nat] :
% 5.49/5.86 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.86 => ( ( ( power_power_int @ A @ M )
% 5.49/5.86 = ( power_power_int @ A @ N ) )
% 5.49/5.86 = ( M = N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_inject_exp
% 5.49/5.86 thf(fact_764_Nat_Oadd__diff__assoc,axiom,
% 5.49/5.86 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.86 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.49/5.86 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % Nat.add_diff_assoc
% 5.49/5.86 thf(fact_765_Nat_Oadd__diff__assoc2,axiom,
% 5.49/5.86 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.86 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.49/5.86 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % Nat.add_diff_assoc2
% 5.49/5.86 thf(fact_766_Nat_Odiff__diff__right,axiom,
% 5.49/5.86 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.86 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.49/5.86 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % Nat.diff_diff_right
% 5.49/5.86 thf(fact_767_diff__Suc__1,axiom,
% 5.49/5.86 ! [N: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.49/5.86 = N ) ).
% 5.49/5.86
% 5.49/5.86 % diff_Suc_1
% 5.49/5.86 thf(fact_768_option_Ocollapse,axiom,
% 5.49/5.86 ! [Option: option_nat] :
% 5.49/5.86 ( ( Option != none_nat )
% 5.49/5.86 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.49/5.86 = Option ) ) ).
% 5.49/5.86
% 5.49/5.86 % option.collapse
% 5.49/5.86 thf(fact_769_option_Ocollapse,axiom,
% 5.49/5.86 ! [Option: option4927543243414619207at_nat] :
% 5.49/5.86 ( ( Option != none_P5556105721700978146at_nat )
% 5.49/5.86 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.49/5.86 = Option ) ) ).
% 5.49/5.86
% 5.49/5.86 % option.collapse
% 5.49/5.86 thf(fact_770_option_Ocollapse,axiom,
% 5.49/5.86 ! [Option: option_num] :
% 5.49/5.86 ( ( Option != none_num )
% 5.49/5.86 => ( ( some_num @ ( the_num @ Option ) )
% 5.49/5.86 = Option ) ) ).
% 5.49/5.86
% 5.49/5.86 % option.collapse
% 5.49/5.86 thf(fact_771_power__strict__increasing__iff,axiom,
% 5.49/5.86 ! [B: real,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_real @ one_one_real @ B )
% 5.49/5.86 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_strict_increasing_iff
% 5.49/5.86 thf(fact_772_power__strict__increasing__iff,axiom,
% 5.49/5.86 ! [B: rat,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_rat @ one_one_rat @ B )
% 5.49/5.86 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_strict_increasing_iff
% 5.49/5.86 thf(fact_773_power__strict__increasing__iff,axiom,
% 5.49/5.86 ! [B: nat,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_nat @ one_one_nat @ B )
% 5.49/5.86 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_strict_increasing_iff
% 5.49/5.86 thf(fact_774_power__strict__increasing__iff,axiom,
% 5.49/5.86 ! [B: int,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_int @ one_one_int @ B )
% 5.49/5.86 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_strict_increasing_iff
% 5.49/5.86 thf(fact_775_diff__Suc__diff__eq1,axiom,
% 5.49/5.86 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.86 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.49/5.86 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_Suc_diff_eq1
% 5.49/5.86 thf(fact_776_diff__Suc__diff__eq2,axiom,
% 5.49/5.86 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.86 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.86 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.49/5.86 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_Suc_diff_eq2
% 5.49/5.86 thf(fact_777_one__add__one,axiom,
% 5.49/5.86 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.49/5.86 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_add_one
% 5.49/5.86 thf(fact_778_one__add__one,axiom,
% 5.49/5.86 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.49/5.86 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_add_one
% 5.49/5.86 thf(fact_779_one__add__one,axiom,
% 5.49/5.86 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.49/5.86 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_add_one
% 5.49/5.86 thf(fact_780_one__add__one,axiom,
% 5.49/5.86 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.49/5.86 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_add_one
% 5.49/5.86 thf(fact_781_one__add__one,axiom,
% 5.49/5.86 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.49/5.86 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_add_one
% 5.49/5.86 thf(fact_782_power__increasing__iff,axiom,
% 5.49/5.86 ! [B: real,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_real @ one_one_real @ B )
% 5.49/5.86 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_increasing_iff
% 5.49/5.86 thf(fact_783_power__increasing__iff,axiom,
% 5.49/5.86 ! [B: rat,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_rat @ one_one_rat @ B )
% 5.49/5.86 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_increasing_iff
% 5.49/5.86 thf(fact_784_power__increasing__iff,axiom,
% 5.49/5.86 ! [B: nat,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_nat @ one_one_nat @ B )
% 5.49/5.86 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_increasing_iff
% 5.49/5.86 thf(fact_785_power__increasing__iff,axiom,
% 5.49/5.86 ! [B: int,X: nat,Y2: nat] :
% 5.49/5.86 ( ( ord_less_int @ one_one_int @ B )
% 5.49/5.86 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 5.49/5.86 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % power_increasing_iff
% 5.49/5.86 thf(fact_786_Suc__1,axiom,
% 5.49/5.86 ( ( suc @ one_one_nat )
% 5.49/5.86 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % Suc_1
% 5.49/5.86 thf(fact_787_numeral__plus__one,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.49/5.86 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_plus_one
% 5.49/5.86 thf(fact_788_numeral__plus__one,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.49/5.86 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_plus_one
% 5.49/5.86 thf(fact_789_numeral__plus__one,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.49/5.86 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_plus_one
% 5.49/5.86 thf(fact_790_numeral__plus__one,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.49/5.86 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_plus_one
% 5.49/5.86 thf(fact_791_numeral__plus__one,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.49/5.86 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_plus_one
% 5.49/5.86 thf(fact_792_one__plus__numeral,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.49/5.86 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_plus_numeral
% 5.49/5.86 thf(fact_793_one__plus__numeral,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.49/5.86 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_plus_numeral
% 5.49/5.86 thf(fact_794_one__plus__numeral,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.49/5.86 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_plus_numeral
% 5.49/5.86 thf(fact_795_one__plus__numeral,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.49/5.86 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_plus_numeral
% 5.49/5.86 thf(fact_796_one__plus__numeral,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.49/5.86 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_plus_numeral
% 5.49/5.86 thf(fact_797_numeral__le__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.49/5.86 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_le_one_iff
% 5.49/5.86 thf(fact_798_numeral__le__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.49/5.86 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_le_one_iff
% 5.49/5.86 thf(fact_799_numeral__le__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.49/5.86 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_le_one_iff
% 5.49/5.86 thf(fact_800_numeral__le__one__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.49/5.86 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.49/5.86
% 5.49/5.86 % numeral_le_one_iff
% 5.49/5.86 thf(fact_801_one__less__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.49/5.86 = ( ord_less_num @ one @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_less_numeral_iff
% 5.49/5.86 thf(fact_802_one__less__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.49/5.86 = ( ord_less_num @ one @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_less_numeral_iff
% 5.49/5.86 thf(fact_803_one__less__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.49/5.86 = ( ord_less_num @ one @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_less_numeral_iff
% 5.49/5.86 thf(fact_804_one__less__numeral__iff,axiom,
% 5.49/5.86 ! [N: num] :
% 5.49/5.86 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.49/5.86 = ( ord_less_num @ one @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_less_numeral_iff
% 5.49/5.86 thf(fact_805_diff__eq__diff__eq,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ( minus_minus_real @ A @ B )
% 5.49/5.86 = ( minus_minus_real @ C @ D ) )
% 5.49/5.86 => ( ( A = B )
% 5.49/5.86 = ( C = D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_eq
% 5.49/5.86 thf(fact_806_diff__eq__diff__eq,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ( minus_minus_rat @ A @ B )
% 5.49/5.86 = ( minus_minus_rat @ C @ D ) )
% 5.49/5.86 => ( ( A = B )
% 5.49/5.86 = ( C = D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_eq
% 5.49/5.86 thf(fact_807_diff__eq__diff__eq,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ( minus_minus_int @ A @ B )
% 5.49/5.86 = ( minus_minus_int @ C @ D ) )
% 5.49/5.86 => ( ( A = B )
% 5.49/5.86 = ( C = D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_eq
% 5.49/5.86 thf(fact_808_diff__right__commute,axiom,
% 5.49/5.86 ! [A: real,C: real,B: real] :
% 5.49/5.86 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.49/5.86 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_commute
% 5.49/5.86 thf(fact_809_diff__right__commute,axiom,
% 5.49/5.86 ! [A: rat,C: rat,B: rat] :
% 5.49/5.86 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.49/5.86 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_commute
% 5.49/5.86 thf(fact_810_diff__right__commute,axiom,
% 5.49/5.86 ! [A: nat,C: nat,B: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.49/5.86 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_commute
% 5.49/5.86 thf(fact_811_diff__right__commute,axiom,
% 5.49/5.86 ! [A: int,C: int,B: int] :
% 5.49/5.86 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.49/5.86 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_commute
% 5.49/5.86 thf(fact_812_one__reorient,axiom,
% 5.49/5.86 ! [X: complex] :
% 5.49/5.86 ( ( one_one_complex = X )
% 5.49/5.86 = ( X = one_one_complex ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_reorient
% 5.49/5.86 thf(fact_813_one__reorient,axiom,
% 5.49/5.86 ! [X: real] :
% 5.49/5.86 ( ( one_one_real = X )
% 5.49/5.86 = ( X = one_one_real ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_reorient
% 5.49/5.86 thf(fact_814_one__reorient,axiom,
% 5.49/5.86 ! [X: rat] :
% 5.49/5.86 ( ( one_one_rat = X )
% 5.49/5.86 = ( X = one_one_rat ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_reorient
% 5.49/5.86 thf(fact_815_one__reorient,axiom,
% 5.49/5.86 ! [X: nat] :
% 5.49/5.86 ( ( one_one_nat = X )
% 5.49/5.86 = ( X = one_one_nat ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_reorient
% 5.49/5.86 thf(fact_816_one__reorient,axiom,
% 5.49/5.86 ! [X: int] :
% 5.49/5.86 ( ( one_one_int = X )
% 5.49/5.86 = ( X = one_one_int ) ) ).
% 5.49/5.86
% 5.49/5.86 % one_reorient
% 5.49/5.86 thf(fact_817_diff__commute,axiom,
% 5.49/5.86 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.49/5.86 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_commute
% 5.49/5.86 thf(fact_818_diff__Suc__eq__diff__pred,axiom,
% 5.49/5.86 ! [M: nat,N: nat] :
% 5.49/5.86 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.49/5.86 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_Suc_eq_diff_pred
% 5.49/5.86 thf(fact_819_diff__eq__diff__less__eq,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ( minus_minus_real @ A @ B )
% 5.49/5.86 = ( minus_minus_real @ C @ D ) )
% 5.49/5.86 => ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_less_eq
% 5.49/5.86 thf(fact_820_diff__eq__diff__less__eq,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ( minus_minus_rat @ A @ B )
% 5.49/5.86 = ( minus_minus_rat @ C @ D ) )
% 5.49/5.86 => ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_less_eq
% 5.49/5.86 thf(fact_821_diff__eq__diff__less__eq,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.86 ( ( ( minus_minus_int @ A @ B )
% 5.49/5.86 = ( minus_minus_int @ C @ D ) )
% 5.49/5.86 => ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_less_eq
% 5.49/5.86 thf(fact_822_diff__right__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_mono
% 5.49/5.86 thf(fact_823_diff__right__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_mono
% 5.49/5.86 thf(fact_824_diff__right__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,C: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_right_mono
% 5.49/5.86 thf(fact_825_diff__left__mono,axiom,
% 5.49/5.86 ! [B: real,A: real,C: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.86 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_left_mono
% 5.49/5.86 thf(fact_826_diff__left__mono,axiom,
% 5.49/5.86 ! [B: rat,A: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.86 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_left_mono
% 5.49/5.86 thf(fact_827_diff__left__mono,axiom,
% 5.49/5.86 ! [B: int,A: int,C: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.86 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_left_mono
% 5.49/5.86 thf(fact_828_diff__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,D: real,C: real] :
% 5.49/5.86 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_real @ D @ C )
% 5.49/5.86 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_mono
% 5.49/5.86 thf(fact_829_diff__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_rat @ D @ C )
% 5.49/5.86 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_mono
% 5.49/5.86 thf(fact_830_diff__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,D: int,C: int] :
% 5.49/5.86 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_eq_int @ D @ C )
% 5.49/5.86 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_mono
% 5.49/5.86 thf(fact_831_diff__strict__mono,axiom,
% 5.49/5.86 ! [A: real,B: real,D: real,C: real] :
% 5.49/5.86 ( ( ord_less_real @ A @ B )
% 5.49/5.86 => ( ( ord_less_real @ D @ C )
% 5.49/5.86 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_strict_mono
% 5.49/5.86 thf(fact_832_diff__strict__mono,axiom,
% 5.49/5.86 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.49/5.86 ( ( ord_less_rat @ A @ B )
% 5.49/5.86 => ( ( ord_less_rat @ D @ C )
% 5.49/5.86 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_strict_mono
% 5.49/5.86 thf(fact_833_diff__strict__mono,axiom,
% 5.49/5.86 ! [A: int,B: int,D: int,C: int] :
% 5.49/5.86 ( ( ord_less_int @ A @ B )
% 5.49/5.86 => ( ( ord_less_int @ D @ C )
% 5.49/5.86 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_strict_mono
% 5.49/5.86 thf(fact_834_diff__eq__diff__less,axiom,
% 5.49/5.86 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.86 ( ( ( minus_minus_real @ A @ B )
% 5.49/5.86 = ( minus_minus_real @ C @ D ) )
% 5.49/5.86 => ( ( ord_less_real @ A @ B )
% 5.49/5.86 = ( ord_less_real @ C @ D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_less
% 5.49/5.86 thf(fact_835_diff__eq__diff__less,axiom,
% 5.49/5.86 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.86 ( ( ( minus_minus_rat @ A @ B )
% 5.49/5.86 = ( minus_minus_rat @ C @ D ) )
% 5.49/5.86 => ( ( ord_less_rat @ A @ B )
% 5.49/5.86 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.49/5.86
% 5.49/5.86 % diff_eq_diff_less
% 5.49/5.86 thf(fact_836_diff__eq__diff__less,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.87 ( ( ( minus_minus_int @ A @ B )
% 5.49/5.87 = ( minus_minus_int @ C @ D ) )
% 5.49/5.87 => ( ( ord_less_int @ A @ B )
% 5.49/5.87 = ( ord_less_int @ C @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_eq_diff_less
% 5.49/5.87 thf(fact_837_diff__strict__left__mono,axiom,
% 5.49/5.87 ! [B: real,A: real,C: real] :
% 5.49/5.87 ( ( ord_less_real @ B @ A )
% 5.49/5.87 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_left_mono
% 5.49/5.87 thf(fact_838_diff__strict__left__mono,axiom,
% 5.49/5.87 ! [B: rat,A: rat,C: rat] :
% 5.49/5.87 ( ( ord_less_rat @ B @ A )
% 5.49/5.87 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_left_mono
% 5.49/5.87 thf(fact_839_diff__strict__left__mono,axiom,
% 5.49/5.87 ! [B: int,A: int,C: int] :
% 5.49/5.87 ( ( ord_less_int @ B @ A )
% 5.49/5.87 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_left_mono
% 5.49/5.87 thf(fact_840_diff__strict__right__mono,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( ord_less_real @ A @ B )
% 5.49/5.87 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_right_mono
% 5.49/5.87 thf(fact_841_diff__strict__right__mono,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( ord_less_rat @ A @ B )
% 5.49/5.87 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_right_mono
% 5.49/5.87 thf(fact_842_diff__strict__right__mono,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( ord_less_int @ A @ B )
% 5.49/5.87 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_strict_right_mono
% 5.49/5.87 thf(fact_843_add__diff__add,axiom,
% 5.49/5.87 ! [A: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.49/5.87 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_add
% 5.49/5.87 thf(fact_844_add__diff__add,axiom,
% 5.49/5.87 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.49/5.87 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_add
% 5.49/5.87 thf(fact_845_add__diff__add,axiom,
% 5.49/5.87 ! [A: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.49/5.87 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_add
% 5.49/5.87 thf(fact_846_diff__diff__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq
% 5.49/5.87 thf(fact_847_diff__diff__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq
% 5.49/5.87 thf(fact_848_diff__diff__eq,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq
% 5.49/5.87 thf(fact_849_diff__diff__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq
% 5.49/5.87 thf(fact_850_add__implies__diff,axiom,
% 5.49/5.87 ! [C: real,B: real,A: real] :
% 5.49/5.87 ( ( ( plus_plus_real @ C @ B )
% 5.49/5.87 = A )
% 5.49/5.87 => ( C
% 5.49/5.87 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_implies_diff
% 5.49/5.87 thf(fact_851_add__implies__diff,axiom,
% 5.49/5.87 ! [C: rat,B: rat,A: rat] :
% 5.49/5.87 ( ( ( plus_plus_rat @ C @ B )
% 5.49/5.87 = A )
% 5.49/5.87 => ( C
% 5.49/5.87 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_implies_diff
% 5.49/5.87 thf(fact_852_add__implies__diff,axiom,
% 5.49/5.87 ! [C: nat,B: nat,A: nat] :
% 5.49/5.87 ( ( ( plus_plus_nat @ C @ B )
% 5.49/5.87 = A )
% 5.49/5.87 => ( C
% 5.49/5.87 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_implies_diff
% 5.49/5.87 thf(fact_853_add__implies__diff,axiom,
% 5.49/5.87 ! [C: int,B: int,A: int] :
% 5.49/5.87 ( ( ( plus_plus_int @ C @ B )
% 5.49/5.87 = A )
% 5.49/5.87 => ( C
% 5.49/5.87 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_implies_diff
% 5.49/5.87 thf(fact_854_diff__add__eq__diff__diff__swap,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.49/5.87 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq_diff_diff_swap
% 5.49/5.87 thf(fact_855_diff__add__eq__diff__diff__swap,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq_diff_diff_swap
% 5.49/5.87 thf(fact_856_diff__add__eq__diff__diff__swap,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.49/5.87 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq_diff_diff_swap
% 5.49/5.87 thf(fact_857_diff__add__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq
% 5.49/5.87 thf(fact_858_diff__add__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq
% 5.49/5.87 thf(fact_859_diff__add__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_eq
% 5.49/5.87 thf(fact_860_diff__diff__eq2,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.49/5.87 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq2
% 5.49/5.87 thf(fact_861_diff__diff__eq2,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq2
% 5.49/5.87 thf(fact_862_diff__diff__eq2,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.49/5.87 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_diff_eq2
% 5.49/5.87 thf(fact_863_add__diff__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.49/5.87 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_eq
% 5.49/5.87 thf(fact_864_add__diff__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_eq
% 5.49/5.87 thf(fact_865_add__diff__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.49/5.87 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_eq
% 5.49/5.87 thf(fact_866_eq__diff__eq,axiom,
% 5.49/5.87 ! [A: real,C: real,B: real] :
% 5.49/5.87 ( ( A
% 5.49/5.87 = ( minus_minus_real @ C @ B ) )
% 5.49/5.87 = ( ( plus_plus_real @ A @ B )
% 5.49/5.87 = C ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_diff_eq
% 5.49/5.87 thf(fact_867_eq__diff__eq,axiom,
% 5.49/5.87 ! [A: rat,C: rat,B: rat] :
% 5.49/5.87 ( ( A
% 5.49/5.87 = ( minus_minus_rat @ C @ B ) )
% 5.49/5.87 = ( ( plus_plus_rat @ A @ B )
% 5.49/5.87 = C ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_diff_eq
% 5.49/5.87 thf(fact_868_eq__diff__eq,axiom,
% 5.49/5.87 ! [A: int,C: int,B: int] :
% 5.49/5.87 ( ( A
% 5.49/5.87 = ( minus_minus_int @ C @ B ) )
% 5.49/5.87 = ( ( plus_plus_int @ A @ B )
% 5.49/5.87 = C ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_diff_eq
% 5.49/5.87 thf(fact_869_diff__eq__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( ( minus_minus_real @ A @ B )
% 5.49/5.87 = C )
% 5.49/5.87 = ( A
% 5.49/5.87 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_eq_eq
% 5.49/5.87 thf(fact_870_diff__eq__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( ( minus_minus_rat @ A @ B )
% 5.49/5.87 = C )
% 5.49/5.87 = ( A
% 5.49/5.87 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_eq_eq
% 5.49/5.87 thf(fact_871_diff__eq__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( ( minus_minus_int @ A @ B )
% 5.49/5.87 = C )
% 5.49/5.87 = ( A
% 5.49/5.87 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_eq_eq
% 5.49/5.87 thf(fact_872_group__cancel_Osub1,axiom,
% 5.49/5.87 ! [A2: real,K: real,A: real,B: real] :
% 5.49/5.87 ( ( A2
% 5.49/5.87 = ( plus_plus_real @ K @ A ) )
% 5.49/5.87 => ( ( minus_minus_real @ A2 @ B )
% 5.49/5.87 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % group_cancel.sub1
% 5.49/5.87 thf(fact_873_group__cancel_Osub1,axiom,
% 5.49/5.87 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.49/5.87 ( ( A2
% 5.49/5.87 = ( plus_plus_rat @ K @ A ) )
% 5.49/5.87 => ( ( minus_minus_rat @ A2 @ B )
% 5.49/5.87 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % group_cancel.sub1
% 5.49/5.87 thf(fact_874_group__cancel_Osub1,axiom,
% 5.49/5.87 ! [A2: int,K: int,A: int,B: int] :
% 5.49/5.87 ( ( A2
% 5.49/5.87 = ( plus_plus_int @ K @ A ) )
% 5.49/5.87 => ( ( minus_minus_int @ A2 @ B )
% 5.49/5.87 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % group_cancel.sub1
% 5.49/5.87 thf(fact_875_diff__divide__distrib,axiom,
% 5.49/5.87 ! [A: complex,B: complex,C: complex] :
% 5.49/5.87 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_divide_distrib
% 5.49/5.87 thf(fact_876_diff__divide__distrib,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_divide_distrib
% 5.49/5.87 thf(fact_877_diff__divide__distrib,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_divide_distrib
% 5.49/5.87 thf(fact_878_zero__induct__lemma,axiom,
% 5.49/5.87 ! [P: nat > $o,K: nat,I2: nat] :
% 5.49/5.87 ( ( P @ K )
% 5.49/5.87 => ( ! [N3: nat] :
% 5.49/5.87 ( ( P @ ( suc @ N3 ) )
% 5.49/5.87 => ( P @ N3 ) )
% 5.49/5.87 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % zero_induct_lemma
% 5.49/5.87 thf(fact_879_diff__less__mono2,axiom,
% 5.49/5.87 ! [M: nat,N: nat,L2: nat] :
% 5.49/5.87 ( ( ord_less_nat @ M @ N )
% 5.49/5.87 => ( ( ord_less_nat @ M @ L2 )
% 5.49/5.87 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_mono2
% 5.49/5.87 thf(fact_880_less__imp__diff__less,axiom,
% 5.49/5.87 ! [J: nat,K: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ J @ K )
% 5.49/5.87 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_imp_diff_less
% 5.49/5.87 thf(fact_881_diff__le__mono2,axiom,
% 5.49/5.87 ! [M: nat,N: nat,L2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.87 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_mono2
% 5.49/5.87 thf(fact_882_le__diff__iff_H,axiom,
% 5.49/5.87 ! [A: nat,C: nat,B: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ C )
% 5.49/5.87 => ( ( ord_less_eq_nat @ B @ C )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.49/5.87 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_iff'
% 5.49/5.87 thf(fact_883_diff__le__self,axiom,
% 5.49/5.87 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_self
% 5.49/5.87 thf(fact_884_diff__le__mono,axiom,
% 5.49/5.87 ! [M: nat,N: nat,L2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.87 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_mono
% 5.49/5.87 thf(fact_885_Nat_Odiff__diff__eq,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ M )
% 5.49/5.87 => ( ( ord_less_eq_nat @ K @ N )
% 5.49/5.87 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.49/5.87 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.diff_diff_eq
% 5.49/5.87 thf(fact_886_le__diff__iff,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ M )
% 5.49/5.87 => ( ( ord_less_eq_nat @ K @ N )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.49/5.87 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_iff
% 5.49/5.87 thf(fact_887_eq__diff__iff,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ M )
% 5.49/5.87 => ( ( ord_less_eq_nat @ K @ N )
% 5.49/5.87 => ( ( ( minus_minus_nat @ M @ K )
% 5.49/5.87 = ( minus_minus_nat @ N @ K ) )
% 5.49/5.87 = ( M = N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_diff_iff
% 5.49/5.87 thf(fact_888_diff__add__inverse2,axiom,
% 5.49/5.87 ! [M: nat,N: nat] :
% 5.49/5.87 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.49/5.87 = M ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_inverse2
% 5.49/5.87 thf(fact_889_diff__add__inverse,axiom,
% 5.49/5.87 ! [N: nat,M: nat] :
% 5.49/5.87 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.49/5.87 = M ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add_inverse
% 5.49/5.87 thf(fact_890_diff__cancel2,axiom,
% 5.49/5.87 ! [M: nat,K: nat,N: nat] :
% 5.49/5.87 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.49/5.87 = ( minus_minus_nat @ M @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_cancel2
% 5.49/5.87 thf(fact_891_Nat_Odiff__cancel,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.49/5.87 = ( minus_minus_nat @ M @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.diff_cancel
% 5.49/5.87 thf(fact_892_le__numeral__extra_I4_J,axiom,
% 5.49/5.87 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.49/5.87
% 5.49/5.87 % le_numeral_extra(4)
% 5.49/5.87 thf(fact_893_le__numeral__extra_I4_J,axiom,
% 5.49/5.87 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.49/5.87
% 5.49/5.87 % le_numeral_extra(4)
% 5.49/5.87 thf(fact_894_le__numeral__extra_I4_J,axiom,
% 5.49/5.87 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.49/5.87
% 5.49/5.87 % le_numeral_extra(4)
% 5.49/5.87 thf(fact_895_le__numeral__extra_I4_J,axiom,
% 5.49/5.87 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.49/5.87
% 5.49/5.87 % le_numeral_extra(4)
% 5.49/5.87 thf(fact_896_less__numeral__extra_I4_J,axiom,
% 5.49/5.87 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.49/5.87
% 5.49/5.87 % less_numeral_extra(4)
% 5.49/5.87 thf(fact_897_less__numeral__extra_I4_J,axiom,
% 5.49/5.87 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.49/5.87
% 5.49/5.87 % less_numeral_extra(4)
% 5.49/5.87 thf(fact_898_less__numeral__extra_I4_J,axiom,
% 5.49/5.87 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.49/5.87
% 5.49/5.87 % less_numeral_extra(4)
% 5.49/5.87 thf(fact_899_less__numeral__extra_I4_J,axiom,
% 5.49/5.87 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.49/5.87
% 5.49/5.87 % less_numeral_extra(4)
% 5.49/5.87 thf(fact_900_diff__mult__distrib2,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.87 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_mult_distrib2
% 5.49/5.87 thf(fact_901_diff__mult__distrib,axiom,
% 5.49/5.87 ! [M: nat,N: nat,K: nat] :
% 5.49/5.87 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.49/5.87 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_mult_distrib
% 5.49/5.87 thf(fact_902_mult_Ocomm__neutral,axiom,
% 5.49/5.87 ! [A: complex] :
% 5.49/5.87 ( ( times_times_complex @ A @ one_one_complex )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % mult.comm_neutral
% 5.49/5.87 thf(fact_903_mult_Ocomm__neutral,axiom,
% 5.49/5.87 ! [A: real] :
% 5.49/5.87 ( ( times_times_real @ A @ one_one_real )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % mult.comm_neutral
% 5.49/5.87 thf(fact_904_mult_Ocomm__neutral,axiom,
% 5.49/5.87 ! [A: rat] :
% 5.49/5.87 ( ( times_times_rat @ A @ one_one_rat )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % mult.comm_neutral
% 5.49/5.87 thf(fact_905_mult_Ocomm__neutral,axiom,
% 5.49/5.87 ! [A: nat] :
% 5.49/5.87 ( ( times_times_nat @ A @ one_one_nat )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % mult.comm_neutral
% 5.49/5.87 thf(fact_906_mult_Ocomm__neutral,axiom,
% 5.49/5.87 ! [A: int] :
% 5.49/5.87 ( ( times_times_int @ A @ one_one_int )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % mult.comm_neutral
% 5.49/5.87 thf(fact_907_comm__monoid__mult__class_Omult__1,axiom,
% 5.49/5.87 ! [A: complex] :
% 5.49/5.87 ( ( times_times_complex @ one_one_complex @ A )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % comm_monoid_mult_class.mult_1
% 5.49/5.87 thf(fact_908_comm__monoid__mult__class_Omult__1,axiom,
% 5.49/5.87 ! [A: real] :
% 5.49/5.87 ( ( times_times_real @ one_one_real @ A )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % comm_monoid_mult_class.mult_1
% 5.49/5.87 thf(fact_909_comm__monoid__mult__class_Omult__1,axiom,
% 5.49/5.87 ! [A: rat] :
% 5.49/5.87 ( ( times_times_rat @ one_one_rat @ A )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % comm_monoid_mult_class.mult_1
% 5.49/5.87 thf(fact_910_comm__monoid__mult__class_Omult__1,axiom,
% 5.49/5.87 ! [A: nat] :
% 5.49/5.87 ( ( times_times_nat @ one_one_nat @ A )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % comm_monoid_mult_class.mult_1
% 5.49/5.87 thf(fact_911_comm__monoid__mult__class_Omult__1,axiom,
% 5.49/5.87 ! [A: int] :
% 5.49/5.87 ( ( times_times_int @ one_one_int @ A )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % comm_monoid_mult_class.mult_1
% 5.49/5.87 thf(fact_912_nat__mult__1__right,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ( ( times_times_nat @ N @ one_one_nat )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % nat_mult_1_right
% 5.49/5.87 thf(fact_913_nat__mult__1,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ( ( times_times_nat @ one_one_nat @ N )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % nat_mult_1
% 5.49/5.87 thf(fact_914_option_Osel,axiom,
% 5.49/5.87 ! [X22: nat] :
% 5.49/5.87 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.49/5.87 = X22 ) ).
% 5.49/5.87
% 5.49/5.87 % option.sel
% 5.49/5.87 thf(fact_915_option_Osel,axiom,
% 5.49/5.87 ! [X22: product_prod_nat_nat] :
% 5.49/5.87 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.49/5.87 = X22 ) ).
% 5.49/5.87
% 5.49/5.87 % option.sel
% 5.49/5.87 thf(fact_916_option_Osel,axiom,
% 5.49/5.87 ! [X22: num] :
% 5.49/5.87 ( ( the_num @ ( some_num @ X22 ) )
% 5.49/5.87 = X22 ) ).
% 5.49/5.87
% 5.49/5.87 % option.sel
% 5.49/5.87 thf(fact_917_option_Oexpand,axiom,
% 5.49/5.87 ! [Option: option_nat,Option2: option_nat] :
% 5.49/5.87 ( ( ( Option = none_nat )
% 5.49/5.87 = ( Option2 = none_nat ) )
% 5.49/5.87 => ( ( ( Option != none_nat )
% 5.49/5.87 => ( ( Option2 != none_nat )
% 5.49/5.87 => ( ( the_nat @ Option )
% 5.49/5.87 = ( the_nat @ Option2 ) ) ) )
% 5.49/5.87 => ( Option = Option2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.expand
% 5.49/5.87 thf(fact_918_option_Oexpand,axiom,
% 5.49/5.87 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.49/5.87 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.49/5.87 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.49/5.87 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.49/5.87 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.49/5.87 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.49/5.87 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.49/5.87 => ( Option = Option2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.expand
% 5.49/5.87 thf(fact_919_option_Oexpand,axiom,
% 5.49/5.87 ! [Option: option_num,Option2: option_num] :
% 5.49/5.87 ( ( ( Option = none_num )
% 5.49/5.87 = ( Option2 = none_num ) )
% 5.49/5.87 => ( ( ( Option != none_num )
% 5.49/5.87 => ( ( Option2 != none_num )
% 5.49/5.87 => ( ( the_num @ Option )
% 5.49/5.87 = ( the_num @ Option2 ) ) ) )
% 5.49/5.87 => ( Option = Option2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.expand
% 5.49/5.87 thf(fact_920_diff__le__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_eq
% 5.49/5.87 thf(fact_921_diff__le__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_eq
% 5.49/5.87 thf(fact_922_diff__le__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_eq
% 5.49/5.87 thf(fact_923_le__diff__eq,axiom,
% 5.49/5.87 ! [A: real,C: real,B: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.49/5.87 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_eq
% 5.49/5.87 thf(fact_924_le__diff__eq,axiom,
% 5.49/5.87 ! [A: rat,C: rat,B: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.49/5.87 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_eq
% 5.49/5.87 thf(fact_925_le__diff__eq,axiom,
% 5.49/5.87 ! [A: int,C: int,B: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.49/5.87 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_eq
% 5.49/5.87 thf(fact_926_diff__add,axiom,
% 5.49/5.87 ! [A: nat,B: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.49/5.87 = B ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_add
% 5.49/5.87 thf(fact_927_le__add__diff,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff
% 5.49/5.87 thf(fact_928_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.49/5.87 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.49/5.87 thf(fact_929_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.49/5.87 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.49/5.87 thf(fact_930_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.49/5.87 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.49/5.87 thf(fact_931_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.49/5.87 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.49/5.87 thf(fact_932_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.49/5.87 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.49/5.87 thf(fact_933_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.49/5.87 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.49/5.87 thf(fact_934_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.49/5.87 ! [A: nat,B: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.49/5.87 = B ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.49/5.87 thf(fact_935_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.87 => ( ( ( minus_minus_nat @ B @ A )
% 5.49/5.87 = C )
% 5.49/5.87 = ( B
% 5.49/5.87 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.49/5.87 thf(fact_936_diff__less__eq,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_eq
% 5.49/5.87 thf(fact_937_diff__less__eq,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_eq
% 5.49/5.87 thf(fact_938_diff__less__eq,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.87 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_eq
% 5.49/5.87 thf(fact_939_less__diff__eq,axiom,
% 5.49/5.87 ! [A: real,C: real,B: real] :
% 5.49/5.87 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.49/5.87 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_eq
% 5.49/5.87 thf(fact_940_less__diff__eq,axiom,
% 5.49/5.87 ! [A: rat,C: rat,B: rat] :
% 5.49/5.87 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.49/5.87 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_eq
% 5.49/5.87 thf(fact_941_less__diff__eq,axiom,
% 5.49/5.87 ! [A: int,C: int,B: int] :
% 5.49/5.87 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.49/5.87 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_eq
% 5.49/5.87 thf(fact_942_mult__diff__mult,axiom,
% 5.49/5.87 ! [X: real,Y2: real,A: real,B: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( times_times_real @ X @ Y2 ) @ ( times_times_real @ A @ B ) )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y2 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_diff_mult
% 5.49/5.87 thf(fact_943_mult__diff__mult,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat,A: rat,B: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y2 ) @ ( times_times_rat @ A @ B ) )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y2 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_diff_mult
% 5.49/5.87 thf(fact_944_mult__diff__mult,axiom,
% 5.49/5.87 ! [X: int,Y2: int,A: int,B: int] :
% 5.49/5.87 ( ( minus_minus_int @ ( times_times_int @ X @ Y2 ) @ ( times_times_int @ A @ B ) )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y2 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_diff_mult
% 5.49/5.87 thf(fact_945_diff__less__Suc,axiom,
% 5.49/5.87 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_Suc
% 5.49/5.87 thf(fact_946_Suc__diff__Suc,axiom,
% 5.49/5.87 ! [N: nat,M: nat] :
% 5.49/5.87 ( ( ord_less_nat @ N @ M )
% 5.49/5.87 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.49/5.87 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Suc_diff_Suc
% 5.49/5.87 thf(fact_947_Suc__diff__le,axiom,
% 5.49/5.87 ! [N: nat,M: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.87 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.49/5.87 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Suc_diff_le
% 5.49/5.87 thf(fact_948_less__diff__iff,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ M )
% 5.49/5.87 => ( ( ord_less_eq_nat @ K @ N )
% 5.49/5.87 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.49/5.87 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_iff
% 5.49/5.87 thf(fact_949_diff__less__mono,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( ord_less_nat @ A @ B )
% 5.49/5.87 => ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.87 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_less_mono
% 5.49/5.87 thf(fact_950_less__diff__conv,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.49/5.87 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_conv
% 5.49/5.87 thf(fact_951_add__diff__inverse__nat,axiom,
% 5.49/5.87 ! [M: nat,N: nat] :
% 5.49/5.87 ( ~ ( ord_less_nat @ M @ N )
% 5.49/5.87 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.87 = M ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_inverse_nat
% 5.49/5.87 thf(fact_952_le__diff__conv,axiom,
% 5.49/5.87 ! [J: nat,K: nat,I2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.49/5.87 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_diff_conv
% 5.49/5.87 thf(fact_953_Nat_Ole__diff__conv2,axiom,
% 5.49/5.87 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.87 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.49/5.87 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.le_diff_conv2
% 5.49/5.87 thf(fact_954_Nat_Odiff__add__assoc,axiom,
% 5.49/5.87 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.49/5.87 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.diff_add_assoc
% 5.49/5.87 thf(fact_955_Nat_Odiff__add__assoc2,axiom,
% 5.49/5.87 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.49/5.87 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.diff_add_assoc2
% 5.49/5.87 thf(fact_956_Nat_Ole__imp__diff__is__add,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.87 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.49/5.87 = K )
% 5.49/5.87 = ( J
% 5.49/5.87 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Nat.le_imp_diff_is_add
% 5.49/5.87 thf(fact_957_one__le__numeral,axiom,
% 5.49/5.87 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_numeral
% 5.49/5.87 thf(fact_958_one__le__numeral,axiom,
% 5.49/5.87 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_numeral
% 5.49/5.87 thf(fact_959_one__le__numeral,axiom,
% 5.49/5.87 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_numeral
% 5.49/5.87 thf(fact_960_one__le__numeral,axiom,
% 5.49/5.87 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_numeral
% 5.49/5.87 thf(fact_961_not__numeral__less__one,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.49/5.87
% 5.49/5.87 % not_numeral_less_one
% 5.49/5.87 thf(fact_962_not__numeral__less__one,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.49/5.87
% 5.49/5.87 % not_numeral_less_one
% 5.49/5.87 thf(fact_963_not__numeral__less__one,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.49/5.87
% 5.49/5.87 % not_numeral_less_one
% 5.49/5.87 thf(fact_964_not__numeral__less__one,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.49/5.87
% 5.49/5.87 % not_numeral_less_one
% 5.49/5.87 thf(fact_965_one__plus__numeral__commute,axiom,
% 5.49/5.87 ! [X: num] :
% 5.49/5.87 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.49/5.87 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_plus_numeral_commute
% 5.49/5.87 thf(fact_966_one__plus__numeral__commute,axiom,
% 5.49/5.87 ! [X: num] :
% 5.49/5.87 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.49/5.87 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_plus_numeral_commute
% 5.49/5.87 thf(fact_967_one__plus__numeral__commute,axiom,
% 5.49/5.87 ! [X: num] :
% 5.49/5.87 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.49/5.87 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_plus_numeral_commute
% 5.49/5.87 thf(fact_968_one__plus__numeral__commute,axiom,
% 5.49/5.87 ! [X: num] :
% 5.49/5.87 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.49/5.87 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_plus_numeral_commute
% 5.49/5.87 thf(fact_969_one__plus__numeral__commute,axiom,
% 5.49/5.87 ! [X: num] :
% 5.49/5.87 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.49/5.87 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_plus_numeral_commute
% 5.49/5.87 thf(fact_970_numeral__One,axiom,
% 5.49/5.87 ( ( numera6690914467698888265omplex @ one )
% 5.49/5.87 = one_one_complex ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_One
% 5.49/5.87 thf(fact_971_numeral__One,axiom,
% 5.49/5.87 ( ( numeral_numeral_real @ one )
% 5.49/5.87 = one_one_real ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_One
% 5.49/5.87 thf(fact_972_numeral__One,axiom,
% 5.49/5.87 ( ( numeral_numeral_rat @ one )
% 5.49/5.87 = one_one_rat ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_One
% 5.49/5.87 thf(fact_973_numeral__One,axiom,
% 5.49/5.87 ( ( numeral_numeral_nat @ one )
% 5.49/5.87 = one_one_nat ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_One
% 5.49/5.87 thf(fact_974_numeral__One,axiom,
% 5.49/5.87 ( ( numeral_numeral_int @ one )
% 5.49/5.87 = one_one_int ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_One
% 5.49/5.87 thf(fact_975_one__le__power,axiom,
% 5.49/5.87 ! [A: real,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_power
% 5.49/5.87 thf(fact_976_one__le__power,axiom,
% 5.49/5.87 ! [A: rat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_power
% 5.49/5.87 thf(fact_977_one__le__power,axiom,
% 5.49/5.87 ! [A: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_power
% 5.49/5.87 thf(fact_978_one__le__power,axiom,
% 5.49/5.87 ! [A: int,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % one_le_power
% 5.49/5.87 thf(fact_979_left__right__inverse__power,axiom,
% 5.49/5.87 ! [X: complex,Y2: complex,N: nat] :
% 5.49/5.87 ( ( ( times_times_complex @ X @ Y2 )
% 5.49/5.87 = one_one_complex )
% 5.49/5.87 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.49/5.87 = one_one_complex ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_right_inverse_power
% 5.49/5.87 thf(fact_980_left__right__inverse__power,axiom,
% 5.49/5.87 ! [X: real,Y2: real,N: nat] :
% 5.49/5.87 ( ( ( times_times_real @ X @ Y2 )
% 5.49/5.87 = one_one_real )
% 5.49/5.87 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.49/5.87 = one_one_real ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_right_inverse_power
% 5.49/5.87 thf(fact_981_left__right__inverse__power,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat,N: nat] :
% 5.49/5.87 ( ( ( times_times_rat @ X @ Y2 )
% 5.49/5.87 = one_one_rat )
% 5.49/5.87 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.49/5.87 = one_one_rat ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_right_inverse_power
% 5.49/5.87 thf(fact_982_left__right__inverse__power,axiom,
% 5.49/5.87 ! [X: nat,Y2: nat,N: nat] :
% 5.49/5.87 ( ( ( times_times_nat @ X @ Y2 )
% 5.49/5.87 = one_one_nat )
% 5.49/5.87 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) )
% 5.49/5.87 = one_one_nat ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_right_inverse_power
% 5.49/5.87 thf(fact_983_left__right__inverse__power,axiom,
% 5.49/5.87 ! [X: int,Y2: int,N: nat] :
% 5.49/5.87 ( ( ( times_times_int @ X @ Y2 )
% 5.49/5.87 = one_one_int )
% 5.49/5.87 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.49/5.87 = one_one_int ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_right_inverse_power
% 5.49/5.87 thf(fact_984_power__one__over,axiom,
% 5.49/5.87 ! [A: complex,N: nat] :
% 5.49/5.87 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.49/5.87 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_one_over
% 5.49/5.87 thf(fact_985_power__one__over,axiom,
% 5.49/5.87 ! [A: real,N: nat] :
% 5.49/5.87 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.49/5.87 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_one_over
% 5.49/5.87 thf(fact_986_power__one__over,axiom,
% 5.49/5.87 ! [A: rat,N: nat] :
% 5.49/5.87 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.49/5.87 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_one_over
% 5.49/5.87 thf(fact_987_numerals_I1_J,axiom,
% 5.49/5.87 ( ( numeral_numeral_nat @ one )
% 5.49/5.87 = one_one_nat ) ).
% 5.49/5.87
% 5.49/5.87 % numerals(1)
% 5.49/5.87 thf(fact_988_Suc__eq__plus1,axiom,
% 5.49/5.87 ( suc
% 5.49/5.87 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Suc_eq_plus1
% 5.49/5.87 thf(fact_989_plus__1__eq__Suc,axiom,
% 5.49/5.87 ( ( plus_plus_nat @ one_one_nat )
% 5.49/5.87 = suc ) ).
% 5.49/5.87
% 5.49/5.87 % plus_1_eq_Suc
% 5.49/5.87 thf(fact_990_Suc__eq__plus1__left,axiom,
% 5.49/5.87 ( suc
% 5.49/5.87 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.49/5.87
% 5.49/5.87 % Suc_eq_plus1_left
% 5.49/5.87 thf(fact_991_option_Oexhaust__sel,axiom,
% 5.49/5.87 ! [Option: option_nat] :
% 5.49/5.87 ( ( Option != none_nat )
% 5.49/5.87 => ( Option
% 5.49/5.87 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.exhaust_sel
% 5.49/5.87 thf(fact_992_option_Oexhaust__sel,axiom,
% 5.49/5.87 ! [Option: option4927543243414619207at_nat] :
% 5.49/5.87 ( ( Option != none_P5556105721700978146at_nat )
% 5.49/5.87 => ( Option
% 5.49/5.87 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.exhaust_sel
% 5.49/5.87 thf(fact_993_option_Oexhaust__sel,axiom,
% 5.49/5.87 ! [Option: option_num] :
% 5.49/5.87 ( ( Option != none_num )
% 5.49/5.87 => ( Option
% 5.49/5.87 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % option.exhaust_sel
% 5.49/5.87 thf(fact_994_less__diff__conv2,axiom,
% 5.49/5.87 ! [K: nat,J: nat,I2: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ K @ J )
% 5.49/5.87 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.49/5.87 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_diff_conv2
% 5.49/5.87 thf(fact_995_nat__eq__add__iff1,axiom,
% 5.49/5.87 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ J @ I2 )
% 5.49/5.87 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 5.49/5.87 = N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_eq_add_iff1
% 5.49/5.87 thf(fact_996_nat__eq__add__iff2,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.87 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( M
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_eq_add_iff2
% 5.49/5.87 thf(fact_997_nat__le__add__iff1,axiom,
% 5.49/5.87 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ J @ I2 )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_le_add_iff1
% 5.49/5.87 thf(fact_998_nat__le__add__iff2,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_le_add_iff2
% 5.49/5.87 thf(fact_999_nat__diff__add__eq1,axiom,
% 5.49/5.87 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ J @ I2 )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_diff_add_eq1
% 5.49/5.87 thf(fact_1000_nat__diff__add__eq2,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.87 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_diff_add_eq2
% 5.49/5.87 thf(fact_1001_gt__half__sum,axiom,
% 5.49/5.87 ! [A: real,B: real] :
% 5.49/5.87 ( ( ord_less_real @ A @ B )
% 5.49/5.87 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % gt_half_sum
% 5.49/5.87 thf(fact_1002_gt__half__sum,axiom,
% 5.49/5.87 ! [A: rat,B: rat] :
% 5.49/5.87 ( ( ord_less_rat @ A @ B )
% 5.49/5.87 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.49/5.87
% 5.49/5.87 % gt_half_sum
% 5.49/5.87 thf(fact_1003_less__half__sum,axiom,
% 5.49/5.87 ! [A: real,B: real] :
% 5.49/5.87 ( ( ord_less_real @ A @ B )
% 5.49/5.87 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_half_sum
% 5.49/5.87 thf(fact_1004_less__half__sum,axiom,
% 5.49/5.87 ! [A: rat,B: rat] :
% 5.49/5.87 ( ( ord_less_rat @ A @ B )
% 5.49/5.87 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_half_sum
% 5.49/5.87 thf(fact_1005_power__less__power__Suc,axiom,
% 5.49/5.87 ! [A: real,N: nat] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_power_Suc
% 5.49/5.87 thf(fact_1006_power__less__power__Suc,axiom,
% 5.49/5.87 ! [A: rat,N: nat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_power_Suc
% 5.49/5.87 thf(fact_1007_power__less__power__Suc,axiom,
% 5.49/5.87 ! [A: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_power_Suc
% 5.49/5.87 thf(fact_1008_power__less__power__Suc,axiom,
% 5.49/5.87 ! [A: int,N: nat] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_power_Suc
% 5.49/5.87 thf(fact_1009_power__gt1__lemma,axiom,
% 5.49/5.87 ! [A: real,N: nat] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1_lemma
% 5.49/5.87 thf(fact_1010_power__gt1__lemma,axiom,
% 5.49/5.87 ! [A: rat,N: nat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1_lemma
% 5.49/5.87 thf(fact_1011_power__gt1__lemma,axiom,
% 5.49/5.87 ! [A: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1_lemma
% 5.49/5.87 thf(fact_1012_power__gt1__lemma,axiom,
% 5.49/5.87 ! [A: int,N: nat] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1_lemma
% 5.49/5.87 thf(fact_1013_power__gt1,axiom,
% 5.49/5.87 ! [A: real,N: nat] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1
% 5.49/5.87 thf(fact_1014_power__gt1,axiom,
% 5.49/5.87 ! [A: rat,N: nat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1
% 5.49/5.87 thf(fact_1015_power__gt1,axiom,
% 5.49/5.87 ! [A: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1
% 5.49/5.87 thf(fact_1016_power__gt1,axiom,
% 5.49/5.87 ! [A: int,N: nat] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_gt1
% 5.49/5.87 thf(fact_1017_power__less__imp__less__exp,axiom,
% 5.49/5.87 ! [A: real,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.49/5.87 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_imp_less_exp
% 5.49/5.87 thf(fact_1018_power__less__imp__less__exp,axiom,
% 5.49/5.87 ! [A: rat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.49/5.87 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_imp_less_exp
% 5.49/5.87 thf(fact_1019_power__less__imp__less__exp,axiom,
% 5.49/5.87 ! [A: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.49/5.87 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_imp_less_exp
% 5.49/5.87 thf(fact_1020_power__less__imp__less__exp,axiom,
% 5.49/5.87 ! [A: int,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.49/5.87 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_less_imp_less_exp
% 5.49/5.87 thf(fact_1021_power__strict__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: real] :
% 5.49/5.87 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_strict_increasing
% 5.49/5.87 thf(fact_1022_power__strict__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: rat] :
% 5.49/5.87 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_strict_increasing
% 5.49/5.87 thf(fact_1023_power__strict__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: nat] :
% 5.49/5.87 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_strict_increasing
% 5.49/5.87 thf(fact_1024_power__strict__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: int] :
% 5.49/5.87 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_strict_increasing
% 5.49/5.87 thf(fact_1025_power__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: real] :
% 5.49/5.87 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.49/5.87 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_increasing
% 5.49/5.87 thf(fact_1026_power__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: rat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_increasing
% 5.49/5.87 thf(fact_1027_power__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_increasing
% 5.49/5.87 thf(fact_1028_power__increasing,axiom,
% 5.49/5.87 ! [N: nat,N5: nat,A: int] :
% 5.49/5.87 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.87 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.49/5.87 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_increasing
% 5.49/5.87 thf(fact_1029_power2__commute,axiom,
% 5.49/5.87 ! [X: complex,Y2: complex] :
% 5.49/5.87 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( power_power_complex @ ( minus_minus_complex @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_commute
% 5.49/5.87 thf(fact_1030_power2__commute,axiom,
% 5.49/5.87 ! [X: real,Y2: real] :
% 5.49/5.87 ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( power_power_real @ ( minus_minus_real @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_commute
% 5.49/5.87 thf(fact_1031_power2__commute,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat] :
% 5.49/5.87 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( power_power_rat @ ( minus_minus_rat @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_commute
% 5.49/5.87 thf(fact_1032_power2__commute,axiom,
% 5.49/5.87 ! [X: int,Y2: int] :
% 5.49/5.87 ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( power_power_int @ ( minus_minus_int @ Y2 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_commute
% 5.49/5.87 thf(fact_1033_nat__less__add__iff2,axiom,
% 5.49/5.87 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.87 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_less_add_iff2
% 5.49/5.87 thf(fact_1034_nat__less__add__iff1,axiom,
% 5.49/5.87 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ J @ I2 )
% 5.49/5.87 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.49/5.87 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_less_add_iff1
% 5.49/5.87 thf(fact_1035_power__le__imp__le__exp,axiom,
% 5.49/5.87 ! [A: real,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.87 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.49/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_le_imp_le_exp
% 5.49/5.87 thf(fact_1036_power__le__imp__le__exp,axiom,
% 5.49/5.87 ! [A: rat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.87 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.49/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_le_imp_le_exp
% 5.49/5.87 thf(fact_1037_power__le__imp__le__exp,axiom,
% 5.49/5.87 ! [A: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.49/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_le_imp_le_exp
% 5.49/5.87 thf(fact_1038_power__le__imp__le__exp,axiom,
% 5.49/5.87 ! [A: int,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.87 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.49/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_le_imp_le_exp
% 5.49/5.87 thf(fact_1039_one__power2,axiom,
% 5.49/5.87 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = one_one_rat ) ).
% 5.49/5.87
% 5.49/5.87 % one_power2
% 5.49/5.87 thf(fact_1040_one__power2,axiom,
% 5.49/5.87 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = one_one_nat ) ).
% 5.49/5.87
% 5.49/5.87 % one_power2
% 5.49/5.87 thf(fact_1041_one__power2,axiom,
% 5.49/5.87 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = one_one_real ) ).
% 5.49/5.87
% 5.49/5.87 % one_power2
% 5.49/5.87 thf(fact_1042_one__power2,axiom,
% 5.49/5.87 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = one_one_int ) ).
% 5.49/5.87
% 5.49/5.87 % one_power2
% 5.49/5.87 thf(fact_1043_one__power2,axiom,
% 5.49/5.87 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = one_one_complex ) ).
% 5.49/5.87
% 5.49/5.87 % one_power2
% 5.49/5.87 thf(fact_1044_nat__1__add__1,axiom,
% 5.49/5.87 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.49/5.87 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nat_1_add_1
% 5.49/5.87 thf(fact_1045_diff__le__diff__pow,axiom,
% 5.49/5.87 ! [K: nat,M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.49/5.87 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % diff_le_diff_pow
% 5.49/5.87 thf(fact_1046_power2__diff,axiom,
% 5.49/5.87 ! [X: complex,Y2: complex] :
% 5.49/5.87 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_diff
% 5.49/5.87 thf(fact_1047_power2__diff,axiom,
% 5.49/5.87 ! [X: real,Y2: real] :
% 5.49/5.87 ( ( power_power_real @ ( minus_minus_real @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_diff
% 5.49/5.87 thf(fact_1048_power2__diff,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat] :
% 5.49/5.87 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_diff
% 5.49/5.87 thf(fact_1049_power2__diff,axiom,
% 5.49/5.87 ! [X: int,Y2: int] :
% 5.49/5.87 ( ( power_power_int @ ( minus_minus_int @ X @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.87 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power2_diff
% 5.49/5.87 thf(fact_1050_ex__power__ivl1,axiom,
% 5.49/5.87 ! [B: nat,K: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.49/5.87 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.49/5.87 => ? [N3: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.49/5.87 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ex_power_ivl1
% 5.49/5.87 thf(fact_1051_ex__power__ivl2,axiom,
% 5.49/5.87 ! [B: nat,K: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.49/5.87 => ? [N3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.49/5.87 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ex_power_ivl2
% 5.49/5.87 thf(fact_1052_le__add__diff__inverse,axiom,
% 5.49/5.87 ! [B: real,A: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.87 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse
% 5.49/5.87 thf(fact_1053_le__add__diff__inverse,axiom,
% 5.49/5.87 ! [B: rat,A: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.87 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse
% 5.49/5.87 thf(fact_1054_le__add__diff__inverse,axiom,
% 5.49/5.87 ! [B: nat,A: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.87 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse
% 5.49/5.87 thf(fact_1055_le__add__diff__inverse,axiom,
% 5.49/5.87 ! [B: int,A: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.87 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse
% 5.49/5.87 thf(fact_1056_le__add__diff__inverse2,axiom,
% 5.49/5.87 ! [B: real,A: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.87 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse2
% 5.49/5.87 thf(fact_1057_le__add__diff__inverse2,axiom,
% 5.49/5.87 ! [B: rat,A: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.87 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse2
% 5.49/5.87 thf(fact_1058_le__add__diff__inverse2,axiom,
% 5.49/5.87 ! [B: nat,A: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.87 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse2
% 5.49/5.87 thf(fact_1059_le__add__diff__inverse2,axiom,
% 5.49/5.87 ! [B: int,A: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.87 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % le_add_diff_inverse2
% 5.49/5.87 thf(fact_1060_vebt__insert_Osimps_I4_J,axiom,
% 5.49/5.87 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.49/5.87 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_insert.simps(4)
% 5.49/5.87 thf(fact_1061__C1_C,axiom,
% 5.49/5.87 ( ( ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 != none_nat )
% 5.49/5.87 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.49/5.87 = ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 & ( ~ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 != none_nat )
% 5.49/5.87 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.49/5.87 = ( if_option_nat
% 5.49/5.87 @ ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.87 = none_nat )
% 5.49/5.87 @ ( if_option_nat @ ( ord_less_nat @ mi @ xa ) @ ( some_nat @ mi ) @ none_nat )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % "1"
% 5.49/5.87 thf(fact_1062_vebt__maxt_Osimps_I3_J,axiom,
% 5.49/5.87 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.49/5.87 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.49/5.87 = ( some_nat @ Ma ) ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_maxt.simps(3)
% 5.49/5.87 thf(fact_1063_vebt__mint_Osimps_I3_J,axiom,
% 5.49/5.87 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.49/5.87 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.49/5.87 = ( some_nat @ Mi ) ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_mint.simps(3)
% 5.49/5.87 thf(fact_1064_div__by__1,axiom,
% 5.49/5.87 ! [A: complex] :
% 5.49/5.87 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % div_by_1
% 5.49/5.87 thf(fact_1065_div__by__1,axiom,
% 5.49/5.87 ! [A: real] :
% 5.49/5.87 ( ( divide_divide_real @ A @ one_one_real )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % div_by_1
% 5.49/5.87 thf(fact_1066_div__by__1,axiom,
% 5.49/5.87 ! [A: rat] :
% 5.49/5.87 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % div_by_1
% 5.49/5.87 thf(fact_1067_div__by__1,axiom,
% 5.49/5.87 ! [A: nat] :
% 5.49/5.87 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % div_by_1
% 5.49/5.87 thf(fact_1068_div__by__1,axiom,
% 5.49/5.87 ! [A: int] :
% 5.49/5.87 ( ( divide_divide_int @ A @ one_one_int )
% 5.49/5.87 = A ) ).
% 5.49/5.87
% 5.49/5.87 % div_by_1
% 5.49/5.87 thf(fact_1069_vebt__maxt_Osimps_I2_J,axiom,
% 5.49/5.87 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.49/5.87 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.49/5.87 = none_nat ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_maxt.simps(2)
% 5.49/5.87 thf(fact_1070_pred__less__length__list,axiom,
% 5.49/5.87 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.87 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.49/5.87 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( if_option_nat
% 5.49/5.87 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 != none_nat )
% 5.49/5.87 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.49/5.87 @ ( if_option_nat
% 5.49/5.87 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.87 = none_nat )
% 5.49/5.87 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % pred_less_length_list
% 5.49/5.87 thf(fact_1071_pred__lesseq__max,axiom,
% 5.49/5.87 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.87 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 @ ( if_option_nat
% 5.49/5.87 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 != none_nat )
% 5.49/5.87 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.49/5.87 @ ( if_option_nat
% 5.49/5.87 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.87 = none_nat )
% 5.49/5.87 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.87 @ none_nat ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % pred_lesseq_max
% 5.49/5.87 thf(fact_1072_vebt__mint_Osimps_I2_J,axiom,
% 5.49/5.87 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.49/5.87 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.49/5.87 = none_nat ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_mint.simps(2)
% 5.49/5.87 thf(fact_1073_set__vebt_H__def,axiom,
% 5.49/5.87 ( vEBT_VEBT_set_vebt
% 5.49/5.87 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_vebt'_def
% 5.49/5.87 thf(fact_1074_lambda__one,axiom,
% 5.49/5.87 ( ( ^ [X2: complex] : X2 )
% 5.49/5.87 = ( times_times_complex @ one_one_complex ) ) ).
% 5.49/5.87
% 5.49/5.87 % lambda_one
% 5.49/5.87 thf(fact_1075_lambda__one,axiom,
% 5.49/5.87 ( ( ^ [X2: real] : X2 )
% 5.49/5.87 = ( times_times_real @ one_one_real ) ) ).
% 5.49/5.87
% 5.49/5.87 % lambda_one
% 5.49/5.87 thf(fact_1076_lambda__one,axiom,
% 5.49/5.87 ( ( ^ [X2: rat] : X2 )
% 5.49/5.87 = ( times_times_rat @ one_one_rat ) ) ).
% 5.49/5.87
% 5.49/5.87 % lambda_one
% 5.49/5.87 thf(fact_1077_lambda__one,axiom,
% 5.49/5.87 ( ( ^ [X2: nat] : X2 )
% 5.49/5.87 = ( times_times_nat @ one_one_nat ) ) ).
% 5.49/5.87
% 5.49/5.87 % lambda_one
% 5.49/5.87 thf(fact_1078_lambda__one,axiom,
% 5.49/5.87 ( ( ^ [X2: int] : X2 )
% 5.49/5.87 = ( times_times_int @ one_one_int ) ) ).
% 5.49/5.87
% 5.49/5.87 % lambda_one
% 5.49/5.87 thf(fact_1079_numeral__code_I2_J,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.49/5.87 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_code(2)
% 5.49/5.87 thf(fact_1080_numeral__code_I2_J,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.49/5.87 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_code(2)
% 5.49/5.87 thf(fact_1081_numeral__code_I2_J,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.49/5.87 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_code(2)
% 5.49/5.87 thf(fact_1082_numeral__code_I2_J,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.49/5.87 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_code(2)
% 5.49/5.87 thf(fact_1083_numeral__code_I2_J,axiom,
% 5.49/5.87 ! [N: num] :
% 5.49/5.87 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.49/5.87 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % numeral_code(2)
% 5.49/5.87 thf(fact_1084_set__vebt__def,axiom,
% 5.49/5.87 ( vEBT_set_vebt
% 5.49/5.87 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_vebt_def
% 5.49/5.87 thf(fact_1085_add__diff__assoc__enat,axiom,
% 5.49/5.87 ! [Z: extended_enat,Y2: extended_enat,X: extended_enat] :
% 5.49/5.87 ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 5.49/5.87 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 5.49/5.87 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y2 ) @ Z ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_diff_assoc_enat
% 5.49/5.87 thf(fact_1086_power__numeral__even,axiom,
% 5.49/5.87 ! [Z: complex,W: num] :
% 5.49/5.87 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_numeral_even
% 5.49/5.87 thf(fact_1087_power__numeral__even,axiom,
% 5.49/5.87 ! [Z: real,W: num] :
% 5.49/5.87 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_numeral_even
% 5.49/5.87 thf(fact_1088_power__numeral__even,axiom,
% 5.49/5.87 ! [Z: rat,W: num] :
% 5.49/5.87 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_numeral_even
% 5.49/5.87 thf(fact_1089_power__numeral__even,axiom,
% 5.49/5.87 ! [Z: nat,W: num] :
% 5.49/5.87 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_numeral_even
% 5.49/5.87 thf(fact_1090_power__numeral__even,axiom,
% 5.49/5.87 ! [Z: int,W: num] :
% 5.49/5.87 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % power_numeral_even
% 5.49/5.87 thf(fact_1091_real__arch__pow,axiom,
% 5.49/5.87 ! [X: real,Y2: real] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ X )
% 5.49/5.87 => ? [N3: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X @ N3 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % real_arch_pow
% 5.49/5.87 thf(fact_1092_linorder__neqE__linordered__idom,axiom,
% 5.49/5.87 ! [X: real,Y2: real] :
% 5.49/5.87 ( ( X != Y2 )
% 5.49/5.87 => ( ~ ( ord_less_real @ X @ Y2 )
% 5.49/5.87 => ( ord_less_real @ Y2 @ X ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % linorder_neqE_linordered_idom
% 5.49/5.87 thf(fact_1093_linorder__neqE__linordered__idom,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat] :
% 5.49/5.87 ( ( X != Y2 )
% 5.49/5.87 => ( ~ ( ord_less_rat @ X @ Y2 )
% 5.49/5.87 => ( ord_less_rat @ Y2 @ X ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % linorder_neqE_linordered_idom
% 5.49/5.87 thf(fact_1094_linorder__neqE__linordered__idom,axiom,
% 5.49/5.87 ! [X: int,Y2: int] :
% 5.49/5.87 ( ( X != Y2 )
% 5.49/5.87 => ( ~ ( ord_less_int @ X @ Y2 )
% 5.49/5.87 => ( ord_less_int @ Y2 @ X ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % linorder_neqE_linordered_idom
% 5.49/5.87 thf(fact_1095_two__realpow__ge__one,axiom,
% 5.49/5.87 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.49/5.87
% 5.49/5.87 % two_realpow_ge_one
% 5.49/5.87 thf(fact_1096_ring__class_Oring__distribs_I2_J,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(2)
% 5.49/5.87 thf(fact_1097_ring__class_Oring__distribs_I2_J,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(2)
% 5.49/5.87 thf(fact_1098_ring__class_Oring__distribs_I2_J,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(2)
% 5.49/5.87 thf(fact_1099_ring__class_Oring__distribs_I1_J,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(1)
% 5.49/5.87 thf(fact_1100_ring__class_Oring__distribs_I1_J,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(1)
% 5.49/5.87 thf(fact_1101_ring__class_Oring__distribs_I1_J,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ring_class.ring_distribs(1)
% 5.49/5.87 thf(fact_1102_comm__semiring__class_Odistrib,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % comm_semiring_class.distrib
% 5.49/5.87 thf(fact_1103_comm__semiring__class_Odistrib,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % comm_semiring_class.distrib
% 5.49/5.87 thf(fact_1104_comm__semiring__class_Odistrib,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % comm_semiring_class.distrib
% 5.49/5.87 thf(fact_1105_comm__semiring__class_Odistrib,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % comm_semiring_class.distrib
% 5.49/5.87 thf(fact_1106_distrib__left,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_left
% 5.49/5.87 thf(fact_1107_distrib__left,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_left
% 5.49/5.87 thf(fact_1108_distrib__left,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_left
% 5.49/5.87 thf(fact_1109_distrib__left,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_left
% 5.49/5.87 thf(fact_1110_distrib__right,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_right
% 5.49/5.87 thf(fact_1111_distrib__right,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_right
% 5.49/5.87 thf(fact_1112_distrib__right,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_right
% 5.49/5.87 thf(fact_1113_distrib__right,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % distrib_right
% 5.49/5.87 thf(fact_1114_combine__common__factor,axiom,
% 5.49/5.87 ! [A: real,E: real,B: real,C: real] :
% 5.49/5.87 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % combine_common_factor
% 5.49/5.87 thf(fact_1115_combine__common__factor,axiom,
% 5.49/5.87 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % combine_common_factor
% 5.49/5.87 thf(fact_1116_combine__common__factor,axiom,
% 5.49/5.87 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.49/5.87 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % combine_common_factor
% 5.49/5.87 thf(fact_1117_combine__common__factor,axiom,
% 5.49/5.87 ! [A: int,E: int,B: int,C: int] :
% 5.49/5.87 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % combine_common_factor
% 5.49/5.87 thf(fact_1118_left__diff__distrib,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib
% 5.49/5.87 thf(fact_1119_left__diff__distrib,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib
% 5.49/5.87 thf(fact_1120_left__diff__distrib,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.87 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib
% 5.49/5.87 thf(fact_1121_right__diff__distrib,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.49/5.87 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib
% 5.49/5.87 thf(fact_1122_right__diff__distrib,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib
% 5.49/5.87 thf(fact_1123_right__diff__distrib,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.49/5.87 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib
% 5.49/5.87 thf(fact_1124_left__diff__distrib_H,axiom,
% 5.49/5.87 ! [B: real,C: real,A: real] :
% 5.49/5.87 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.49/5.87 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib'
% 5.49/5.87 thf(fact_1125_left__diff__distrib_H,axiom,
% 5.49/5.87 ! [B: rat,C: rat,A: rat] :
% 5.49/5.87 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.49/5.87 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib'
% 5.49/5.87 thf(fact_1126_left__diff__distrib_H,axiom,
% 5.49/5.87 ! [B: nat,C: nat,A: nat] :
% 5.49/5.87 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.49/5.87 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib'
% 5.49/5.87 thf(fact_1127_left__diff__distrib_H,axiom,
% 5.49/5.87 ! [B: int,C: int,A: int] :
% 5.49/5.87 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.49/5.87 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % left_diff_distrib'
% 5.49/5.87 thf(fact_1128_right__diff__distrib_H,axiom,
% 5.49/5.87 ! [A: real,B: real,C: real] :
% 5.49/5.87 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.49/5.87 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib'
% 5.49/5.87 thf(fact_1129_right__diff__distrib_H,axiom,
% 5.49/5.87 ! [A: rat,B: rat,C: rat] :
% 5.49/5.87 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib'
% 5.49/5.87 thf(fact_1130_right__diff__distrib_H,axiom,
% 5.49/5.87 ! [A: nat,B: nat,C: nat] :
% 5.49/5.87 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.49/5.87 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib'
% 5.49/5.87 thf(fact_1131_right__diff__distrib_H,axiom,
% 5.49/5.87 ! [A: int,B: int,C: int] :
% 5.49/5.87 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.49/5.87 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % right_diff_distrib'
% 5.49/5.87 thf(fact_1132_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.49/5.87 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.49/5.87 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.49/5.87 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(3)
% 5.49/5.87 thf(fact_1133_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.49/5.87 ! [F: num > num > num,A: num,B: num] :
% 5.49/5.87 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.49/5.87 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(3)
% 5.49/5.87 thf(fact_1134_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.49/5.87 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.49/5.87 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.49/5.87 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(3)
% 5.49/5.87 thf(fact_1135_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.49/5.87 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.49/5.87 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.49/5.87 = none_P5556105721700978146at_nat ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(1)
% 5.49/5.87 thf(fact_1136_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.49/5.87 ! [Uu: num > num > num,Uv: option_num] :
% 5.49/5.87 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.49/5.87 = none_num ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(1)
% 5.49/5.87 thf(fact_1137_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.49/5.87 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.49/5.87 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.49/5.87 = none_nat ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(1)
% 5.49/5.87 thf(fact_1138_less__1__mult,axiom,
% 5.49/5.87 ! [M: real,N: real] :
% 5.49/5.87 ( ( ord_less_real @ one_one_real @ M )
% 5.49/5.87 => ( ( ord_less_real @ one_one_real @ N )
% 5.49/5.87 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_1_mult
% 5.49/5.87 thf(fact_1139_less__1__mult,axiom,
% 5.49/5.87 ! [M: rat,N: rat] :
% 5.49/5.87 ( ( ord_less_rat @ one_one_rat @ M )
% 5.49/5.87 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.49/5.87 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_1_mult
% 5.49/5.87 thf(fact_1140_less__1__mult,axiom,
% 5.49/5.87 ! [M: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_nat @ one_one_nat @ M )
% 5.49/5.87 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.49/5.87 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_1_mult
% 5.49/5.87 thf(fact_1141_less__1__mult,axiom,
% 5.49/5.87 ! [M: int,N: int] :
% 5.49/5.87 ( ( ord_less_int @ one_one_int @ M )
% 5.49/5.87 => ( ( ord_less_int @ one_one_int @ N )
% 5.49/5.87 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_1_mult
% 5.49/5.87 thf(fact_1142_add__le__add__imp__diff__le,axiom,
% 5.49/5.87 ! [I2: real,K: real,N: real,J: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.49/5.87 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.49/5.87 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_add_imp_diff_le
% 5.49/5.87 thf(fact_1143_add__le__add__imp__diff__le,axiom,
% 5.49/5.87 ! [I2: rat,K: rat,N: rat,J: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.49/5.87 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.49/5.87 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_add_imp_diff_le
% 5.49/5.87 thf(fact_1144_add__le__add__imp__diff__le,axiom,
% 5.49/5.87 ! [I2: nat,K: nat,N: nat,J: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.49/5.87 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.49/5.87 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_add_imp_diff_le
% 5.49/5.87 thf(fact_1145_add__le__add__imp__diff__le,axiom,
% 5.49/5.87 ! [I2: int,K: int,N: int,J: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.49/5.87 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.49/5.87 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.49/5.87 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_add_imp_diff_le
% 5.49/5.87 thf(fact_1146_add__le__imp__le__diff,axiom,
% 5.49/5.87 ! [I2: real,K: real,N: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N )
% 5.49/5.87 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_imp_le_diff
% 5.49/5.87 thf(fact_1147_add__le__imp__le__diff,axiom,
% 5.49/5.87 ! [I2: rat,K: rat,N: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_imp_le_diff
% 5.49/5.87 thf(fact_1148_add__le__imp__le__diff,axiom,
% 5.49/5.87 ! [I2: nat,K: nat,N: nat] :
% 5.49/5.87 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N )
% 5.49/5.87 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_imp_le_diff
% 5.49/5.87 thf(fact_1149_add__le__imp__le__diff,axiom,
% 5.49/5.87 ! [I2: int,K: int,N: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N )
% 5.49/5.87 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_le_imp_le_diff
% 5.49/5.87 thf(fact_1150_add__mono1,axiom,
% 5.49/5.87 ! [A: real,B: real] :
% 5.49/5.87 ( ( ord_less_real @ A @ B )
% 5.49/5.87 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_mono1
% 5.49/5.87 thf(fact_1151_add__mono1,axiom,
% 5.49/5.87 ! [A: rat,B: rat] :
% 5.49/5.87 ( ( ord_less_rat @ A @ B )
% 5.49/5.87 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_mono1
% 5.49/5.87 thf(fact_1152_add__mono1,axiom,
% 5.49/5.87 ! [A: nat,B: nat] :
% 5.49/5.87 ( ( ord_less_nat @ A @ B )
% 5.49/5.87 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_mono1
% 5.49/5.87 thf(fact_1153_add__mono1,axiom,
% 5.49/5.87 ! [A: int,B: int] :
% 5.49/5.87 ( ( ord_less_int @ A @ B )
% 5.49/5.87 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % add_mono1
% 5.49/5.87 thf(fact_1154_less__add__one,axiom,
% 5.49/5.87 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_one
% 5.49/5.87 thf(fact_1155_less__add__one,axiom,
% 5.49/5.87 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_one
% 5.49/5.87 thf(fact_1156_less__add__one,axiom,
% 5.49/5.87 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_one
% 5.49/5.87 thf(fact_1157_less__add__one,axiom,
% 5.49/5.87 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_one
% 5.49/5.87 thf(fact_1158_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.49/5.87 ! [A: real,B: real] :
% 5.49/5.87 ( ~ ( ord_less_real @ A @ B )
% 5.49/5.87 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % linordered_semidom_class.add_diff_inverse
% 5.49/5.87 thf(fact_1159_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.49/5.87 ! [A: rat,B: rat] :
% 5.49/5.87 ( ~ ( ord_less_rat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % linordered_semidom_class.add_diff_inverse
% 5.49/5.87 thf(fact_1160_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.49/5.87 ! [A: nat,B: nat] :
% 5.49/5.87 ( ~ ( ord_less_nat @ A @ B )
% 5.49/5.87 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % linordered_semidom_class.add_diff_inverse
% 5.49/5.87 thf(fact_1161_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.49/5.87 ! [A: int,B: int] :
% 5.49/5.87 ( ~ ( ord_less_int @ A @ B )
% 5.49/5.87 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.49/5.87 = A ) ) ).
% 5.49/5.87
% 5.49/5.87 % linordered_semidom_class.add_diff_inverse
% 5.49/5.87 thf(fact_1162_square__diff__square__factored,axiom,
% 5.49/5.87 ! [X: real,Y2: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.49/5.87 = ( times_times_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ X @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_square_factored
% 5.49/5.87 thf(fact_1163_square__diff__square__factored,axiom,
% 5.49/5.87 ! [X: rat,Y2: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.49/5.87 = ( times_times_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( minus_minus_rat @ X @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_square_factored
% 5.49/5.87 thf(fact_1164_square__diff__square__factored,axiom,
% 5.49/5.87 ! [X: int,Y2: int] :
% 5.49/5.87 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.49/5.87 = ( times_times_int @ ( plus_plus_int @ X @ Y2 ) @ ( minus_minus_int @ X @ Y2 ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_square_factored
% 5.49/5.87 thf(fact_1165_eq__add__iff2,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( C
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff2
% 5.49/5.87 thf(fact_1166_eq__add__iff2,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( C
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff2
% 5.49/5.87 thf(fact_1167_eq__add__iff2,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( C
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff2
% 5.49/5.87 thf(fact_1168_eq__add__iff1,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.49/5.87 = D ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff1
% 5.49/5.87 thf(fact_1169_eq__add__iff1,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.49/5.87 = D ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff1
% 5.49/5.87 thf(fact_1170_eq__add__iff1,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.49/5.87 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.49/5.87 = D ) ) ).
% 5.49/5.87
% 5.49/5.87 % eq_add_iff1
% 5.49/5.87 thf(fact_1171_vebt__pred_Osimps_I7_J,axiom,
% 5.49/5.87 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.49/5.87 ( ( ( ord_less_nat @ Ma @ X )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( some_nat @ Ma ) ) )
% 5.49/5.87 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.49/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 @ ( if_option_nat
% 5.49/5.87 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 != none_nat )
% 5.49/5.87 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 @ ( if_option_nat
% 5.49/5.87 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.87 = none_nat )
% 5.49/5.87 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.49/5.87 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.87 @ none_nat ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_pred.simps(7)
% 5.49/5.87 thf(fact_1172_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.49/5.87 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.49/5.87 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.49/5.87 = none_P5556105721700978146at_nat ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(2)
% 5.49/5.87 thf(fact_1173_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.49/5.87 ! [Uw: num > num > num,V: num] :
% 5.49/5.87 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.49/5.87 = none_num ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(2)
% 5.49/5.87 thf(fact_1174_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.49/5.87 ! [Uw: nat > nat > nat,V: nat] :
% 5.49/5.87 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.49/5.87 = none_nat ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.simps(2)
% 5.49/5.87 thf(fact_1175_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.49/5.87 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb2: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 5.49/5.87 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb2 )
% 5.49/5.87 = Y2 )
% 5.49/5.87 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.49/5.87 => ( Y2 != none_P5556105721700978146at_nat ) )
% 5.49/5.87 => ( ( ? [V2: product_prod_nat_nat] :
% 5.49/5.87 ( Xa2
% 5.49/5.87 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.49/5.87 => ( ( Xb2 = none_P5556105721700978146at_nat )
% 5.49/5.87 => ( Y2 != none_P5556105721700978146at_nat ) ) )
% 5.49/5.87 => ~ ! [A3: product_prod_nat_nat] :
% 5.49/5.87 ( ( Xa2
% 5.49/5.87 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.49/5.87 => ! [B2: product_prod_nat_nat] :
% 5.49/5.87 ( ( Xb2
% 5.49/5.87 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.49/5.87 => ( Y2
% 5.49/5.87 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.elims
% 5.49/5.87 thf(fact_1176_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.49/5.87 ! [X: num > num > num,Xa2: option_num,Xb2: option_num,Y2: option_num] :
% 5.49/5.87 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb2 )
% 5.49/5.87 = Y2 )
% 5.49/5.87 => ( ( ( Xa2 = none_num )
% 5.49/5.87 => ( Y2 != none_num ) )
% 5.49/5.87 => ( ( ? [V2: num] :
% 5.49/5.87 ( Xa2
% 5.49/5.87 = ( some_num @ V2 ) )
% 5.49/5.87 => ( ( Xb2 = none_num )
% 5.49/5.87 => ( Y2 != none_num ) ) )
% 5.49/5.87 => ~ ! [A3: num] :
% 5.49/5.87 ( ( Xa2
% 5.49/5.87 = ( some_num @ A3 ) )
% 5.49/5.87 => ! [B2: num] :
% 5.49/5.87 ( ( Xb2
% 5.49/5.87 = ( some_num @ B2 ) )
% 5.49/5.87 => ( Y2
% 5.49/5.87 != ( some_num @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.elims
% 5.49/5.87 thf(fact_1177_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.49/5.87 ! [X: nat > nat > nat,Xa2: option_nat,Xb2: option_nat,Y2: option_nat] :
% 5.49/5.87 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb2 )
% 5.49/5.87 = Y2 )
% 5.49/5.87 => ( ( ( Xa2 = none_nat )
% 5.49/5.87 => ( Y2 != none_nat ) )
% 5.49/5.87 => ( ( ? [V2: nat] :
% 5.49/5.87 ( Xa2
% 5.49/5.87 = ( some_nat @ V2 ) )
% 5.49/5.87 => ( ( Xb2 = none_nat )
% 5.49/5.87 => ( Y2 != none_nat ) ) )
% 5.49/5.87 => ~ ! [A3: nat] :
% 5.49/5.87 ( ( Xa2
% 5.49/5.87 = ( some_nat @ A3 ) )
% 5.49/5.87 => ! [B2: nat] :
% 5.49/5.87 ( ( Xb2
% 5.49/5.87 = ( some_nat @ B2 ) )
% 5.49/5.87 => ( Y2
% 5.49/5.87 != ( some_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.elims
% 5.49/5.87 thf(fact_1178_ordered__ring__class_Ole__add__iff2,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff2
% 5.49/5.87 thf(fact_1179_ordered__ring__class_Ole__add__iff2,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff2
% 5.49/5.87 thf(fact_1180_ordered__ring__class_Ole__add__iff2,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff2
% 5.49/5.87 thf(fact_1181_ordered__ring__class_Ole__add__iff1,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff1
% 5.49/5.87 thf(fact_1182_ordered__ring__class_Ole__add__iff1,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff1
% 5.49/5.87 thf(fact_1183_ordered__ring__class_Ole__add__iff1,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % ordered_ring_class.le_add_iff1
% 5.49/5.87 thf(fact_1184_less__add__iff2,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff2
% 5.49/5.87 thf(fact_1185_less__add__iff2,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff2
% 5.49/5.87 thf(fact_1186_less__add__iff2,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff2
% 5.49/5.87 thf(fact_1187_less__add__iff1,axiom,
% 5.49/5.87 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.49/5.87 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff1
% 5.49/5.87 thf(fact_1188_less__add__iff1,axiom,
% 5.49/5.87 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.49/5.87 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff1
% 5.49/5.87 thf(fact_1189_less__add__iff1,axiom,
% 5.49/5.87 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.49/5.87 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.49/5.87 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.49/5.87
% 5.49/5.87 % less_add_iff1
% 5.49/5.87 thf(fact_1190_square__diff__one__factored,axiom,
% 5.49/5.87 ! [X: complex] :
% 5.49/5.87 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.49/5.87 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_one_factored
% 5.49/5.87 thf(fact_1191_square__diff__one__factored,axiom,
% 5.49/5.87 ! [X: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.49/5.87 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_one_factored
% 5.49/5.87 thf(fact_1192_square__diff__one__factored,axiom,
% 5.49/5.87 ! [X: rat] :
% 5.49/5.87 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.49/5.87 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_one_factored
% 5.49/5.87 thf(fact_1193_square__diff__one__factored,axiom,
% 5.49/5.87 ! [X: int] :
% 5.49/5.87 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.49/5.87 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % square_diff_one_factored
% 5.49/5.87 thf(fact_1194_vebt__member_Osimps_I5_J,axiom,
% 5.49/5.87 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.49/5.87 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.49/5.87 = ( ( X != Mi )
% 5.49/5.87 => ( ( X != Ma )
% 5.49/5.87 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.49/5.87 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.49/5.87 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.49/5.87 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.49/5.87 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.87 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % vebt_member.simps(5)
% 5.49/5.87 thf(fact_1195_real__average__minus__first,axiom,
% 5.49/5.87 ! [A: real,B: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.49/5.87 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % real_average_minus_first
% 5.49/5.87 thf(fact_1196_real__average__minus__second,axiom,
% 5.49/5.87 ! [B: real,A: real] :
% 5.49/5.87 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.49/5.87 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % real_average_minus_second
% 5.49/5.87 thf(fact_1197_set__conv__nth,axiom,
% 5.49/5.87 ( set_complex2
% 5.49/5.87 = ( ^ [Xs: list_complex] :
% 5.49/5.87 ( collect_complex
% 5.49/5.87 @ ^ [Uu2: complex] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_complex @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1198_set__conv__nth,axiom,
% 5.49/5.87 ( set_real2
% 5.49/5.87 = ( ^ [Xs: list_real] :
% 5.49/5.87 ( collect_real
% 5.49/5.87 @ ^ [Uu2: real] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_real @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1199_set__conv__nth,axiom,
% 5.49/5.87 ( set_list_nat2
% 5.49/5.87 = ( ^ [Xs: list_list_nat] :
% 5.49/5.87 ( collect_list_nat
% 5.49/5.87 @ ^ [Uu2: list_nat] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_list_nat @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_s3023201423986296836st_nat @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1200_set__conv__nth,axiom,
% 5.49/5.87 ( set_VEBT_VEBT2
% 5.49/5.87 = ( ^ [Xs: list_VEBT_VEBT] :
% 5.49/5.87 ( collect_VEBT_VEBT
% 5.49/5.87 @ ^ [Uu2: vEBT_VEBT] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1201_set__conv__nth,axiom,
% 5.49/5.87 ( set_o2
% 5.49/5.87 = ( ^ [Xs: list_o] :
% 5.49/5.87 ( collect_o
% 5.49/5.87 @ ^ [Uu2: $o] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_o @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1202_set__conv__nth,axiom,
% 5.49/5.87 ( set_nat2
% 5.49/5.87 = ( ^ [Xs: list_nat] :
% 5.49/5.87 ( collect_nat
% 5.49/5.87 @ ^ [Uu2: nat] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_nat @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1203_set__conv__nth,axiom,
% 5.49/5.87 ( set_int2
% 5.49/5.87 = ( ^ [Xs: list_int] :
% 5.49/5.87 ( collect_int
% 5.49/5.87 @ ^ [Uu2: int] :
% 5.49/5.87 ? [I3: nat] :
% 5.49/5.87 ( ( Uu2
% 5.49/5.87 = ( nth_int @ Xs @ I3 ) )
% 5.49/5.87 & ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % set_conv_nth
% 5.49/5.87 thf(fact_1204_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.49/5.87 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.49/5.87 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 5.49/5.87 = ( ( X = Mi )
% 5.49/5.87 | ( X = Ma )
% 5.49/5.87 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.49/5.87 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.membermima.simps(4)
% 5.49/5.87 thf(fact_1205_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.49/5.87 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.49/5.87 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S2 ) @ X )
% 5.49/5.87 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.49/5.87 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.naive_member.simps(3)
% 5.49/5.87 thf(fact_1206_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.49/5.87 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.49/5.87 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 5.49/5.87 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.87 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 5.49/5.87 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.membermima.simps(5)
% 5.49/5.87 thf(fact_1207_divmod__step__eq,axiom,
% 5.49/5.87 ! [L2: num,R2: nat,Q2: nat] :
% 5.49/5.87 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.49/5.87 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.49/5.87 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.49/5.87 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % divmod_step_eq
% 5.49/5.87 thf(fact_1208_divmod__step__eq,axiom,
% 5.49/5.87 ! [L2: num,R2: int,Q2: int] :
% 5.49/5.87 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.49/5.87 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.49/5.87 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.49/5.87 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % divmod_step_eq
% 5.49/5.87 thf(fact_1209_divmod__step__eq,axiom,
% 5.49/5.87 ! [L2: num,R2: code_integer,Q2: code_integer] :
% 5.49/5.87 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.49/5.87 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.49/5.87 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.49/5.87 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.49/5.87 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % divmod_step_eq
% 5.49/5.87 thf(fact_1210_maxt__corr__help__empty,axiom,
% 5.49/5.87 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.87 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.87 => ( ( ( vEBT_vebt_maxt @ T )
% 5.49/5.87 = none_nat )
% 5.49/5.87 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.49/5.87 = bot_bot_set_nat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % maxt_corr_help_empty
% 5.49/5.87 thf(fact_1211_mint__corr__help__empty,axiom,
% 5.49/5.87 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.87 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.87 => ( ( ( vEBT_vebt_mint @ T )
% 5.49/5.87 = none_nat )
% 5.49/5.87 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.49/5.87 = bot_bot_set_nat ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % mint_corr_help_empty
% 5.49/5.87 thf(fact_1212_both__member__options__def,axiom,
% 5.49/5.87 ( vEBT_V8194947554948674370ptions
% 5.49/5.87 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.49/5.87 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.49/5.87 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % both_member_options_def
% 5.49/5.87 thf(fact_1213_zdiv__numeral__Bit0,axiom,
% 5.49/5.87 ! [V: num,W: num] :
% 5.49/5.87 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.49/5.87 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % zdiv_numeral_Bit0
% 5.49/5.87 thf(fact_1214_member__valid__both__member__options,axiom,
% 5.49/5.87 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 5.49/5.87 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.49/5.87 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.49/5.87 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.49/5.87 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % member_valid_both_member_options
% 5.49/5.87 thf(fact_1215_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc8306885398267862888on_nat] :
% 5.49/5.87 ( ! [Uu3: nat > nat > nat,Uv2: option_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc8929957630744042906on_nat @ Uu3 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.49/5.87 => ~ ! [F2: nat > nat > nat,A3: nat,B2: nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.cases
% 5.49/5.87 thf(fact_1216_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc5542196010084753463at_nat] :
% 5.49/5.87 ( ! [Uu3: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc2899441246263362727at_nat @ Uu3 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.49/5.87 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.cases
% 5.49/5.87 thf(fact_1217_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc1193250871479095198on_num] :
% 5.49/5.87 ( ! [Uu3: num > num > num,Uv2: option_num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc5778274026573060048on_num @ Uu3 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: num > num > num,V2: num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.49/5.87 => ~ ! [F2: num > num > num,A3: num,B2: num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_shift.cases
% 5.49/5.87 thf(fact_1218_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc2233624965454879586on_nat] :
% 5.49/5.87 ( ! [Uu3: nat > nat > $o,Uv2: option_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc4035269172776083154on_nat @ Uu3 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.49/5.87 => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_comp_shift.cases
% 5.49/5.87 thf(fact_1219_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc5491161045314408544at_nat] :
% 5.49/5.87 ( ! [Uu3: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3994169339658061776at_nat @ Uu3 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.49/5.87 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_comp_shift.cases
% 5.49/5.87 thf(fact_1220_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.49/5.87 ! [X: produc7036089656553540234on_num] :
% 5.49/5.87 ( ! [Uu3: num > num > $o,Uv2: option_num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3576312749637752826on_num @ Uu3 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.49/5.87 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.49/5.87 => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 5.49/5.87 ( X
% 5.49/5.87 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % VEBT_internal.option_comp_shift.cases
% 5.49/5.87 thf(fact_1221_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_real,B4: set_real] :
% 5.49/5.87 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: real] :
% 5.49/5.87 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.49/5.87 => ( member_real @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1222_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_complex,B4: set_complex] :
% 5.49/5.87 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: complex] :
% 5.49/5.87 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.49/5.87 => ( member_complex @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1223_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_P6011104703257516679at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.49/5.87 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: product_prod_nat_nat] :
% 5.49/5.87 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.49/5.87 => ( member8440522571783428010at_nat @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1224_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 5.49/5.87 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: vEBT_VEBT] :
% 5.49/5.87 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.87 => ( member_VEBT_VEBT @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1225_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_nat,B4: set_nat] :
% 5.49/5.87 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: nat] :
% 5.49/5.87 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.49/5.87 => ( member_nat @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1226_subset__code_I1_J,axiom,
% 5.49/5.87 ! [Xs2: list_int,B4: set_int] :
% 5.49/5.87 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B4 )
% 5.49/5.87 = ( ! [X2: int] :
% 5.49/5.87 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.49/5.87 => ( member_int @ X2 @ B4 ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % subset_code(1)
% 5.49/5.87 thf(fact_1227_neq__if__length__neq,axiom,
% 5.49/5.87 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.49/5.87 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.49/5.87 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.49/5.87 => ( Xs2 != Ys ) ) ).
% 5.49/5.87
% 5.49/5.87 % neq_if_length_neq
% 5.49/5.87 thf(fact_1228_neq__if__length__neq,axiom,
% 5.49/5.87 ! [Xs2: list_o,Ys: list_o] :
% 5.49/5.87 ( ( ( size_size_list_o @ Xs2 )
% 5.49/5.87 != ( size_size_list_o @ Ys ) )
% 5.49/5.87 => ( Xs2 != Ys ) ) ).
% 5.49/5.87
% 5.49/5.87 % neq_if_length_neq
% 5.49/5.87 thf(fact_1229_neq__if__length__neq,axiom,
% 5.49/5.87 ! [Xs2: list_nat,Ys: list_nat] :
% 5.49/5.87 ( ( ( size_size_list_nat @ Xs2 )
% 5.49/5.87 != ( size_size_list_nat @ Ys ) )
% 5.49/5.87 => ( Xs2 != Ys ) ) ).
% 5.49/5.87
% 5.49/5.87 % neq_if_length_neq
% 5.49/5.87 thf(fact_1230_neq__if__length__neq,axiom,
% 5.49/5.87 ! [Xs2: list_int,Ys: list_int] :
% 5.49/5.87 ( ( ( size_size_list_int @ Xs2 )
% 5.49/5.87 != ( size_size_list_int @ Ys ) )
% 5.49/5.87 => ( Xs2 != Ys ) ) ).
% 5.49/5.87
% 5.49/5.87 % neq_if_length_neq
% 5.49/5.87 thf(fact_1231_Ex__list__of__length,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ? [Xs3: list_VEBT_VEBT] :
% 5.49/5.87 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % Ex_list_of_length
% 5.49/5.87 thf(fact_1232_Ex__list__of__length,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ? [Xs3: list_o] :
% 5.49/5.87 ( ( size_size_list_o @ Xs3 )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % Ex_list_of_length
% 5.49/5.87 thf(fact_1233_Ex__list__of__length,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ? [Xs3: list_nat] :
% 5.49/5.87 ( ( size_size_list_nat @ Xs3 )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % Ex_list_of_length
% 5.49/5.87 thf(fact_1234_Ex__list__of__length,axiom,
% 5.49/5.87 ! [N: nat] :
% 5.49/5.87 ? [Xs3: list_int] :
% 5.49/5.87 ( ( size_size_list_int @ Xs3 )
% 5.49/5.87 = N ) ).
% 5.49/5.87
% 5.49/5.87 % Ex_list_of_length
% 5.49/5.87 thf(fact_1235_mult__commute__abs,axiom,
% 5.49/5.87 ! [C: real] :
% 5.49/5.87 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.49/5.87 = ( times_times_real @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_commute_abs
% 5.49/5.87 thf(fact_1236_mult__commute__abs,axiom,
% 5.49/5.87 ! [C: rat] :
% 5.49/5.87 ( ( ^ [X2: rat] : ( times_times_rat @ X2 @ C ) )
% 5.49/5.87 = ( times_times_rat @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_commute_abs
% 5.49/5.87 thf(fact_1237_mult__commute__abs,axiom,
% 5.49/5.87 ! [C: nat] :
% 5.49/5.87 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.49/5.87 = ( times_times_nat @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_commute_abs
% 5.49/5.87 thf(fact_1238_mult__commute__abs,axiom,
% 5.49/5.87 ! [C: int] :
% 5.49/5.87 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.49/5.87 = ( times_times_int @ C ) ) ).
% 5.49/5.87
% 5.49/5.87 % mult_commute_abs
% 5.49/5.87 thf(fact_1239_length__induct,axiom,
% 5.49/5.87 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.49/5.87 ( ! [Xs3: list_VEBT_VEBT] :
% 5.49/5.87 ( ! [Ys2: list_VEBT_VEBT] :
% 5.49/5.87 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.49/5.87 => ( P @ Ys2 ) )
% 5.49/5.87 => ( P @ Xs3 ) )
% 5.49/5.87 => ( P @ Xs2 ) ) ).
% 5.49/5.87
% 5.49/5.87 % length_induct
% 5.49/5.87 thf(fact_1240_length__induct,axiom,
% 5.49/5.87 ! [P: list_o > $o,Xs2: list_o] :
% 5.49/5.87 ( ! [Xs3: list_o] :
% 5.49/5.87 ( ! [Ys2: list_o] :
% 5.49/5.87 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.49/5.87 => ( P @ Ys2 ) )
% 5.49/5.87 => ( P @ Xs3 ) )
% 5.49/5.87 => ( P @ Xs2 ) ) ).
% 5.49/5.87
% 5.49/5.87 % length_induct
% 5.49/5.87 thf(fact_1241_length__induct,axiom,
% 5.49/5.87 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.49/5.87 ( ! [Xs3: list_nat] :
% 5.49/5.87 ( ! [Ys2: list_nat] :
% 5.49/5.87 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.49/5.87 => ( P @ Ys2 ) )
% 5.49/5.87 => ( P @ Xs3 ) )
% 5.49/5.87 => ( P @ Xs2 ) ) ).
% 5.49/5.87
% 5.49/5.87 % length_induct
% 5.49/5.87 thf(fact_1242_length__induct,axiom,
% 5.49/5.87 ! [P: list_int > $o,Xs2: list_int] :
% 5.49/5.87 ( ! [Xs3: list_int] :
% 5.49/5.87 ( ! [Ys2: list_int] :
% 5.49/5.87 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.49/5.87 => ( P @ Ys2 ) )
% 5.49/5.87 => ( P @ Xs3 ) )
% 5.49/5.87 => ( P @ Xs2 ) ) ).
% 5.49/5.87
% 5.49/5.87 % length_induct
% 5.49/5.87 thf(fact_1243_nth__equalityI,axiom,
% 5.49/5.87 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.49/5.87 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.49/5.87 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.49/5.87 => ( ! [I4: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.87 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.49/5.87 = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 5.49/5.87 => ( Xs2 = Ys ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nth_equalityI
% 5.49/5.87 thf(fact_1244_nth__equalityI,axiom,
% 5.49/5.87 ! [Xs2: list_o,Ys: list_o] :
% 5.49/5.87 ( ( ( size_size_list_o @ Xs2 )
% 5.49/5.87 = ( size_size_list_o @ Ys ) )
% 5.49/5.87 => ( ! [I4: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.87 => ( ( nth_o @ Xs2 @ I4 )
% 5.49/5.87 = ( nth_o @ Ys @ I4 ) ) )
% 5.49/5.87 => ( Xs2 = Ys ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nth_equalityI
% 5.49/5.87 thf(fact_1245_nth__equalityI,axiom,
% 5.49/5.87 ! [Xs2: list_nat,Ys: list_nat] :
% 5.49/5.87 ( ( ( size_size_list_nat @ Xs2 )
% 5.49/5.87 = ( size_size_list_nat @ Ys ) )
% 5.49/5.87 => ( ! [I4: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.87 => ( ( nth_nat @ Xs2 @ I4 )
% 5.49/5.87 = ( nth_nat @ Ys @ I4 ) ) )
% 5.49/5.87 => ( Xs2 = Ys ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nth_equalityI
% 5.49/5.87 thf(fact_1246_nth__equalityI,axiom,
% 5.49/5.87 ! [Xs2: list_int,Ys: list_int] :
% 5.49/5.87 ( ( ( size_size_list_int @ Xs2 )
% 5.49/5.87 = ( size_size_list_int @ Ys ) )
% 5.49/5.87 => ( ! [I4: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.87 => ( ( nth_int @ Xs2 @ I4 )
% 5.49/5.87 = ( nth_int @ Ys @ I4 ) ) )
% 5.49/5.87 => ( Xs2 = Ys ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % nth_equalityI
% 5.49/5.87 thf(fact_1247_Skolem__list__nth,axiom,
% 5.49/5.87 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.49/5.87 ( ( ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ? [X6: vEBT_VEBT] : ( P @ I3 @ X6 ) ) )
% 5.49/5.87 = ( ? [Xs: list_VEBT_VEBT] :
% 5.49/5.87 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.49/5.87 = K )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Skolem_list_nth
% 5.49/5.87 thf(fact_1248_Skolem__list__nth,axiom,
% 5.49/5.87 ! [K: nat,P: nat > $o > $o] :
% 5.49/5.87 ( ( ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ? [X6: $o] : ( P @ I3 @ X6 ) ) )
% 5.49/5.87 = ( ? [Xs: list_o] :
% 5.49/5.87 ( ( ( size_size_list_o @ Xs )
% 5.49/5.87 = K )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ( P @ I3 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Skolem_list_nth
% 5.49/5.87 thf(fact_1249_Skolem__list__nth,axiom,
% 5.49/5.87 ! [K: nat,P: nat > nat > $o] :
% 5.49/5.87 ( ( ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ? [X6: nat] : ( P @ I3 @ X6 ) ) )
% 5.49/5.87 = ( ? [Xs: list_nat] :
% 5.49/5.87 ( ( ( size_size_list_nat @ Xs )
% 5.49/5.87 = K )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ( P @ I3 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Skolem_list_nth
% 5.49/5.87 thf(fact_1250_Skolem__list__nth,axiom,
% 5.49/5.87 ! [K: nat,P: nat > int > $o] :
% 5.49/5.87 ( ( ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ? [X6: int] : ( P @ I3 @ X6 ) ) )
% 5.49/5.87 = ( ? [Xs: list_int] :
% 5.49/5.87 ( ( ( size_size_list_int @ Xs )
% 5.49/5.87 = K )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ K )
% 5.49/5.87 => ( P @ I3 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % Skolem_list_nth
% 5.49/5.87 thf(fact_1251_list__eq__iff__nth__eq,axiom,
% 5.49/5.87 ( ( ^ [Y5: list_VEBT_VEBT,Z5: list_VEBT_VEBT] : ( Y5 = Z5 ) )
% 5.49/5.87 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.49/5.87 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.49/5.87 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.49/5.87 => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 5.49/5.87 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % list_eq_iff_nth_eq
% 5.49/5.87 thf(fact_1252_list__eq__iff__nth__eq,axiom,
% 5.49/5.87 ( ( ^ [Y5: list_o,Z5: list_o] : ( Y5 = Z5 ) )
% 5.49/5.87 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.49/5.87 ( ( ( size_size_list_o @ Xs )
% 5.49/5.87 = ( size_size_list_o @ Ys3 ) )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.49/5.87 => ( ( nth_o @ Xs @ I3 )
% 5.49/5.87 = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % list_eq_iff_nth_eq
% 5.49/5.87 thf(fact_1253_list__eq__iff__nth__eq,axiom,
% 5.49/5.87 ( ( ^ [Y5: list_nat,Z5: list_nat] : ( Y5 = Z5 ) )
% 5.49/5.87 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.49/5.87 ( ( ( size_size_list_nat @ Xs )
% 5.49/5.87 = ( size_size_list_nat @ Ys3 ) )
% 5.49/5.87 & ! [I3: nat] :
% 5.49/5.87 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.49/5.87 => ( ( nth_nat @ Xs @ I3 )
% 5.49/5.87 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.49/5.87
% 5.49/5.87 % list_eq_iff_nth_eq
% 5.49/5.87 thf(fact_1254_list__eq__iff__nth__eq,axiom,
% 5.49/5.87 ( ( ^ [Y5: list_int,Z5: list_int] : ( Y5 = Z5 ) )
% 5.49/5.88 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.49/5.88 ( ( ( size_size_list_int @ Xs )
% 5.49/5.88 = ( size_size_list_int @ Ys3 ) )
% 5.49/5.88 & ! [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.49/5.88 => ( ( nth_int @ Xs @ I3 )
% 5.49/5.88 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % list_eq_iff_nth_eq
% 5.49/5.88 thf(fact_1255_vebt__member_Osimps_I2_J,axiom,
% 5.49/5.88 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.49/5.88 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.49/5.88
% 5.49/5.88 % vebt_member.simps(2)
% 5.49/5.88 thf(fact_1256_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.49/5.88 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.49/5.88 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.49/5.88
% 5.49/5.88 % VEBT_internal.minNull.simps(5)
% 5.49/5.88 thf(fact_1257_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.49/5.88 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.49/5.88
% 5.49/5.88 % VEBT_internal.minNull.simps(4)
% 5.49/5.88 thf(fact_1258_discrete,axiom,
% 5.49/5.88 ( ord_less_nat
% 5.49/5.88 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % discrete
% 5.49/5.88 thf(fact_1259_discrete,axiom,
% 5.49/5.88 ( ord_less_int
% 5.49/5.88 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % discrete
% 5.49/5.88 thf(fact_1260_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_real] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.49/5.88 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1261_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_complex] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.49/5.88 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1262_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.49/5.88 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1263_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.88 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1264_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_o] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.88 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1265_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_nat] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.88 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1266_nth__mem,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_int] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.88 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_mem
% 5.49/5.88 thf(fact_1267_list__ball__nth,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.88 => ( ! [X3: vEBT_VEBT] :
% 5.49/5.88 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X3 ) )
% 5.49/5.88 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % list_ball_nth
% 5.49/5.88 thf(fact_1268_list__ball__nth,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.88 => ( ! [X3: $o] :
% 5.49/5.88 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X3 ) )
% 5.49/5.88 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % list_ball_nth
% 5.49/5.88 thf(fact_1269_list__ball__nth,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.88 => ( ! [X3: nat] :
% 5.49/5.88 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X3 ) )
% 5.49/5.88 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % list_ball_nth
% 5.49/5.88 thf(fact_1270_list__ball__nth,axiom,
% 5.49/5.88 ! [N: nat,Xs2: list_int,P: int > $o] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.88 => ( ! [X3: int] :
% 5.49/5.88 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X3 ) )
% 5.49/5.88 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % list_ball_nth
% 5.49/5.88 thf(fact_1271_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: real,Xs2: list_real] :
% 5.49/5.88 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.49/5.88 & ( ( nth_real @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1272_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: complex,Xs2: list_complex] :
% 5.49/5.88 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.49/5.88 & ( ( nth_complex @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1273_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.49/5.88 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.49/5.88 & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1274_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.49/5.88 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.88 & ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1275_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: $o,Xs2: list_o] :
% 5.49/5.88 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.88 & ( ( nth_o @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1276_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: nat,Xs2: list_nat] :
% 5.49/5.88 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.88 & ( ( nth_nat @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1277_in__set__conv__nth,axiom,
% 5.49/5.88 ! [X: int,Xs2: list_int] :
% 5.49/5.88 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.49/5.88 = ( ? [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.88 & ( ( nth_int @ Xs2 @ I3 )
% 5.49/5.88 = X ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % in_set_conv_nth
% 5.49/5.88 thf(fact_1278_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_real,P: real > $o,X: real] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_real @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1279_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_complex @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1280_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1281_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1282_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_o @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1283_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1284_all__nth__imp__all__set,axiom,
% 5.49/5.88 ! [Xs2: list_int,P: int > $o,X: int] :
% 5.49/5.88 ( ! [I4: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_int @ Xs2 @ I4 ) ) )
% 5.49/5.88 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_nth_imp_all_set
% 5.49/5.88 thf(fact_1285_all__set__conv__all__nth,axiom,
% 5.49/5.88 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.49/5.88 ( ( ! [X2: vEBT_VEBT] :
% 5.49/5.88 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X2 ) ) )
% 5.49/5.88 = ( ! [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_set_conv_all_nth
% 5.49/5.88 thf(fact_1286_all__set__conv__all__nth,axiom,
% 5.49/5.88 ! [Xs2: list_o,P: $o > $o] :
% 5.49/5.88 ( ( ! [X2: $o] :
% 5.49/5.88 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X2 ) ) )
% 5.49/5.88 = ( ! [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_set_conv_all_nth
% 5.49/5.88 thf(fact_1287_all__set__conv__all__nth,axiom,
% 5.49/5.88 ! [Xs2: list_nat,P: nat > $o] :
% 5.49/5.88 ( ( ! [X2: nat] :
% 5.49/5.88 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X2 ) ) )
% 5.49/5.88 = ( ! [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_set_conv_all_nth
% 5.49/5.88 thf(fact_1288_all__set__conv__all__nth,axiom,
% 5.49/5.88 ! [Xs2: list_int,P: int > $o] :
% 5.49/5.88 ( ( ! [X2: int] :
% 5.49/5.88 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.49/5.88 => ( P @ X2 ) ) )
% 5.49/5.88 = ( ! [I3: nat] :
% 5.49/5.88 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.88 => ( P @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % all_set_conv_all_nth
% 5.49/5.88 thf(fact_1289_buildup__gives__empty,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.49/5.88 = bot_bot_set_nat ) ).
% 5.49/5.88
% 5.49/5.88 % buildup_gives_empty
% 5.49/5.88 thf(fact_1290_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.49/5.88 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.88 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.88 => ( ! [Mi2: nat,Ma2: nat] :
% 5.49/5.88 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.88 => ~ ( ( Xa2 = Mi2 )
% 5.49/5.88 | ( Xa2 = Ma2 ) ) )
% 5.49/5.88 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.88 ( ? [Vc2: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.88 => ~ ( ( Xa2 = Mi2 )
% 5.49/5.88 | ( Xa2 = Ma2 )
% 5.49/5.88 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.88 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.88 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.49/5.88 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.88 ( ? [Vd2: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.88 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.88 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.88 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % VEBT_internal.membermima.elims(2)
% 5.49/5.88 thf(fact_1291_vebt__pred_Oelims,axiom,
% 5.49/5.88 ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.49/5.88 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.49/5.88 = Y2 )
% 5.49/5.88 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.88 => ( ( Xa2 = zero_zero_nat )
% 5.49/5.88 => ( Y2 != none_nat ) ) )
% 5.49/5.88 => ( ! [A3: $o] :
% 5.49/5.88 ( ? [Uw2: $o] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.49/5.88 => ( ( Xa2
% 5.49/5.88 = ( suc @ zero_zero_nat ) )
% 5.49/5.88 => ~ ( ( A3
% 5.49/5.88 => ( Y2
% 5.49/5.88 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.88 & ( ~ A3
% 5.49/5.88 => ( Y2 = none_nat ) ) ) ) )
% 5.49/5.88 => ( ! [A3: $o,B2: $o] :
% 5.49/5.88 ( ( X
% 5.49/5.88 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.88 => ( ? [Va3: nat] :
% 5.49/5.88 ( Xa2
% 5.49/5.88 = ( suc @ ( suc @ Va3 ) ) )
% 5.49/5.88 => ~ ( ( B2
% 5.49/5.88 => ( Y2
% 5.49/5.88 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.88 & ( ~ B2
% 5.49/5.88 => ( ( A3
% 5.49/5.88 => ( Y2
% 5.49/5.88 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.88 & ( ~ A3
% 5.49/5.88 => ( Y2 = none_nat ) ) ) ) ) ) )
% 5.49/5.88 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.49/5.88 => ( Y2 != none_nat ) )
% 5.49/5.88 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.49/5.88 => ( Y2 != none_nat ) )
% 5.49/5.88 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.49/5.88 ( X
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.49/5.88 => ( Y2 != none_nat ) )
% 5.49/5.88 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.88 ( ( X
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.88 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.88 => ( Y2
% 5.49/5.88 = ( some_nat @ Ma2 ) ) )
% 5.49/5.88 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.88 => ( Y2
% 5.49/5.88 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.88 @ ( if_option_nat
% 5.49/5.88 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.88 != none_nat )
% 5.49/5.88 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.88 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.88 @ ( if_option_nat
% 5.49/5.88 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.88 = none_nat )
% 5.49/5.88 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.49/5.88 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.88 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % vebt_pred.elims
% 5.49/5.88 thf(fact_1292_low__def,axiom,
% 5.49/5.88 ( vEBT_VEBT_low
% 5.49/5.88 = ( ^ [X2: nat,N2: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % low_def
% 5.49/5.88 thf(fact_1293_buildup__nothing__in__leaf,axiom,
% 5.49/5.88 ! [N: nat,X: nat] :
% 5.49/5.88 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.49/5.88
% 5.49/5.88 % buildup_nothing_in_leaf
% 5.49/5.88 thf(fact_1294_obtain__set__pred,axiom,
% 5.49/5.88 ! [Z: nat,X: nat,A2: set_nat] :
% 5.49/5.88 ( ( ord_less_nat @ Z @ X )
% 5.49/5.88 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.49/5.88 => ( ( finite_finite_nat @ A2 )
% 5.49/5.88 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % obtain_set_pred
% 5.49/5.88 thf(fact_1295_buildup__nothing__in__min__max,axiom,
% 5.49/5.88 ! [N: nat,X: nat] :
% 5.49/5.88 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.49/5.88
% 5.49/5.88 % buildup_nothing_in_min_max
% 5.49/5.88 thf(fact_1296_insert__simp__excp,axiom,
% 5.49/5.88 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.49/5.88 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.88 => ( ( ord_less_nat @ X @ Mi )
% 5.49/5.88 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.88 => ( ( X != Ma )
% 5.49/5.88 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % insert_simp_excp
% 5.49/5.88 thf(fact_1297_insert__simp__norm,axiom,
% 5.49/5.88 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.49/5.88 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.88 => ( ( ord_less_nat @ Mi @ X )
% 5.49/5.88 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.49/5.88 => ( ( X != Ma )
% 5.49/5.88 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.49/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % insert_simp_norm
% 5.49/5.88 thf(fact_1298_valid__0__not,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT] :
% 5.49/5.88 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % valid_0_not
% 5.49/5.88 thf(fact_1299_valid__tree__deg__neq__0,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT] :
% 5.49/5.88 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % valid_tree_deg_neq_0
% 5.49/5.88 thf(fact_1300_deg__not__0,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.88 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.88 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.49/5.88
% 5.49/5.88 % deg_not_0
% 5.49/5.88 thf(fact_1301_Leaf__0__not,axiom,
% 5.49/5.88 ! [A: $o,B: $o] :
% 5.49/5.88 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % Leaf_0_not
% 5.49/5.88 thf(fact_1302_deg1Leaf,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT] :
% 5.49/5.88 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.49/5.88 = ( ? [A4: $o,B3: $o] :
% 5.49/5.88 ( T
% 5.49/5.88 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % deg1Leaf
% 5.49/5.88 thf(fact_1303_deg__1__Leaf,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT] :
% 5.49/5.88 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.49/5.88 => ? [A3: $o,B2: $o] :
% 5.49/5.88 ( T
% 5.49/5.88 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % deg_1_Leaf
% 5.49/5.88 thf(fact_1304_deg__1__Leafy,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.88 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.88 => ( ( N = one_one_nat )
% 5.49/5.88 => ? [A3: $o,B2: $o] :
% 5.49/5.88 ( T
% 5.49/5.88 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % deg_1_Leafy
% 5.49/5.88 thf(fact_1305_set__vebt__finite,axiom,
% 5.49/5.88 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.88 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.88 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % set_vebt_finite
% 5.49/5.88 thf(fact_1306_pred__none__empty,axiom,
% 5.49/5.88 ! [Xs2: set_nat,A: nat] :
% 5.49/5.88 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.49/5.88 => ( ( finite_finite_nat @ Xs2 )
% 5.49/5.88 => ~ ? [X5: nat] :
% 5.49/5.88 ( ( member_nat @ X5 @ Xs2 )
% 5.49/5.88 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % pred_none_empty
% 5.49/5.88 thf(fact_1307_buildup__gives__valid,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.88 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.49/5.88
% 5.49/5.88 % buildup_gives_valid
% 5.49/5.88 thf(fact_1308_mod__mod__trivial,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mod_trivial
% 5.49/5.88 thf(fact_1309_mod__mod__trivial,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mod_trivial
% 5.49/5.88 thf(fact_1310_mod__mod__trivial,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mod_trivial
% 5.49/5.88 thf(fact_1311_le__zero__eq,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.49/5.88 = ( N = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_zero_eq
% 5.49/5.88 thf(fact_1312_not__gr__zero,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.49/5.88 = ( N = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % not_gr_zero
% 5.49/5.88 thf(fact_1313_mult__zero__left,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_left
% 5.49/5.88 thf(fact_1314_mult__zero__left,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( times_times_real @ zero_zero_real @ A )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_left
% 5.49/5.88 thf(fact_1315_mult__zero__left,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_left
% 5.49/5.88 thf(fact_1316_mult__zero__left,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_left
% 5.49/5.88 thf(fact_1317_mult__zero__left,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( times_times_int @ zero_zero_int @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_left
% 5.49/5.88 thf(fact_1318_mult__zero__right,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_right
% 5.49/5.88 thf(fact_1319_mult__zero__right,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( times_times_real @ A @ zero_zero_real )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_right
% 5.49/5.88 thf(fact_1320_mult__zero__right,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_right
% 5.49/5.88 thf(fact_1321_mult__zero__right,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_right
% 5.49/5.88 thf(fact_1322_mult__zero__right,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( times_times_int @ A @ zero_zero_int )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % mult_zero_right
% 5.49/5.88 thf(fact_1323_mult__eq__0__iff,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( ( times_times_complex @ A @ B )
% 5.49/5.88 = zero_zero_complex )
% 5.49/5.88 = ( ( A = zero_zero_complex )
% 5.49/5.88 | ( B = zero_zero_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_0_iff
% 5.49/5.88 thf(fact_1324_mult__eq__0__iff,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ( times_times_real @ A @ B )
% 5.49/5.88 = zero_zero_real )
% 5.49/5.88 = ( ( A = zero_zero_real )
% 5.49/5.88 | ( B = zero_zero_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_0_iff
% 5.49/5.88 thf(fact_1325_mult__eq__0__iff,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ( times_times_rat @ A @ B )
% 5.49/5.88 = zero_zero_rat )
% 5.49/5.88 = ( ( A = zero_zero_rat )
% 5.49/5.88 | ( B = zero_zero_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_0_iff
% 5.49/5.88 thf(fact_1326_mult__eq__0__iff,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ A @ B )
% 5.49/5.88 = zero_zero_nat )
% 5.49/5.88 = ( ( A = zero_zero_nat )
% 5.49/5.88 | ( B = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_0_iff
% 5.49/5.88 thf(fact_1327_mult__eq__0__iff,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ( times_times_int @ A @ B )
% 5.49/5.88 = zero_zero_int )
% 5.49/5.88 = ( ( A = zero_zero_int )
% 5.49/5.88 | ( B = zero_zero_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_0_iff
% 5.49/5.88 thf(fact_1328_mult__cancel__left,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( ( times_times_complex @ C @ A )
% 5.49/5.88 = ( times_times_complex @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left
% 5.49/5.88 thf(fact_1329_mult__cancel__left,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( ( times_times_real @ C @ A )
% 5.49/5.88 = ( times_times_real @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left
% 5.49/5.88 thf(fact_1330_mult__cancel__left,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( ( times_times_rat @ C @ A )
% 5.49/5.88 = ( times_times_rat @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left
% 5.49/5.88 thf(fact_1331_mult__cancel__left,axiom,
% 5.49/5.88 ! [C: nat,A: nat,B: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ C @ A )
% 5.49/5.88 = ( times_times_nat @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_nat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left
% 5.49/5.88 thf(fact_1332_mult__cancel__left,axiom,
% 5.49/5.88 ! [C: int,A: int,B: int] :
% 5.49/5.88 ( ( ( times_times_int @ C @ A )
% 5.49/5.88 = ( times_times_int @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left
% 5.49/5.88 thf(fact_1333_mult__cancel__right,axiom,
% 5.49/5.88 ! [A: complex,C: complex,B: complex] :
% 5.49/5.88 ( ( ( times_times_complex @ A @ C )
% 5.49/5.88 = ( times_times_complex @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right
% 5.49/5.88 thf(fact_1334_mult__cancel__right,axiom,
% 5.49/5.88 ! [A: real,C: real,B: real] :
% 5.49/5.88 ( ( ( times_times_real @ A @ C )
% 5.49/5.88 = ( times_times_real @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right
% 5.49/5.88 thf(fact_1335_mult__cancel__right,axiom,
% 5.49/5.88 ! [A: rat,C: rat,B: rat] :
% 5.49/5.88 ( ( ( times_times_rat @ A @ C )
% 5.49/5.88 = ( times_times_rat @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right
% 5.49/5.88 thf(fact_1336_mult__cancel__right,axiom,
% 5.49/5.88 ! [A: nat,C: nat,B: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ A @ C )
% 5.49/5.88 = ( times_times_nat @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_nat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right
% 5.49/5.88 thf(fact_1337_mult__cancel__right,axiom,
% 5.49/5.88 ! [A: int,C: int,B: int] :
% 5.49/5.88 ( ( ( times_times_int @ A @ C )
% 5.49/5.88 = ( times_times_int @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right
% 5.49/5.88 thf(fact_1338_add_Oright__neutral,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add.right_neutral
% 5.49/5.88 thf(fact_1339_add_Oright__neutral,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add.right_neutral
% 5.49/5.88 thf(fact_1340_add_Oright__neutral,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add.right_neutral
% 5.49/5.88 thf(fact_1341_add_Oright__neutral,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add.right_neutral
% 5.49/5.88 thf(fact_1342_add_Oright__neutral,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add.right_neutral
% 5.49/5.88 thf(fact_1343_double__zero__sym,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( zero_zero_real
% 5.49/5.88 = ( plus_plus_real @ A @ A ) )
% 5.49/5.88 = ( A = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_zero_sym
% 5.49/5.88 thf(fact_1344_double__zero__sym,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( zero_zero_rat
% 5.49/5.88 = ( plus_plus_rat @ A @ A ) )
% 5.49/5.88 = ( A = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_zero_sym
% 5.49/5.88 thf(fact_1345_double__zero__sym,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( zero_zero_int
% 5.49/5.88 = ( plus_plus_int @ A @ A ) )
% 5.49/5.88 = ( A = zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_zero_sym
% 5.49/5.88 thf(fact_1346_add__cancel__left__left,axiom,
% 5.49/5.88 ! [B: complex,A: complex] :
% 5.49/5.88 ( ( ( plus_plus_complex @ B @ A )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_left
% 5.49/5.88 thf(fact_1347_add__cancel__left__left,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( ( plus_plus_real @ B @ A )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_left
% 5.49/5.88 thf(fact_1348_add__cancel__left__left,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( ( plus_plus_rat @ B @ A )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_left
% 5.49/5.88 thf(fact_1349_add__cancel__left__left,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( ( plus_plus_nat @ B @ A )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_left
% 5.49/5.88 thf(fact_1350_add__cancel__left__left,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( ( plus_plus_int @ B @ A )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_left
% 5.49/5.88 thf(fact_1351_add__cancel__left__right,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( ( plus_plus_complex @ A @ B )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_right
% 5.49/5.88 thf(fact_1352_add__cancel__left__right,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ( plus_plus_real @ A @ B )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_right
% 5.49/5.88 thf(fact_1353_add__cancel__left__right,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ( plus_plus_rat @ A @ B )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_right
% 5.49/5.88 thf(fact_1354_add__cancel__left__right,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ( plus_plus_nat @ A @ B )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_right
% 5.49/5.88 thf(fact_1355_add__cancel__left__right,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ( plus_plus_int @ A @ B )
% 5.49/5.88 = A )
% 5.49/5.88 = ( B = zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_left_right
% 5.49/5.88 thf(fact_1356_add__cancel__right__left,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_complex @ B @ A ) )
% 5.49/5.88 = ( B = zero_zero_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_left
% 5.49/5.88 thf(fact_1357_add__cancel__right__left,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_real @ B @ A ) )
% 5.49/5.88 = ( B = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_left
% 5.49/5.88 thf(fact_1358_add__cancel__right__left,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_rat @ B @ A ) )
% 5.49/5.88 = ( B = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_left
% 5.49/5.88 thf(fact_1359_add__cancel__right__left,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_nat @ B @ A ) )
% 5.49/5.88 = ( B = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_left
% 5.49/5.88 thf(fact_1360_add__cancel__right__left,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_int @ B @ A ) )
% 5.49/5.88 = ( B = zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_left
% 5.49/5.88 thf(fact_1361_add__cancel__right__right,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_complex @ A @ B ) )
% 5.49/5.88 = ( B = zero_zero_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_right
% 5.49/5.88 thf(fact_1362_add__cancel__right__right,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_real @ A @ B ) )
% 5.49/5.88 = ( B = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_right
% 5.49/5.88 thf(fact_1363_add__cancel__right__right,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_rat @ A @ B ) )
% 5.49/5.88 = ( B = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_right
% 5.49/5.88 thf(fact_1364_add__cancel__right__right,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_nat @ A @ B ) )
% 5.49/5.88 = ( B = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_right
% 5.49/5.88 thf(fact_1365_add__cancel__right__right,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( A
% 5.49/5.88 = ( plus_plus_int @ A @ B ) )
% 5.49/5.88 = ( B = zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_cancel_right_right
% 5.49/5.88 thf(fact_1366_add__eq__0__iff__both__eq__0,axiom,
% 5.49/5.88 ! [X: nat,Y2: nat] :
% 5.49/5.88 ( ( ( plus_plus_nat @ X @ Y2 )
% 5.49/5.88 = zero_zero_nat )
% 5.49/5.88 = ( ( X = zero_zero_nat )
% 5.49/5.88 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_eq_0_iff_both_eq_0
% 5.49/5.88 thf(fact_1367_zero__eq__add__iff__both__eq__0,axiom,
% 5.49/5.88 ! [X: nat,Y2: nat] :
% 5.49/5.88 ( ( zero_zero_nat
% 5.49/5.88 = ( plus_plus_nat @ X @ Y2 ) )
% 5.49/5.88 = ( ( X = zero_zero_nat )
% 5.49/5.88 & ( Y2 = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_eq_add_iff_both_eq_0
% 5.49/5.88 thf(fact_1368_add__0,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add_0
% 5.49/5.88 thf(fact_1369_add__0,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add_0
% 5.49/5.88 thf(fact_1370_add__0,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add_0
% 5.49/5.88 thf(fact_1371_add__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add_0
% 5.49/5.88 thf(fact_1372_add__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % add_0
% 5.49/5.88 thf(fact_1373_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( minus_minus_complex @ A @ A )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % cancel_comm_monoid_add_class.diff_cancel
% 5.49/5.88 thf(fact_1374_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( minus_minus_real @ A @ A )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % cancel_comm_monoid_add_class.diff_cancel
% 5.49/5.88 thf(fact_1375_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( minus_minus_rat @ A @ A )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % cancel_comm_monoid_add_class.diff_cancel
% 5.49/5.88 thf(fact_1376_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ A @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % cancel_comm_monoid_add_class.diff_cancel
% 5.49/5.88 thf(fact_1377_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( minus_minus_int @ A @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % cancel_comm_monoid_add_class.diff_cancel
% 5.49/5.88 thf(fact_1378_diff__zero,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_zero
% 5.49/5.88 thf(fact_1379_diff__zero,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_zero
% 5.49/5.88 thf(fact_1380_diff__zero,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_zero
% 5.49/5.88 thf(fact_1381_diff__zero,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_zero
% 5.49/5.88 thf(fact_1382_diff__zero,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_zero
% 5.49/5.88 thf(fact_1383_zero__diff,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % zero_diff
% 5.49/5.88 thf(fact_1384_diff__0__right,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_0_right
% 5.49/5.88 thf(fact_1385_diff__0__right,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_0_right
% 5.49/5.88 thf(fact_1386_diff__0__right,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_0_right
% 5.49/5.88 thf(fact_1387_diff__0__right,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % diff_0_right
% 5.49/5.88 thf(fact_1388_diff__self,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( minus_minus_complex @ A @ A )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % diff_self
% 5.49/5.88 thf(fact_1389_diff__self,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( minus_minus_real @ A @ A )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % diff_self
% 5.49/5.88 thf(fact_1390_diff__self,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( minus_minus_rat @ A @ A )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % diff_self
% 5.49/5.88 thf(fact_1391_diff__self,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( minus_minus_int @ A @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % diff_self
% 5.49/5.88 thf(fact_1392_div__by__0,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % div_by_0
% 5.49/5.88 thf(fact_1393_div__by__0,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % div_by_0
% 5.49/5.88 thf(fact_1394_div__by__0,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % div_by_0
% 5.49/5.88 thf(fact_1395_div__by__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % div_by_0
% 5.49/5.88 thf(fact_1396_div__by__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % div_by_0
% 5.49/5.88 thf(fact_1397_div__0,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % div_0
% 5.49/5.88 thf(fact_1398_div__0,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % div_0
% 5.49/5.88 thf(fact_1399_div__0,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % div_0
% 5.49/5.88 thf(fact_1400_div__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % div_0
% 5.49/5.88 thf(fact_1401_div__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % div_0
% 5.49/5.88 thf(fact_1402_division__ring__divide__zero,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % division_ring_divide_zero
% 5.49/5.88 thf(fact_1403_division__ring__divide__zero,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % division_ring_divide_zero
% 5.49/5.88 thf(fact_1404_division__ring__divide__zero,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % division_ring_divide_zero
% 5.49/5.88 thf(fact_1405_divide__cancel__right,axiom,
% 5.49/5.88 ! [A: complex,C: complex,B: complex] :
% 5.49/5.88 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.49/5.88 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_right
% 5.49/5.88 thf(fact_1406_divide__cancel__right,axiom,
% 5.49/5.88 ! [A: real,C: real,B: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ A @ C )
% 5.49/5.88 = ( divide_divide_real @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_right
% 5.49/5.88 thf(fact_1407_divide__cancel__right,axiom,
% 5.49/5.88 ! [A: rat,C: rat,B: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ A @ C )
% 5.49/5.88 = ( divide_divide_rat @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_right
% 5.49/5.88 thf(fact_1408_divide__cancel__left,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.49/5.88 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_left
% 5.49/5.88 thf(fact_1409_divide__cancel__left,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ C @ A )
% 5.49/5.88 = ( divide_divide_real @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_left
% 5.49/5.88 thf(fact_1410_divide__cancel__left,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ C @ A )
% 5.49/5.88 = ( divide_divide_rat @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_cancel_left
% 5.49/5.88 thf(fact_1411_divide__eq__0__iff,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.49/5.88 = zero_zero_complex )
% 5.49/5.88 = ( ( A = zero_zero_complex )
% 5.49/5.88 | ( B = zero_zero_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_0_iff
% 5.49/5.88 thf(fact_1412_divide__eq__0__iff,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ A @ B )
% 5.49/5.88 = zero_zero_real )
% 5.49/5.88 = ( ( A = zero_zero_real )
% 5.49/5.88 | ( B = zero_zero_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_0_iff
% 5.49/5.88 thf(fact_1413_divide__eq__0__iff,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ A @ B )
% 5.49/5.88 = zero_zero_rat )
% 5.49/5.88 = ( ( A = zero_zero_rat )
% 5.49/5.88 | ( B = zero_zero_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_0_iff
% 5.49/5.88 thf(fact_1414_bits__div__by__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % bits_div_by_0
% 5.49/5.88 thf(fact_1415_bits__div__by__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % bits_div_by_0
% 5.49/5.88 thf(fact_1416_bits__div__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % bits_div_0
% 5.49/5.88 thf(fact_1417_bits__div__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % bits_div_0
% 5.49/5.88 thf(fact_1418_bits__mod__0,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_0
% 5.49/5.88 thf(fact_1419_bits__mod__0,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_0
% 5.49/5.88 thf(fact_1420_bits__mod__0,axiom,
% 5.49/5.88 ! [A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_0
% 5.49/5.88 thf(fact_1421_less__nat__zero__code,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % less_nat_zero_code
% 5.49/5.88 thf(fact_1422_neq0__conv,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( N != zero_zero_nat )
% 5.49/5.88 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.49/5.88
% 5.49/5.88 % neq0_conv
% 5.49/5.88 thf(fact_1423_bot__nat__0_Onot__eq__extremum,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( A != zero_zero_nat )
% 5.49/5.88 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % bot_nat_0.not_eq_extremum
% 5.49/5.88 thf(fact_1424_bot__nat__0_Oextremum,axiom,
% 5.49/5.88 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.49/5.88
% 5.49/5.88 % bot_nat_0.extremum
% 5.49/5.88 thf(fact_1425_le0,axiom,
% 5.49/5.88 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.49/5.88
% 5.49/5.88 % le0
% 5.49/5.88 thf(fact_1426_mod__add__self2,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self2
% 5.49/5.88 thf(fact_1427_mod__add__self2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self2
% 5.49/5.88 thf(fact_1428_mod__add__self2,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self2
% 5.49/5.88 thf(fact_1429_mod__add__self1,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self1
% 5.49/5.88 thf(fact_1430_mod__add__self1,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self1
% 5.49/5.88 thf(fact_1431_mod__add__self1,axiom,
% 5.49/5.88 ! [B: code_integer,A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_add_self1
% 5.49/5.88 thf(fact_1432_minus__mod__self2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % minus_mod_self2
% 5.49/5.88 thf(fact_1433_minus__mod__self2,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % minus_mod_self2
% 5.49/5.88 thf(fact_1434_List_Ofinite__set,axiom,
% 5.49/5.88 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % List.finite_set
% 5.49/5.88 thf(fact_1435_List_Ofinite__set,axiom,
% 5.49/5.88 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % List.finite_set
% 5.49/5.88 thf(fact_1436_List_Ofinite__set,axiom,
% 5.49/5.88 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % List.finite_set
% 5.49/5.88 thf(fact_1437_List_Ofinite__set,axiom,
% 5.49/5.88 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % List.finite_set
% 5.49/5.88 thf(fact_1438_add__is__0,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ( plus_plus_nat @ M @ N )
% 5.49/5.88 = zero_zero_nat )
% 5.49/5.88 = ( ( M = zero_zero_nat )
% 5.49/5.88 & ( N = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_is_0
% 5.49/5.88 thf(fact_1439_Nat_Oadd__0__right,axiom,
% 5.49/5.88 ! [M: nat] :
% 5.49/5.88 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.49/5.88 = M ) ).
% 5.49/5.88
% 5.49/5.88 % Nat.add_0_right
% 5.49/5.88 thf(fact_1440_diff__self__eq__0,axiom,
% 5.49/5.88 ! [M: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ M @ M )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % diff_self_eq_0
% 5.49/5.88 thf(fact_1441_diff__0__eq__0,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % diff_0_eq_0
% 5.49/5.88 thf(fact_1442_mult__is__0,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ M @ N )
% 5.49/5.88 = zero_zero_nat )
% 5.49/5.88 = ( ( M = zero_zero_nat )
% 5.49/5.88 | ( N = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_is_0
% 5.49/5.88 thf(fact_1443_mult__0__right,axiom,
% 5.49/5.88 ! [M: nat] :
% 5.49/5.88 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mult_0_right
% 5.49/5.88 thf(fact_1444_mult__cancel1,axiom,
% 5.49/5.88 ! [K: nat,M: nat,N: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ K @ M )
% 5.49/5.88 = ( times_times_nat @ K @ N ) )
% 5.49/5.88 = ( ( M = N )
% 5.49/5.88 | ( K = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel1
% 5.49/5.88 thf(fact_1445_mult__cancel2,axiom,
% 5.49/5.88 ! [M: nat,K: nat,N: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ M @ K )
% 5.49/5.88 = ( times_times_nat @ N @ K ) )
% 5.49/5.88 = ( ( M = N )
% 5.49/5.88 | ( K = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel2
% 5.49/5.88 thf(fact_1446_mod__less,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ord_less_nat @ M @ N )
% 5.49/5.88 => ( ( modulo_modulo_nat @ M @ N )
% 5.49/5.88 = M ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_less
% 5.49/5.88 thf(fact_1447_length__list__update,axiom,
% 5.49/5.88 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.49/5.88 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 5.49/5.88 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % length_list_update
% 5.49/5.88 thf(fact_1448_length__list__update,axiom,
% 5.49/5.88 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.49/5.88 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 5.49/5.88 = ( size_size_list_o @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % length_list_update
% 5.49/5.88 thf(fact_1449_length__list__update,axiom,
% 5.49/5.88 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.49/5.88 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 5.49/5.88 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % length_list_update
% 5.49/5.88 thf(fact_1450_length__list__update,axiom,
% 5.49/5.88 ! [Xs2: list_int,I2: nat,X: int] :
% 5.49/5.88 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 5.49/5.88 = ( size_size_list_int @ Xs2 ) ) ).
% 5.49/5.88
% 5.49/5.88 % length_list_update
% 5.49/5.88 thf(fact_1451_max__Suc__Suc,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.49/5.88 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_Suc_Suc
% 5.49/5.88 thf(fact_1452_max__0R,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.49/5.88 = N ) ).
% 5.49/5.88
% 5.49/5.88 % max_0R
% 5.49/5.88 thf(fact_1453_max__0L,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.49/5.88 = N ) ).
% 5.49/5.88
% 5.49/5.88 % max_0L
% 5.49/5.88 thf(fact_1454_max__nat_Oright__neutral,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % max_nat.right_neutral
% 5.49/5.88 thf(fact_1455_max__nat_Oneutr__eq__iff,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( zero_zero_nat
% 5.49/5.88 = ( ord_max_nat @ A @ B ) )
% 5.49/5.88 = ( ( A = zero_zero_nat )
% 5.49/5.88 & ( B = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_nat.neutr_eq_iff
% 5.49/5.88 thf(fact_1456_max__nat_Oleft__neutral,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % max_nat.left_neutral
% 5.49/5.88 thf(fact_1457_max__nat_Oeq__neutr__iff,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ( ord_max_nat @ A @ B )
% 5.49/5.88 = zero_zero_nat )
% 5.49/5.88 = ( ( A = zero_zero_nat )
% 5.49/5.88 & ( B = zero_zero_nat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_nat.eq_neutr_iff
% 5.49/5.88 thf(fact_1458_nth__list__update__neq,axiom,
% 5.49/5.88 ! [I2: nat,J: nat,Xs2: list_int,X: int] :
% 5.49/5.88 ( ( I2 != J )
% 5.49/5.88 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.88 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_list_update_neq
% 5.49/5.88 thf(fact_1459_nth__list__update__neq,axiom,
% 5.49/5.88 ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 5.49/5.88 ( ( I2 != J )
% 5.49/5.88 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.88 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_list_update_neq
% 5.49/5.88 thf(fact_1460_nth__list__update__neq,axiom,
% 5.49/5.88 ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.49/5.88 ( ( I2 != J )
% 5.49/5.88 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.88 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nth_list_update_neq
% 5.49/5.88 thf(fact_1461_list__update__id,axiom,
% 5.49/5.88 ! [Xs2: list_int,I2: nat] :
% 5.49/5.88 ( ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ I2 ) )
% 5.49/5.88 = Xs2 ) ).
% 5.49/5.88
% 5.49/5.88 % list_update_id
% 5.49/5.88 thf(fact_1462_list__update__id,axiom,
% 5.49/5.88 ! [Xs2: list_nat,I2: nat] :
% 5.49/5.88 ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 5.49/5.88 = Xs2 ) ).
% 5.49/5.88
% 5.49/5.88 % list_update_id
% 5.49/5.88 thf(fact_1463_list__update__id,axiom,
% 5.49/5.88 ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 5.49/5.88 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 5.49/5.88 = Xs2 ) ).
% 5.49/5.88
% 5.49/5.88 % list_update_id
% 5.49/5.88 thf(fact_1464_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.49/5.88 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_le_double_add_iff_zero_le_single_add
% 5.49/5.88 thf(fact_1465_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.49/5.88 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_le_double_add_iff_zero_le_single_add
% 5.49/5.88 thf(fact_1466_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.49/5.88 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_le_double_add_iff_zero_le_single_add
% 5.49/5.88 thf(fact_1467_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.49/5.88 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_le_zero_iff_single_add_le_zero
% 5.49/5.88 thf(fact_1468_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.49/5.88 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_le_zero_iff_single_add_le_zero
% 5.49/5.88 thf(fact_1469_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.49/5.88 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_le_zero_iff_single_add_le_zero
% 5.49/5.88 thf(fact_1470_le__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.49/5.88 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel2
% 5.49/5.88 thf(fact_1471_le__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.49/5.88 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel2
% 5.49/5.88 thf(fact_1472_le__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.49/5.88 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel2
% 5.49/5.88 thf(fact_1473_le__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.49/5.88 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel2
% 5.49/5.88 thf(fact_1474_le__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel1
% 5.49/5.88 thf(fact_1475_le__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel1
% 5.49/5.88 thf(fact_1476_le__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel1
% 5.49/5.88 thf(fact_1477_le__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % le_add_same_cancel1
% 5.49/5.88 thf(fact_1478_add__le__same__cancel2,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel2
% 5.49/5.88 thf(fact_1479_add__le__same__cancel2,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel2
% 5.49/5.88 thf(fact_1480_add__le__same__cancel2,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel2
% 5.49/5.88 thf(fact_1481_add__le__same__cancel2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel2
% 5.49/5.88 thf(fact_1482_add__le__same__cancel1,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel1
% 5.49/5.88 thf(fact_1483_add__le__same__cancel1,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel1
% 5.49/5.88 thf(fact_1484_add__le__same__cancel1,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel1
% 5.49/5.88 thf(fact_1485_add__le__same__cancel1,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_le_same_cancel1
% 5.49/5.88 thf(fact_1486_diff__ge__0__iff__ge,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_ge_0_iff_ge
% 5.49/5.88 thf(fact_1487_diff__ge__0__iff__ge,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_ge_0_iff_ge
% 5.49/5.88 thf(fact_1488_diff__ge__0__iff__ge,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.49/5.88 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_ge_0_iff_ge
% 5.49/5.88 thf(fact_1489_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.49/5.88 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_less_double_add_iff_zero_less_single_add
% 5.49/5.88 thf(fact_1490_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.49/5.88 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_less_double_add_iff_zero_less_single_add
% 5.49/5.88 thf(fact_1491_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.49/5.88 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_less_double_add_iff_zero_less_single_add
% 5.49/5.88 thf(fact_1492_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.49/5.88 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_less_zero_iff_single_add_less_zero
% 5.49/5.88 thf(fact_1493_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.49/5.88 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_less_zero_iff_single_add_less_zero
% 5.49/5.88 thf(fact_1494_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.49/5.88 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % double_add_less_zero_iff_single_add_less_zero
% 5.49/5.88 thf(fact_1495_less__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.49/5.88 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel2
% 5.49/5.88 thf(fact_1496_less__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.49/5.88 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel2
% 5.49/5.88 thf(fact_1497_less__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.49/5.88 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel2
% 5.49/5.88 thf(fact_1498_less__add__same__cancel2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.49/5.88 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel2
% 5.49/5.88 thf(fact_1499_less__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.49/5.88 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel1
% 5.49/5.88 thf(fact_1500_less__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.49/5.88 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel1
% 5.49/5.88 thf(fact_1501_less__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.49/5.88 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel1
% 5.49/5.88 thf(fact_1502_less__add__same__cancel1,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.49/5.88 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_add_same_cancel1
% 5.49/5.88 thf(fact_1503_add__less__same__cancel2,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel2
% 5.49/5.88 thf(fact_1504_add__less__same__cancel2,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel2
% 5.49/5.88 thf(fact_1505_add__less__same__cancel2,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel2
% 5.49/5.88 thf(fact_1506_add__less__same__cancel2,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.88 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel2
% 5.49/5.88 thf(fact_1507_add__less__same__cancel1,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel1
% 5.49/5.88 thf(fact_1508_add__less__same__cancel1,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel1
% 5.49/5.88 thf(fact_1509_add__less__same__cancel1,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel1
% 5.49/5.88 thf(fact_1510_add__less__same__cancel1,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.49/5.88 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_less_same_cancel1
% 5.49/5.88 thf(fact_1511_diff__gt__0__iff__gt,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.49/5.88 = ( ord_less_real @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_gt_0_iff_gt
% 5.49/5.88 thf(fact_1512_diff__gt__0__iff__gt,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.49/5.88 = ( ord_less_rat @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_gt_0_iff_gt
% 5.49/5.88 thf(fact_1513_diff__gt__0__iff__gt,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.49/5.88 = ( ord_less_int @ B @ A ) ) ).
% 5.49/5.88
% 5.49/5.88 % diff_gt_0_iff_gt
% 5.49/5.88 thf(fact_1514_mult__cancel__right2,axiom,
% 5.49/5.88 ! [A: complex,C: complex] :
% 5.49/5.88 ( ( ( times_times_complex @ A @ C )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = one_one_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right2
% 5.49/5.88 thf(fact_1515_mult__cancel__right2,axiom,
% 5.49/5.88 ! [A: real,C: real] :
% 5.49/5.88 ( ( ( times_times_real @ A @ C )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = one_one_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right2
% 5.49/5.88 thf(fact_1516_mult__cancel__right2,axiom,
% 5.49/5.88 ! [A: rat,C: rat] :
% 5.49/5.88 ( ( ( times_times_rat @ A @ C )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = one_one_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right2
% 5.49/5.88 thf(fact_1517_mult__cancel__right2,axiom,
% 5.49/5.88 ! [A: int,C: int] :
% 5.49/5.88 ( ( ( times_times_int @ A @ C )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( A = one_one_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right2
% 5.49/5.88 thf(fact_1518_mult__cancel__right1,axiom,
% 5.49/5.88 ! [C: complex,B: complex] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_complex @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( B = one_one_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right1
% 5.49/5.88 thf(fact_1519_mult__cancel__right1,axiom,
% 5.49/5.88 ! [C: real,B: real] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_real @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( B = one_one_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right1
% 5.49/5.88 thf(fact_1520_mult__cancel__right1,axiom,
% 5.49/5.88 ! [C: rat,B: rat] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_rat @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( B = one_one_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right1
% 5.49/5.88 thf(fact_1521_mult__cancel__right1,axiom,
% 5.49/5.88 ! [C: int,B: int] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_int @ B @ C ) )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( B = one_one_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_right1
% 5.49/5.88 thf(fact_1522_mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: complex,A: complex] :
% 5.49/5.88 ( ( ( times_times_complex @ C @ A )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( A = one_one_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left2
% 5.49/5.88 thf(fact_1523_mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: real,A: real] :
% 5.49/5.88 ( ( ( times_times_real @ C @ A )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( A = one_one_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left2
% 5.49/5.88 thf(fact_1524_mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: rat,A: rat] :
% 5.49/5.88 ( ( ( times_times_rat @ C @ A )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( A = one_one_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left2
% 5.49/5.88 thf(fact_1525_mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: int,A: int] :
% 5.49/5.88 ( ( ( times_times_int @ C @ A )
% 5.49/5.88 = C )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( A = one_one_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left2
% 5.49/5.88 thf(fact_1526_mult__cancel__left1,axiom,
% 5.49/5.88 ! [C: complex,B: complex] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_complex @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_complex )
% 5.49/5.88 | ( B = one_one_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left1
% 5.49/5.88 thf(fact_1527_mult__cancel__left1,axiom,
% 5.49/5.88 ! [C: real,B: real] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_real @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_real )
% 5.49/5.88 | ( B = one_one_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left1
% 5.49/5.88 thf(fact_1528_mult__cancel__left1,axiom,
% 5.49/5.88 ! [C: rat,B: rat] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_rat @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_rat )
% 5.49/5.88 | ( B = one_one_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left1
% 5.49/5.88 thf(fact_1529_mult__cancel__left1,axiom,
% 5.49/5.88 ! [C: int,B: int] :
% 5.49/5.88 ( ( C
% 5.49/5.88 = ( times_times_int @ C @ B ) )
% 5.49/5.88 = ( ( C = zero_zero_int )
% 5.49/5.88 | ( B = one_one_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_cancel_left1
% 5.49/5.88 thf(fact_1530_sum__squares__eq__zero__iff,axiom,
% 5.49/5.88 ! [X: real,Y2: real] :
% 5.49/5.88 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) )
% 5.49/5.88 = zero_zero_real )
% 5.49/5.88 = ( ( X = zero_zero_real )
% 5.49/5.88 & ( Y2 = zero_zero_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % sum_squares_eq_zero_iff
% 5.49/5.88 thf(fact_1531_sum__squares__eq__zero__iff,axiom,
% 5.49/5.88 ! [X: rat,Y2: rat] :
% 5.49/5.88 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) )
% 5.49/5.88 = zero_zero_rat )
% 5.49/5.88 = ( ( X = zero_zero_rat )
% 5.49/5.88 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % sum_squares_eq_zero_iff
% 5.49/5.88 thf(fact_1532_sum__squares__eq__zero__iff,axiom,
% 5.49/5.88 ! [X: int,Y2: int] :
% 5.49/5.88 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) )
% 5.49/5.88 = zero_zero_int )
% 5.49/5.88 = ( ( X = zero_zero_int )
% 5.49/5.88 & ( Y2 = zero_zero_int ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % sum_squares_eq_zero_iff
% 5.49/5.88 thf(fact_1533_nonzero__mult__div__cancel__right,axiom,
% 5.49/5.88 ! [B: complex,A: complex] :
% 5.49/5.88 ( ( B != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.49/5.88 = A ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_right
% 5.49/5.88 thf(fact_1534_nonzero__mult__div__cancel__right,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( B != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.49/5.88 = A ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_right
% 5.49/5.88 thf(fact_1535_nonzero__mult__div__cancel__right,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( B != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.49/5.88 = A ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_right
% 5.49/5.88 thf(fact_1536_nonzero__mult__div__cancel__right,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( B != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.49/5.88 = A ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_right
% 5.49/5.88 thf(fact_1537_nonzero__mult__div__cancel__right,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( B != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.49/5.88 = A ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_right
% 5.49/5.88 thf(fact_1538_nonzero__mult__div__cancel__left,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( A != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.49/5.88 = B ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_left
% 5.49/5.88 thf(fact_1539_nonzero__mult__div__cancel__left,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( A != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.49/5.88 = B ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_left
% 5.49/5.88 thf(fact_1540_nonzero__mult__div__cancel__left,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( A != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.49/5.88 = B ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_left
% 5.49/5.88 thf(fact_1541_nonzero__mult__div__cancel__left,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( A != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.49/5.88 = B ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_left
% 5.49/5.88 thf(fact_1542_nonzero__mult__div__cancel__left,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( A != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.49/5.88 = B ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_div_cancel_left
% 5.49/5.88 thf(fact_1543_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( C != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right2
% 5.49/5.88 thf(fact_1544_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( C != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.49/5.88 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right2
% 5.49/5.88 thf(fact_1545_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( C != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right2
% 5.49/5.88 thf(fact_1546_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( C != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right
% 5.49/5.88 thf(fact_1547_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( C != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.88 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right
% 5.49/5.88 thf(fact_1548_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( C != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_right
% 5.49/5.88 thf(fact_1549_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( C != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left2
% 5.49/5.88 thf(fact_1550_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( C != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.49/5.88 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left2
% 5.49/5.88 thf(fact_1551_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( C != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left2
% 5.49/5.88 thf(fact_1552_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( C != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left
% 5.49/5.88 thf(fact_1553_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( C != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.88 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left
% 5.49/5.88 thf(fact_1554_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( C != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % nonzero_mult_divide_mult_cancel_left
% 5.49/5.88 thf(fact_1555_mult__divide__mult__cancel__left__if,axiom,
% 5.49/5.88 ! [C: complex,A: complex,B: complex] :
% 5.49/5.88 ( ( ( C = zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.49/5.88 = zero_zero_complex ) )
% 5.49/5.88 & ( ( C != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_divide_mult_cancel_left_if
% 5.49/5.88 thf(fact_1556_mult__divide__mult__cancel__left__if,axiom,
% 5.49/5.88 ! [C: real,A: real,B: real] :
% 5.49/5.88 ( ( ( C = zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.88 = zero_zero_real ) )
% 5.49/5.88 & ( ( C != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.88 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_divide_mult_cancel_left_if
% 5.49/5.88 thf(fact_1557_mult__divide__mult__cancel__left__if,axiom,
% 5.49/5.88 ! [C: rat,A: rat,B: rat] :
% 5.49/5.88 ( ( ( C = zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.88 = zero_zero_rat ) )
% 5.49/5.88 & ( ( C != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_divide_mult_cancel_left_if
% 5.49/5.88 thf(fact_1558_div__mult__mult1,axiom,
% 5.49/5.88 ! [C: nat,A: nat,B: nat] :
% 5.49/5.88 ( ( C != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.49/5.88 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult1
% 5.49/5.88 thf(fact_1559_div__mult__mult1,axiom,
% 5.49/5.88 ! [C: int,A: int,B: int] :
% 5.49/5.88 ( ( C != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.88 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult1
% 5.49/5.88 thf(fact_1560_div__mult__mult2,axiom,
% 5.49/5.88 ! [C: nat,A: nat,B: nat] :
% 5.49/5.88 ( ( C != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.49/5.88 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult2
% 5.49/5.88 thf(fact_1561_div__mult__mult2,axiom,
% 5.49/5.88 ! [C: int,A: int,B: int] :
% 5.49/5.88 ( ( C != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.88 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult2
% 5.49/5.88 thf(fact_1562_div__mult__mult1__if,axiom,
% 5.49/5.88 ! [C: nat,A: nat,B: nat] :
% 5.49/5.88 ( ( ( C = zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.49/5.88 = zero_zero_nat ) )
% 5.49/5.88 & ( ( C != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.49/5.88 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult1_if
% 5.49/5.88 thf(fact_1563_div__mult__mult1__if,axiom,
% 5.49/5.88 ! [C: int,A: int,B: int] :
% 5.49/5.88 ( ( ( C = zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.88 = zero_zero_int ) )
% 5.49/5.88 & ( ( C != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.88 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_mult_mult1_if
% 5.49/5.88 thf(fact_1564_diff__numeral__special_I9_J,axiom,
% 5.49/5.88 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % diff_numeral_special(9)
% 5.49/5.88 thf(fact_1565_diff__numeral__special_I9_J,axiom,
% 5.49/5.88 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % diff_numeral_special(9)
% 5.49/5.88 thf(fact_1566_diff__numeral__special_I9_J,axiom,
% 5.49/5.88 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % diff_numeral_special(9)
% 5.49/5.88 thf(fact_1567_diff__numeral__special_I9_J,axiom,
% 5.49/5.88 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % diff_numeral_special(9)
% 5.49/5.88 thf(fact_1568_diff__add__zero,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % diff_add_zero
% 5.49/5.88 thf(fact_1569_div__self,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( A != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.49/5.88 = one_one_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_self
% 5.49/5.88 thf(fact_1570_div__self,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( A != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ A @ A )
% 5.49/5.88 = one_one_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_self
% 5.49/5.88 thf(fact_1571_div__self,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( A != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ A @ A )
% 5.49/5.88 = one_one_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_self
% 5.49/5.88 thf(fact_1572_div__self,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( A != zero_zero_nat )
% 5.49/5.88 => ( ( divide_divide_nat @ A @ A )
% 5.49/5.88 = one_one_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_self
% 5.49/5.88 thf(fact_1573_div__self,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( A != zero_zero_int )
% 5.49/5.88 => ( ( divide_divide_int @ A @ A )
% 5.49/5.88 = one_one_int ) ) ).
% 5.49/5.88
% 5.49/5.88 % div_self
% 5.49/5.88 thf(fact_1574_zero__eq__1__divide__iff,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( zero_zero_real
% 5.49/5.88 = ( divide_divide_real @ one_one_real @ A ) )
% 5.49/5.88 = ( A = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_eq_1_divide_iff
% 5.49/5.88 thf(fact_1575_zero__eq__1__divide__iff,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( zero_zero_rat
% 5.49/5.88 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.49/5.88 = ( A = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_eq_1_divide_iff
% 5.49/5.88 thf(fact_1576_one__divide__eq__0__iff,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.49/5.88 = zero_zero_real )
% 5.49/5.88 = ( A = zero_zero_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_divide_eq_0_iff
% 5.49/5.88 thf(fact_1577_one__divide__eq__0__iff,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.49/5.88 = zero_zero_rat )
% 5.49/5.88 = ( A = zero_zero_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_divide_eq_0_iff
% 5.49/5.88 thf(fact_1578_eq__divide__eq__1,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( one_one_real
% 5.49/5.88 = ( divide_divide_real @ B @ A ) )
% 5.49/5.88 = ( ( A != zero_zero_real )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % eq_divide_eq_1
% 5.49/5.88 thf(fact_1579_eq__divide__eq__1,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( one_one_rat
% 5.49/5.88 = ( divide_divide_rat @ B @ A ) )
% 5.49/5.88 = ( ( A != zero_zero_rat )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % eq_divide_eq_1
% 5.49/5.88 thf(fact_1580_divide__eq__eq__1,axiom,
% 5.49/5.88 ! [B: real,A: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ B @ A )
% 5.49/5.88 = one_one_real )
% 5.49/5.88 = ( ( A != zero_zero_real )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_eq_1
% 5.49/5.88 thf(fact_1581_divide__eq__eq__1,axiom,
% 5.49/5.88 ! [B: rat,A: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ B @ A )
% 5.49/5.88 = one_one_rat )
% 5.49/5.88 = ( ( A != zero_zero_rat )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_eq_1
% 5.49/5.88 thf(fact_1582_divide__self__if,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( ( A = zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.49/5.88 = zero_zero_complex ) )
% 5.49/5.88 & ( ( A != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.49/5.88 = one_one_complex ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self_if
% 5.49/5.88 thf(fact_1583_divide__self__if,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( ( A = zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ A @ A )
% 5.49/5.88 = zero_zero_real ) )
% 5.49/5.88 & ( ( A != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ A @ A )
% 5.49/5.88 = one_one_real ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self_if
% 5.49/5.88 thf(fact_1584_divide__self__if,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( ( A = zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ A @ A )
% 5.49/5.88 = zero_zero_rat ) )
% 5.49/5.88 & ( ( A != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ A @ A )
% 5.49/5.88 = one_one_rat ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self_if
% 5.49/5.88 thf(fact_1585_divide__self,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( A != zero_zero_complex )
% 5.49/5.88 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.49/5.88 = one_one_complex ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self
% 5.49/5.88 thf(fact_1586_divide__self,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( A != zero_zero_real )
% 5.49/5.88 => ( ( divide_divide_real @ A @ A )
% 5.49/5.88 = one_one_real ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self
% 5.49/5.88 thf(fact_1587_divide__self,axiom,
% 5.49/5.88 ! [A: rat] :
% 5.49/5.88 ( ( A != zero_zero_rat )
% 5.49/5.88 => ( ( divide_divide_rat @ A @ A )
% 5.49/5.88 = one_one_rat ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_self
% 5.49/5.88 thf(fact_1588_one__eq__divide__iff,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( one_one_complex
% 5.49/5.88 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.49/5.88 = ( ( B != zero_zero_complex )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_eq_divide_iff
% 5.49/5.88 thf(fact_1589_one__eq__divide__iff,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( one_one_real
% 5.49/5.88 = ( divide_divide_real @ A @ B ) )
% 5.49/5.88 = ( ( B != zero_zero_real )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_eq_divide_iff
% 5.49/5.88 thf(fact_1590_one__eq__divide__iff,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( one_one_rat
% 5.49/5.88 = ( divide_divide_rat @ A @ B ) )
% 5.49/5.88 = ( ( B != zero_zero_rat )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_eq_divide_iff
% 5.49/5.88 thf(fact_1591_divide__eq__1__iff,axiom,
% 5.49/5.88 ! [A: complex,B: complex] :
% 5.49/5.88 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.49/5.88 = one_one_complex )
% 5.49/5.88 = ( ( B != zero_zero_complex )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_1_iff
% 5.49/5.88 thf(fact_1592_divide__eq__1__iff,axiom,
% 5.49/5.88 ! [A: real,B: real] :
% 5.49/5.88 ( ( ( divide_divide_real @ A @ B )
% 5.49/5.88 = one_one_real )
% 5.49/5.88 = ( ( B != zero_zero_real )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_1_iff
% 5.49/5.88 thf(fact_1593_divide__eq__1__iff,axiom,
% 5.49/5.88 ! [A: rat,B: rat] :
% 5.49/5.88 ( ( ( divide_divide_rat @ A @ B )
% 5.49/5.88 = one_one_rat )
% 5.49/5.88 = ( ( B != zero_zero_rat )
% 5.49/5.88 & ( A = B ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % divide_eq_1_iff
% 5.49/5.88 thf(fact_1594_power__0__Suc,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % power_0_Suc
% 5.49/5.88 thf(fact_1595_power__0__Suc,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % power_0_Suc
% 5.49/5.88 thf(fact_1596_power__0__Suc,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % power_0_Suc
% 5.49/5.88 thf(fact_1597_power__0__Suc,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % power_0_Suc
% 5.49/5.88 thf(fact_1598_power__0__Suc,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % power_0_Suc
% 5.49/5.88 thf(fact_1599_power__zero__numeral,axiom,
% 5.49/5.88 ! [K: num] :
% 5.49/5.88 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.49/5.88 = zero_zero_rat ) ).
% 5.49/5.88
% 5.49/5.88 % power_zero_numeral
% 5.49/5.88 thf(fact_1600_power__zero__numeral,axiom,
% 5.49/5.88 ! [K: num] :
% 5.49/5.88 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % power_zero_numeral
% 5.49/5.88 thf(fact_1601_power__zero__numeral,axiom,
% 5.49/5.88 ! [K: num] :
% 5.49/5.88 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.49/5.88 = zero_zero_real ) ).
% 5.49/5.88
% 5.49/5.88 % power_zero_numeral
% 5.49/5.88 thf(fact_1602_power__zero__numeral,axiom,
% 5.49/5.88 ! [K: num] :
% 5.49/5.88 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % power_zero_numeral
% 5.49/5.88 thf(fact_1603_power__zero__numeral,axiom,
% 5.49/5.88 ! [K: num] :
% 5.49/5.88 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.49/5.88 = zero_zero_complex ) ).
% 5.49/5.88
% 5.49/5.88 % power_zero_numeral
% 5.49/5.88 thf(fact_1604_mod__mult__self2__is__0,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2_is_0
% 5.49/5.88 thf(fact_1605_mod__mult__self2__is__0,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2_is_0
% 5.49/5.88 thf(fact_1606_mod__mult__self2__is__0,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2_is_0
% 5.49/5.88 thf(fact_1607_mod__mult__self1__is__0,axiom,
% 5.49/5.88 ! [B: nat,A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1_is_0
% 5.49/5.88 thf(fact_1608_mod__mult__self1__is__0,axiom,
% 5.49/5.88 ! [B: int,A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1_is_0
% 5.49/5.88 thf(fact_1609_mod__mult__self1__is__0,axiom,
% 5.49/5.88 ! [B: code_integer,A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1_is_0
% 5.49/5.88 thf(fact_1610_bits__mod__by__1,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_by_1
% 5.49/5.88 thf(fact_1611_bits__mod__by__1,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_by_1
% 5.49/5.88 thf(fact_1612_bits__mod__by__1,axiom,
% 5.49/5.88 ! [A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_by_1
% 5.49/5.88 thf(fact_1613_bits__mod__div__trivial,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_div_trivial
% 5.49/5.88 thf(fact_1614_bits__mod__div__trivial,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_div_trivial
% 5.49/5.88 thf(fact_1615_bits__mod__div__trivial,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % bits_mod_div_trivial
% 5.49/5.88 thf(fact_1616_mod__div__trivial,axiom,
% 5.49/5.88 ! [A: nat,B: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_nat ) ).
% 5.49/5.88
% 5.49/5.88 % mod_div_trivial
% 5.49/5.88 thf(fact_1617_mod__div__trivial,axiom,
% 5.49/5.88 ! [A: int,B: int] :
% 5.49/5.88 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.49/5.88 = zero_zero_int ) ).
% 5.49/5.88
% 5.49/5.88 % mod_div_trivial
% 5.49/5.88 thf(fact_1618_mod__div__trivial,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer] :
% 5.49/5.88 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.49/5.88 = zero_z3403309356797280102nteger ) ).
% 5.49/5.88
% 5.49/5.88 % mod_div_trivial
% 5.49/5.88 thf(fact_1619_power__Suc0__right,axiom,
% 5.49/5.88 ! [A: nat] :
% 5.49/5.88 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % power_Suc0_right
% 5.49/5.88 thf(fact_1620_power__Suc0__right,axiom,
% 5.49/5.88 ! [A: real] :
% 5.49/5.88 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % power_Suc0_right
% 5.49/5.88 thf(fact_1621_power__Suc0__right,axiom,
% 5.49/5.88 ! [A: int] :
% 5.49/5.88 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % power_Suc0_right
% 5.49/5.88 thf(fact_1622_power__Suc0__right,axiom,
% 5.49/5.88 ! [A: complex] :
% 5.49/5.88 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.49/5.88 = A ) ).
% 5.49/5.88
% 5.49/5.88 % power_Suc0_right
% 5.49/5.88 thf(fact_1623_mod__mult__self4,axiom,
% 5.49/5.88 ! [B: nat,C: nat,A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self4
% 5.49/5.88 thf(fact_1624_mod__mult__self4,axiom,
% 5.49/5.88 ! [B: int,C: int,A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self4
% 5.49/5.88 thf(fact_1625_mod__mult__self4,axiom,
% 5.49/5.88 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self4
% 5.49/5.88 thf(fact_1626_mod__mult__self3,axiom,
% 5.49/5.88 ! [C: nat,B: nat,A: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self3
% 5.49/5.88 thf(fact_1627_mod__mult__self3,axiom,
% 5.49/5.88 ! [C: int,B: int,A: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self3
% 5.49/5.88 thf(fact_1628_mod__mult__self3,axiom,
% 5.49/5.88 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self3
% 5.49/5.88 thf(fact_1629_mod__mult__self2,axiom,
% 5.49/5.88 ! [A: nat,B: nat,C: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2
% 5.49/5.88 thf(fact_1630_mod__mult__self2,axiom,
% 5.49/5.88 ! [A: int,B: int,C: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2
% 5.49/5.88 thf(fact_1631_mod__mult__self2,axiom,
% 5.49/5.88 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self2
% 5.49/5.88 thf(fact_1632_mod__mult__self1,axiom,
% 5.49/5.88 ! [A: nat,C: nat,B: nat] :
% 5.49/5.88 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.49/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1
% 5.49/5.88 thf(fact_1633_mod__mult__self1,axiom,
% 5.49/5.88 ! [A: int,C: int,B: int] :
% 5.49/5.88 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.49/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1
% 5.49/5.88 thf(fact_1634_mod__mult__self1,axiom,
% 5.49/5.88 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.88 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.49/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.88
% 5.49/5.88 % mod_mult_self1
% 5.49/5.88 thf(fact_1635_less__Suc0,axiom,
% 5.49/5.88 ! [N: nat] :
% 5.49/5.88 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.49/5.88 = ( N = zero_zero_nat ) ) ).
% 5.49/5.88
% 5.49/5.88 % less_Suc0
% 5.49/5.88 thf(fact_1636_zero__less__Suc,axiom,
% 5.49/5.88 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_less_Suc
% 5.49/5.88 thf(fact_1637_max__number__of_I1_J,axiom,
% 5.49/5.88 ! [U: num,V: num] :
% 5.49/5.88 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.49/5.88 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.49/5.88 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.49/5.88 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_number_of(1)
% 5.49/5.88 thf(fact_1638_max__number__of_I1_J,axiom,
% 5.49/5.88 ! [U: num,V: num] :
% 5.49/5.88 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.88 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.88 = ( numeral_numeral_real @ V ) ) )
% 5.49/5.88 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.88 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.49/5.88 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_number_of(1)
% 5.49/5.88 thf(fact_1639_max__number__of_I1_J,axiom,
% 5.49/5.88 ! [U: num,V: num] :
% 5.49/5.88 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.88 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.88 = ( numeral_numeral_rat @ V ) ) )
% 5.49/5.88 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.88 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.49/5.88 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_number_of(1)
% 5.49/5.88 thf(fact_1640_max__number__of_I1_J,axiom,
% 5.49/5.88 ! [U: num,V: num] :
% 5.49/5.88 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.49/5.88 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.49/5.88 = ( numeral_numeral_nat @ V ) ) )
% 5.49/5.88 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.49/5.88 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.49/5.88 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_number_of(1)
% 5.49/5.88 thf(fact_1641_max__number__of_I1_J,axiom,
% 5.49/5.88 ! [U: num,V: num] :
% 5.49/5.88 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.88 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.88 = ( numeral_numeral_int @ V ) ) )
% 5.49/5.88 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.88 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.49/5.88 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_number_of(1)
% 5.49/5.88 thf(fact_1642_max__0__1_I4_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(4)
% 5.49/5.88 thf(fact_1643_max__0__1_I4_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.49/5.88 = ( numeral_numeral_real @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(4)
% 5.49/5.88 thf(fact_1644_max__0__1_I4_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.49/5.88 = ( numeral_numeral_rat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(4)
% 5.49/5.88 thf(fact_1645_max__0__1_I4_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.49/5.88 = ( numeral_numeral_nat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(4)
% 5.49/5.88 thf(fact_1646_max__0__1_I4_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.49/5.88 = ( numeral_numeral_int @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(4)
% 5.49/5.88 thf(fact_1647_max__0__1_I3_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(3)
% 5.49/5.88 thf(fact_1648_max__0__1_I3_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.49/5.88 = ( numeral_numeral_real @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(3)
% 5.49/5.88 thf(fact_1649_max__0__1_I3_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.49/5.88 = ( numeral_numeral_rat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(3)
% 5.49/5.88 thf(fact_1650_max__0__1_I3_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.49/5.88 = ( numeral_numeral_nat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(3)
% 5.49/5.88 thf(fact_1651_max__0__1_I3_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.49/5.88 = ( numeral_numeral_int @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(3)
% 5.49/5.88 thf(fact_1652_max__0__1_I1_J,axiom,
% 5.49/5.88 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.49/5.88 = one_one_real ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(1)
% 5.49/5.88 thf(fact_1653_max__0__1_I1_J,axiom,
% 5.49/5.88 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.49/5.88 = one_one_rat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(1)
% 5.49/5.88 thf(fact_1654_max__0__1_I1_J,axiom,
% 5.49/5.88 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.49/5.88 = one_one_nat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(1)
% 5.49/5.88 thf(fact_1655_max__0__1_I1_J,axiom,
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.49/5.88 = one_on7984719198319812577d_enat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(1)
% 5.49/5.88 thf(fact_1656_max__0__1_I1_J,axiom,
% 5.49/5.88 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.49/5.88 = one_one_int ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(1)
% 5.49/5.88 thf(fact_1657_max__0__1_I2_J,axiom,
% 5.49/5.88 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.49/5.88 = one_one_real ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(2)
% 5.49/5.88 thf(fact_1658_max__0__1_I2_J,axiom,
% 5.49/5.88 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.49/5.88 = one_one_rat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(2)
% 5.49/5.88 thf(fact_1659_max__0__1_I2_J,axiom,
% 5.49/5.88 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.49/5.88 = one_one_nat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(2)
% 5.49/5.88 thf(fact_1660_max__0__1_I2_J,axiom,
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.49/5.88 = one_on7984719198319812577d_enat ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(2)
% 5.49/5.88 thf(fact_1661_max__0__1_I2_J,axiom,
% 5.49/5.88 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.49/5.88 = one_one_int ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(2)
% 5.49/5.88 thf(fact_1662_add__gr__0,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.88 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.88 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % add_gr_0
% 5.49/5.88 thf(fact_1663_max__0__1_I6_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(6)
% 5.49/5.88 thf(fact_1664_max__0__1_I6_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.49/5.88 = ( numeral_numeral_real @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(6)
% 5.49/5.88 thf(fact_1665_max__0__1_I6_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.49/5.88 = ( numeral_numeral_rat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(6)
% 5.49/5.88 thf(fact_1666_max__0__1_I6_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.49/5.88 = ( numeral_numeral_nat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(6)
% 5.49/5.88 thf(fact_1667_max__0__1_I6_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.49/5.88 = ( numeral_numeral_int @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(6)
% 5.49/5.88 thf(fact_1668_max__0__1_I5_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.49/5.88 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(5)
% 5.49/5.88 thf(fact_1669_max__0__1_I5_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.49/5.88 = ( numeral_numeral_real @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(5)
% 5.49/5.88 thf(fact_1670_max__0__1_I5_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.49/5.88 = ( numeral_numeral_rat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(5)
% 5.49/5.88 thf(fact_1671_max__0__1_I5_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.49/5.88 = ( numeral_numeral_nat @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(5)
% 5.49/5.88 thf(fact_1672_max__0__1_I5_J,axiom,
% 5.49/5.88 ! [X: num] :
% 5.49/5.88 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.49/5.88 = ( numeral_numeral_int @ X ) ) ).
% 5.49/5.88
% 5.49/5.88 % max_0_1(5)
% 5.49/5.88 thf(fact_1673_mult__eq__1__iff,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ( times_times_nat @ M @ N )
% 5.49/5.88 = ( suc @ zero_zero_nat ) )
% 5.49/5.88 = ( ( M
% 5.49/5.88 = ( suc @ zero_zero_nat ) )
% 5.49/5.88 & ( N
% 5.49/5.88 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % mult_eq_1_iff
% 5.49/5.88 thf(fact_1674_one__eq__mult__iff,axiom,
% 5.49/5.88 ! [M: nat,N: nat] :
% 5.49/5.88 ( ( ( suc @ zero_zero_nat )
% 5.49/5.88 = ( times_times_nat @ M @ N ) )
% 5.49/5.88 = ( ( M
% 5.49/5.88 = ( suc @ zero_zero_nat ) )
% 5.49/5.88 & ( N
% 5.49/5.88 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.49/5.88
% 5.49/5.88 % one_eq_mult_iff
% 5.49/5.88 thf(fact_1675_zero__less__diff,axiom,
% 5.49/5.88 ! [N: nat,M: nat] :
% 5.49/5.88 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.49/5.88 = ( ord_less_nat @ M @ N ) ) ).
% 5.49/5.88
% 5.49/5.88 % zero_less_diff
% 5.49/5.88 thf(fact_1676_div__by__Suc__0,axiom,
% 5.49/5.88 ! [M: nat] :
% 5.49/5.88 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.49/5.89 = M ) ).
% 5.49/5.89
% 5.49/5.89 % div_by_Suc_0
% 5.49/5.89 thf(fact_1677_nat__mult__less__cancel__disj,axiom,
% 5.49/5.89 ! [K: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.89 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_less_cancel_disj
% 5.49/5.89 thf(fact_1678_mult__less__cancel2,axiom,
% 5.49/5.89 ! [M: nat,K: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.89 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_less_cancel2
% 5.49/5.89 thf(fact_1679_nat__0__less__mult__iff,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_0_less_mult_iff
% 5.49/5.89 thf(fact_1680_diff__is__0__eq_H,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.89 => ( ( minus_minus_nat @ M @ N )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % diff_is_0_eq'
% 5.49/5.89 thf(fact_1681_diff__is__0__eq,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ( minus_minus_nat @ M @ N )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % diff_is_0_eq
% 5.49/5.89 thf(fact_1682_div__less,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ M @ N )
% 5.49/5.89 => ( ( divide_divide_nat @ M @ N )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_less
% 5.49/5.89 thf(fact_1683_less__one,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ N @ one_one_nat )
% 5.49/5.89 = ( N = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % less_one
% 5.49/5.89 thf(fact_1684_nat__power__eq__Suc__0__iff,axiom,
% 5.49/5.89 ! [X: nat,M: nat] :
% 5.49/5.89 ( ( ( power_power_nat @ X @ M )
% 5.49/5.89 = ( suc @ zero_zero_nat ) )
% 5.49/5.89 = ( ( M = zero_zero_nat )
% 5.49/5.89 | ( X
% 5.49/5.89 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_power_eq_Suc_0_iff
% 5.49/5.89 thf(fact_1685_power__Suc__0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.49/5.89 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_Suc_0
% 5.49/5.89 thf(fact_1686_nat__zero__less__power__iff,axiom,
% 5.49/5.89 ! [X: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.49/5.89 | ( N = zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_zero_less_power_iff
% 5.49/5.89 thf(fact_1687_nat__mult__div__cancel__disj,axiom,
% 5.49/5.89 ! [K: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ( K = zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.89 = zero_zero_nat ) )
% 5.49/5.89 & ( ( K != zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.89 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_div_cancel_disj
% 5.49/5.89 thf(fact_1688_mod__by__Suc__0,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % mod_by_Suc_0
% 5.49/5.89 thf(fact_1689_list__update__beyond,axiom,
% 5.49/5.89 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 5.49/5.89 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.49/5.89 = Xs2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % list_update_beyond
% 5.49/5.89 thf(fact_1690_list__update__beyond,axiom,
% 5.49/5.89 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 5.49/5.89 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.49/5.89 = Xs2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % list_update_beyond
% 5.49/5.89 thf(fact_1691_list__update__beyond,axiom,
% 5.49/5.89 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 5.49/5.89 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.49/5.89 = Xs2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % list_update_beyond
% 5.49/5.89 thf(fact_1692_list__update__beyond,axiom,
% 5.49/5.89 ! [Xs2: list_int,I2: nat,X: int] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 5.49/5.89 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.49/5.89 = Xs2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % list_update_beyond
% 5.49/5.89 thf(fact_1693_divide__le__0__1__iff,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.49/5.89 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_0_1_iff
% 5.49/5.89 thf(fact_1694_divide__le__0__1__iff,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.49/5.89 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_0_1_iff
% 5.49/5.89 thf(fact_1695_zero__le__divide__1__iff,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.49/5.89 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_le_divide_1_iff
% 5.49/5.89 thf(fact_1696_zero__le__divide__1__iff,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.49/5.89 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_le_divide_1_iff
% 5.49/5.89 thf(fact_1697_zero__less__divide__1__iff,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.49/5.89 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_divide_1_iff
% 5.49/5.89 thf(fact_1698_zero__less__divide__1__iff,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.49/5.89 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_divide_1_iff
% 5.49/5.89 thf(fact_1699_less__divide__eq__1__pos,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.89 = ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % less_divide_eq_1_pos
% 5.49/5.89 thf(fact_1700_less__divide__eq__1__pos,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.89 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % less_divide_eq_1_pos
% 5.49/5.89 thf(fact_1701_less__divide__eq__1__neg,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.89 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.89 = ( ord_less_real @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % less_divide_eq_1_neg
% 5.49/5.89 thf(fact_1702_less__divide__eq__1__neg,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.89 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.89 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % less_divide_eq_1_neg
% 5.49/5.89 thf(fact_1703_divide__less__eq__1__pos,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.89 = ( ord_less_real @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_eq_1_pos
% 5.49/5.89 thf(fact_1704_divide__less__eq__1__pos,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.89 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_eq_1_pos
% 5.49/5.89 thf(fact_1705_divide__less__eq__1__neg,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.89 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.89 = ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_eq_1_neg
% 5.49/5.89 thf(fact_1706_divide__less__eq__1__neg,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.89 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.89 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_eq_1_neg
% 5.49/5.89 thf(fact_1707_divide__less__0__1__iff,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.49/5.89 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_0_1_iff
% 5.49/5.89 thf(fact_1708_divide__less__0__1__iff,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.49/5.89 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_less_0_1_iff
% 5.49/5.89 thf(fact_1709_eq__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [A: complex,B: complex,W: num] :
% 5.49/5.89 ( ( A
% 5.49/5.89 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.49/5.89 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.49/5.89 != zero_zero_complex )
% 5.49/5.89 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.49/5.89 = B ) )
% 5.49/5.89 & ( ( ( numera6690914467698888265omplex @ W )
% 5.49/5.89 = zero_zero_complex )
% 5.49/5.89 => ( A = zero_zero_complex ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_divide_eq_numeral1(1)
% 5.49/5.89 thf(fact_1710_eq__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [A: real,B: real,W: num] :
% 5.49/5.89 ( ( A
% 5.49/5.89 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.49/5.89 = ( ( ( ( numeral_numeral_real @ W )
% 5.49/5.89 != zero_zero_real )
% 5.49/5.89 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.49/5.89 = B ) )
% 5.49/5.89 & ( ( ( numeral_numeral_real @ W )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 => ( A = zero_zero_real ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_divide_eq_numeral1(1)
% 5.49/5.89 thf(fact_1711_eq__divide__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [A: rat,B: rat,W: num] :
% 5.49/5.89 ( ( A
% 5.49/5.89 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.49/5.89 = ( ( ( ( numeral_numeral_rat @ W )
% 5.49/5.89 != zero_zero_rat )
% 5.49/5.89 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.49/5.89 = B ) )
% 5.49/5.89 & ( ( ( numeral_numeral_rat @ W )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 => ( A = zero_zero_rat ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_divide_eq_numeral1(1)
% 5.49/5.89 thf(fact_1712_divide__eq__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [B: complex,W: num,A: complex] :
% 5.49/5.89 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.49/5.89 != zero_zero_complex )
% 5.49/5.89 => ( B
% 5.49/5.89 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.49/5.89 & ( ( ( numera6690914467698888265omplex @ W )
% 5.49/5.89 = zero_zero_complex )
% 5.49/5.89 => ( A = zero_zero_complex ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_eq_eq_numeral1(1)
% 5.49/5.89 thf(fact_1713_divide__eq__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [B: real,W: num,A: real] :
% 5.49/5.89 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( ( ( numeral_numeral_real @ W )
% 5.49/5.89 != zero_zero_real )
% 5.49/5.89 => ( B
% 5.49/5.89 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.49/5.89 & ( ( ( numeral_numeral_real @ W )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 => ( A = zero_zero_real ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_eq_eq_numeral1(1)
% 5.49/5.89 thf(fact_1714_divide__eq__eq__numeral1_I1_J,axiom,
% 5.49/5.89 ! [B: rat,W: num,A: rat] :
% 5.49/5.89 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( ( ( numeral_numeral_rat @ W )
% 5.49/5.89 != zero_zero_rat )
% 5.49/5.89 => ( B
% 5.49/5.89 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.49/5.89 & ( ( ( numeral_numeral_rat @ W )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 => ( A = zero_zero_rat ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_eq_eq_numeral1(1)
% 5.49/5.89 thf(fact_1715_nonzero__divide__mult__cancel__right,axiom,
% 5.49/5.89 ! [B: complex,A: complex] :
% 5.49/5.89 ( ( B != zero_zero_complex )
% 5.49/5.89 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.49/5.89 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_right
% 5.49/5.89 thf(fact_1716_nonzero__divide__mult__cancel__right,axiom,
% 5.49/5.89 ! [B: real,A: real] :
% 5.49/5.89 ( ( B != zero_zero_real )
% 5.49/5.89 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.49/5.89 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_right
% 5.49/5.89 thf(fact_1717_nonzero__divide__mult__cancel__right,axiom,
% 5.49/5.89 ! [B: rat,A: rat] :
% 5.49/5.89 ( ( B != zero_zero_rat )
% 5.49/5.89 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.49/5.89 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_right
% 5.49/5.89 thf(fact_1718_nonzero__divide__mult__cancel__left,axiom,
% 5.49/5.89 ! [A: complex,B: complex] :
% 5.49/5.89 ( ( A != zero_zero_complex )
% 5.49/5.89 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.49/5.89 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_left
% 5.49/5.89 thf(fact_1719_nonzero__divide__mult__cancel__left,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( A != zero_zero_real )
% 5.49/5.89 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.49/5.89 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_left
% 5.49/5.89 thf(fact_1720_nonzero__divide__mult__cancel__left,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( A != zero_zero_rat )
% 5.49/5.89 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.49/5.89 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nonzero_divide_mult_cancel_left
% 5.49/5.89 thf(fact_1721_div__mult__self4,axiom,
% 5.49/5.89 ! [B: nat,C: nat,A: nat] :
% 5.49/5.89 ( ( B != zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.49/5.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self4
% 5.49/5.89 thf(fact_1722_div__mult__self4,axiom,
% 5.49/5.89 ! [B: int,C: int,A: int] :
% 5.49/5.89 ( ( B != zero_zero_int )
% 5.49/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.49/5.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self4
% 5.49/5.89 thf(fact_1723_div__mult__self3,axiom,
% 5.49/5.89 ! [B: nat,C: nat,A: nat] :
% 5.49/5.89 ( ( B != zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.49/5.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self3
% 5.49/5.89 thf(fact_1724_div__mult__self3,axiom,
% 5.49/5.89 ! [B: int,C: int,A: int] :
% 5.49/5.89 ( ( B != zero_zero_int )
% 5.49/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.49/5.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self3
% 5.49/5.89 thf(fact_1725_div__mult__self2,axiom,
% 5.49/5.89 ! [B: nat,A: nat,C: nat] :
% 5.49/5.89 ( ( B != zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.49/5.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self2
% 5.49/5.89 thf(fact_1726_div__mult__self2,axiom,
% 5.49/5.89 ! [B: int,A: int,C: int] :
% 5.49/5.89 ( ( B != zero_zero_int )
% 5.49/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.49/5.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self2
% 5.49/5.89 thf(fact_1727_div__mult__self1,axiom,
% 5.49/5.89 ! [B: nat,A: nat,C: nat] :
% 5.49/5.89 ( ( B != zero_zero_nat )
% 5.49/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.49/5.89 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self1
% 5.49/5.89 thf(fact_1728_div__mult__self1,axiom,
% 5.49/5.89 ! [B: int,A: int,C: int] :
% 5.49/5.89 ( ( B != zero_zero_int )
% 5.49/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.49/5.89 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self1
% 5.49/5.89 thf(fact_1729_power__eq__0__iff,axiom,
% 5.49/5.89 ! [A: rat,N: nat] :
% 5.49/5.89 ( ( ( power_power_rat @ A @ N )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 = ( ( A = zero_zero_rat )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_0_iff
% 5.49/5.89 thf(fact_1730_power__eq__0__iff,axiom,
% 5.49/5.89 ! [A: nat,N: nat] :
% 5.49/5.89 ( ( ( power_power_nat @ A @ N )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 = ( ( A = zero_zero_nat )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_0_iff
% 5.49/5.89 thf(fact_1731_power__eq__0__iff,axiom,
% 5.49/5.89 ! [A: real,N: nat] :
% 5.49/5.89 ( ( ( power_power_real @ A @ N )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 = ( ( A = zero_zero_real )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_0_iff
% 5.49/5.89 thf(fact_1732_power__eq__0__iff,axiom,
% 5.49/5.89 ! [A: int,N: nat] :
% 5.49/5.89 ( ( ( power_power_int @ A @ N )
% 5.49/5.89 = zero_zero_int )
% 5.49/5.89 = ( ( A = zero_zero_int )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_0_iff
% 5.49/5.89 thf(fact_1733_power__eq__0__iff,axiom,
% 5.49/5.89 ! [A: complex,N: nat] :
% 5.49/5.89 ( ( ( power_power_complex @ A @ N )
% 5.49/5.89 = zero_zero_complex )
% 5.49/5.89 = ( ( A = zero_zero_complex )
% 5.49/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_0_iff
% 5.49/5.89 thf(fact_1734_Suc__pred,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.49/5.89 = N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_pred
% 5.49/5.89 thf(fact_1735_one__le__mult__iff,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.49/5.89 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.49/5.89 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % one_le_mult_iff
% 5.49/5.89 thf(fact_1736_nat__mult__le__cancel__disj,axiom,
% 5.49/5.89 ! [K: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.89 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_le_cancel_disj
% 5.49/5.89 thf(fact_1737_mult__le__cancel2,axiom,
% 5.49/5.89 ! [M: nat,K: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.49/5.89 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.89 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_le_cancel2
% 5.49/5.89 thf(fact_1738_div__mult__self1__is__m,axiom,
% 5.49/5.89 ! [N: nat,M: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.49/5.89 = M ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self1_is_m
% 5.49/5.89 thf(fact_1739_div__mult__self__is__m,axiom,
% 5.49/5.89 ! [N: nat,M: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.49/5.89 = M ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_mult_self_is_m
% 5.49/5.89 thf(fact_1740_Suc__mod__mult__self1,axiom,
% 5.49/5.89 ! [M: nat,K: nat,N: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_mod_mult_self1
% 5.49/5.89 thf(fact_1741_Suc__mod__mult__self2,axiom,
% 5.49/5.89 ! [M: nat,N: nat,K: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_mod_mult_self2
% 5.49/5.89 thf(fact_1742_Suc__mod__mult__self3,axiom,
% 5.49/5.89 ! [K: nat,N: nat,M: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_mod_mult_self3
% 5.49/5.89 thf(fact_1743_Suc__mod__mult__self4,axiom,
% 5.49/5.89 ! [N: nat,K: nat,M: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_mod_mult_self4
% 5.49/5.89 thf(fact_1744_nth__list__update__eq,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.89 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 5.49/5.89 = X ) ) ).
% 5.49/5.89
% 5.49/5.89 % nth_list_update_eq
% 5.49/5.89 thf(fact_1745_nth__list__update__eq,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.89 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 5.49/5.89 = X ) ) ).
% 5.49/5.89
% 5.49/5.89 % nth_list_update_eq
% 5.49/5.89 thf(fact_1746_nth__list__update__eq,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.89 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 5.49/5.89 = X ) ) ).
% 5.49/5.89
% 5.49/5.89 % nth_list_update_eq
% 5.49/5.89 thf(fact_1747_nth__list__update__eq,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_int,X: int] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.89 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 5.49/5.89 = X ) ) ).
% 5.49/5.89
% 5.49/5.89 % nth_list_update_eq
% 5.49/5.89 thf(fact_1748_le__divide__eq__1__pos,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.89 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % le_divide_eq_1_pos
% 5.49/5.89 thf(fact_1749_le__divide__eq__1__pos,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.89 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % le_divide_eq_1_pos
% 5.49/5.89 thf(fact_1750_le__divide__eq__1__neg,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.89 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.89 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % le_divide_eq_1_neg
% 5.49/5.89 thf(fact_1751_le__divide__eq__1__neg,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.89 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.89 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % le_divide_eq_1_neg
% 5.49/5.89 thf(fact_1752_divide__le__eq__1__pos,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.89 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_eq_1_pos
% 5.49/5.89 thf(fact_1753_divide__le__eq__1__pos,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.89 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_eq_1_pos
% 5.49/5.89 thf(fact_1754_divide__le__eq__1__neg,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.89 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.89 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_eq_1_neg
% 5.49/5.89 thf(fact_1755_divide__le__eq__1__neg,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.89 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.89 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divide_le_eq_1_neg
% 5.49/5.89 thf(fact_1756_power__strict__decreasing__iff,axiom,
% 5.49/5.89 ! [B: real,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.89 => ( ( ord_less_real @ B @ one_one_real )
% 5.49/5.89 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.49/5.89 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_strict_decreasing_iff
% 5.49/5.89 thf(fact_1757_power__strict__decreasing__iff,axiom,
% 5.49/5.89 ! [B: rat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.89 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.49/5.89 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.49/5.89 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_strict_decreasing_iff
% 5.49/5.89 thf(fact_1758_power__strict__decreasing__iff,axiom,
% 5.49/5.89 ! [B: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.49/5.89 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.49/5.89 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_strict_decreasing_iff
% 5.49/5.89 thf(fact_1759_power__strict__decreasing__iff,axiom,
% 5.49/5.89 ! [B: int,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ( ord_less_int @ B @ one_one_int )
% 5.49/5.89 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.49/5.89 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_strict_decreasing_iff
% 5.49/5.89 thf(fact_1760_power__mono__iff,axiom,
% 5.49/5.89 ! [A: real,B: real,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mono_iff
% 5.49/5.89 thf(fact_1761_power__mono__iff,axiom,
% 5.49/5.89 ! [A: rat,B: rat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mono_iff
% 5.49/5.89 thf(fact_1762_power__mono__iff,axiom,
% 5.49/5.89 ! [A: nat,B: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mono_iff
% 5.49/5.89 thf(fact_1763_power__mono__iff,axiom,
% 5.49/5.89 ! [A: int,B: int,N: nat] :
% 5.49/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mono_iff
% 5.49/5.89 thf(fact_1764_zero__eq__power2,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 = ( A = zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_eq_power2
% 5.49/5.89 thf(fact_1765_zero__eq__power2,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 = ( A = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_eq_power2
% 5.49/5.89 thf(fact_1766_zero__eq__power2,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 = ( A = zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_eq_power2
% 5.49/5.89 thf(fact_1767_zero__eq__power2,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_int )
% 5.49/5.89 = ( A = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_eq_power2
% 5.49/5.89 thf(fact_1768_zero__eq__power2,axiom,
% 5.49/5.89 ! [A: complex] :
% 5.49/5.89 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_complex )
% 5.49/5.89 = ( A = zero_zero_complex ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_eq_power2
% 5.49/5.89 thf(fact_1769_bits__one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_nat ) ).
% 5.49/5.89
% 5.49/5.89 % bits_one_mod_two_eq_one
% 5.49/5.89 thf(fact_1770_bits__one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_int ) ).
% 5.49/5.89
% 5.49/5.89 % bits_one_mod_two_eq_one
% 5.49/5.89 thf(fact_1771_bits__one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_Code_integer ) ).
% 5.49/5.89
% 5.49/5.89 % bits_one_mod_two_eq_one
% 5.49/5.89 thf(fact_1772_one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_nat ) ).
% 5.49/5.89
% 5.49/5.89 % one_mod_two_eq_one
% 5.49/5.89 thf(fact_1773_one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_int ) ).
% 5.49/5.89
% 5.49/5.89 % one_mod_two_eq_one
% 5.49/5.89 thf(fact_1774_one__mod__two__eq__one,axiom,
% 5.49/5.89 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_Code_integer ) ).
% 5.49/5.89
% 5.49/5.89 % one_mod_two_eq_one
% 5.49/5.89 thf(fact_1775_mod2__Suc__Suc,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod2_Suc_Suc
% 5.49/5.89 thf(fact_1776_Suc__diff__1,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.49/5.89 = N ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_diff_1
% 5.49/5.89 thf(fact_1777_Suc__times__numeral__mod__eq,axiom,
% 5.49/5.89 ! [K: num,N: nat] :
% 5.49/5.89 ( ( ( numeral_numeral_nat @ K )
% 5.49/5.89 != one_one_nat )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.49/5.89 = one_one_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_times_numeral_mod_eq
% 5.49/5.89 thf(fact_1778_set__swap,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.89 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.89 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.49/5.89 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_swap
% 5.49/5.89 thf(fact_1779_set__swap,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_o,J: nat] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.89 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.89 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.49/5.89 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_swap
% 5.49/5.89 thf(fact_1780_set__swap,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_nat,J: nat] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.89 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.89 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.49/5.89 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_swap
% 5.49/5.89 thf(fact_1781_set__swap,axiom,
% 5.49/5.89 ! [I2: nat,Xs2: list_int,J: nat] :
% 5.49/5.89 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.89 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.89 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.49/5.89 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_swap
% 5.49/5.89 thf(fact_1782_bits__1__div__2,axiom,
% 5.49/5.89 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % bits_1_div_2
% 5.49/5.89 thf(fact_1783_bits__1__div__2,axiom,
% 5.49/5.89 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_int ) ).
% 5.49/5.89
% 5.49/5.89 % bits_1_div_2
% 5.49/5.89 thf(fact_1784_one__div__two__eq__zero,axiom,
% 5.49/5.89 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % one_div_two_eq_zero
% 5.49/5.89 thf(fact_1785_one__div__two__eq__zero,axiom,
% 5.49/5.89 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_int ) ).
% 5.49/5.89
% 5.49/5.89 % one_div_two_eq_zero
% 5.49/5.89 thf(fact_1786_power__decreasing__iff,axiom,
% 5.49/5.89 ! [B: real,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.89 => ( ( ord_less_real @ B @ one_one_real )
% 5.49/5.89 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_decreasing_iff
% 5.49/5.89 thf(fact_1787_power__decreasing__iff,axiom,
% 5.49/5.89 ! [B: rat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.89 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.49/5.89 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_decreasing_iff
% 5.49/5.89 thf(fact_1788_power__decreasing__iff,axiom,
% 5.49/5.89 ! [B: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.49/5.89 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_decreasing_iff
% 5.49/5.89 thf(fact_1789_power__decreasing__iff,axiom,
% 5.49/5.89 ! [B: int,M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ( ord_less_int @ B @ one_one_int )
% 5.49/5.89 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.49/5.89 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_decreasing_iff
% 5.49/5.89 thf(fact_1790_power2__eq__iff__nonneg,axiom,
% 5.49/5.89 ! [X: real,Y2: real] :
% 5.49/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.89 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( X = Y2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_eq_iff_nonneg
% 5.49/5.89 thf(fact_1791_power2__eq__iff__nonneg,axiom,
% 5.49/5.89 ! [X: rat,Y2: rat] :
% 5.49/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.89 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( X = Y2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_eq_iff_nonneg
% 5.49/5.89 thf(fact_1792_power2__eq__iff__nonneg,axiom,
% 5.49/5.89 ! [X: nat,Y2: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.49/5.89 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( X = Y2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_eq_iff_nonneg
% 5.49/5.89 thf(fact_1793_power2__eq__iff__nonneg,axiom,
% 5.49/5.89 ! [X: int,Y2: int] :
% 5.49/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.89 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( X = Y2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_eq_iff_nonneg
% 5.49/5.89 thf(fact_1794_power2__less__eq__zero__iff,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.49/5.89 = ( A = zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_less_eq_zero_iff
% 5.49/5.89 thf(fact_1795_power2__less__eq__zero__iff,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.49/5.89 = ( A = zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_less_eq_zero_iff
% 5.49/5.89 thf(fact_1796_power2__less__eq__zero__iff,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.49/5.89 = ( A = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % power2_less_eq_zero_iff
% 5.49/5.89 thf(fact_1797_zero__less__power2,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( A != zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_power2
% 5.49/5.89 thf(fact_1798_zero__less__power2,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( A != zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_power2
% 5.49/5.89 thf(fact_1799_zero__less__power2,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( A != zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_power2
% 5.49/5.89 thf(fact_1800_sum__power2__eq__zero__iff,axiom,
% 5.49/5.89 ! [X: rat,Y2: rat] :
% 5.49/5.89 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 = ( ( X = zero_zero_rat )
% 5.49/5.89 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % sum_power2_eq_zero_iff
% 5.49/5.89 thf(fact_1801_sum__power2__eq__zero__iff,axiom,
% 5.49/5.89 ! [X: real,Y2: real] :
% 5.49/5.89 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 = ( ( X = zero_zero_real )
% 5.49/5.89 & ( Y2 = zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % sum_power2_eq_zero_iff
% 5.49/5.89 thf(fact_1802_sum__power2__eq__zero__iff,axiom,
% 5.49/5.89 ! [X: int,Y2: int] :
% 5.49/5.89 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = zero_zero_int )
% 5.49/5.89 = ( ( X = zero_zero_int )
% 5.49/5.89 & ( Y2 = zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % sum_power2_eq_zero_iff
% 5.49/5.89 thf(fact_1803_not__mod__2__eq__1__eq__0,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 != one_one_nat )
% 5.49/5.89 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_1_eq_0
% 5.49/5.89 thf(fact_1804_not__mod__2__eq__1__eq__0,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 != one_one_int )
% 5.49/5.89 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_1_eq_0
% 5.49/5.89 thf(fact_1805_not__mod__2__eq__1__eq__0,axiom,
% 5.49/5.89 ! [A: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 != one_one_Code_integer )
% 5.49/5.89 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_z3403309356797280102nteger ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_1_eq_0
% 5.49/5.89 thf(fact_1806_not__mod__2__eq__0__eq__1,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 != zero_zero_nat )
% 5.49/5.89 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_0_eq_1
% 5.49/5.89 thf(fact_1807_not__mod__2__eq__0__eq__1,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 != zero_zero_int )
% 5.49/5.89 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_0_eq_1
% 5.49/5.89 thf(fact_1808_not__mod__2__eq__0__eq__1,axiom,
% 5.49/5.89 ! [A: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 != zero_z3403309356797280102nteger )
% 5.49/5.89 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_Code_integer ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod_2_eq_0_eq_1
% 5.49/5.89 thf(fact_1809_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 != ( suc @ zero_zero_nat ) )
% 5.49/5.89 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_mod2_eq_Suc_0_eq_0
% 5.49/5.89 thf(fact_1810_add__self__mod__2,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % add_self_mod_2
% 5.49/5.89 thf(fact_1811_mod2__gr__0,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.89 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.89 = one_one_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod2_gr_0
% 5.49/5.89 thf(fact_1812_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer] :
% 5.49/5.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.49/5.89 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.49/5.89 thf(fact_1813_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.89 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.49/5.89 thf(fact_1814_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.89 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.49/5.89 thf(fact_1815_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.49/5.89 ! [B: nat,A: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.49/5.89 thf(fact_1816_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.49/5.89 ! [B: int,A: int] :
% 5.49/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.49/5.89 thf(fact_1817_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.49/5.89 ! [B: code_integer,A: code_integer] :
% 5.49/5.89 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.89 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.49/5.89 thf(fact_1818_VEBT_Osize_I4_J,axiom,
% 5.49/5.89 ! [X21: $o,X222: $o] :
% 5.49/5.89 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT.size(4)
% 5.49/5.89 thf(fact_1819_vebt__buildup_Osimps_I2_J,axiom,
% 5.49/5.89 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.49/5.89 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.49/5.89
% 5.49/5.89 % vebt_buildup.simps(2)
% 5.49/5.89 thf(fact_1820_zero__reorient,axiom,
% 5.49/5.89 ! [X: complex] :
% 5.49/5.89 ( ( zero_zero_complex = X )
% 5.49/5.89 = ( X = zero_zero_complex ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_reorient
% 5.49/5.89 thf(fact_1821_zero__reorient,axiom,
% 5.49/5.89 ! [X: real] :
% 5.49/5.89 ( ( zero_zero_real = X )
% 5.49/5.89 = ( X = zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_reorient
% 5.49/5.89 thf(fact_1822_zero__reorient,axiom,
% 5.49/5.89 ! [X: rat] :
% 5.49/5.89 ( ( zero_zero_rat = X )
% 5.49/5.89 = ( X = zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_reorient
% 5.49/5.89 thf(fact_1823_zero__reorient,axiom,
% 5.49/5.89 ! [X: nat] :
% 5.49/5.89 ( ( zero_zero_nat = X )
% 5.49/5.89 = ( X = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_reorient
% 5.49/5.89 thf(fact_1824_zero__reorient,axiom,
% 5.49/5.89 ! [X: int] :
% 5.49/5.89 ( ( zero_zero_int = X )
% 5.49/5.89 = ( X = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_reorient
% 5.49/5.89 thf(fact_1825_mod__eq__self__iff__div__eq__0,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ A @ B )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( divide_divide_nat @ A @ B )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eq_self_iff_div_eq_0
% 5.49/5.89 thf(fact_1826_mod__eq__self__iff__div__eq__0,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ B )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( divide_divide_int @ A @ B )
% 5.49/5.89 = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eq_self_iff_div_eq_0
% 5.49/5.89 thf(fact_1827_mod__eq__self__iff__div__eq__0,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.49/5.89 = A )
% 5.49/5.89 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.49/5.89 = zero_z3403309356797280102nteger ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eq_self_iff_div_eq_0
% 5.49/5.89 thf(fact_1828_mod__Suc,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.49/5.89 = N )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.49/5.89 = zero_zero_nat ) )
% 5.49/5.89 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.49/5.89 != N )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.49/5.89 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_Suc
% 5.49/5.89 thf(fact_1829_mod__less__divisor,axiom,
% 5.49/5.89 ! [N: nat,M: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_less_divisor
% 5.49/5.89 thf(fact_1830_mod__eq__0D,axiom,
% 5.49/5.89 ! [M: nat,D: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ M @ D )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 => ? [Q3: nat] :
% 5.49/5.89 ( M
% 5.49/5.89 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eq_0D
% 5.49/5.89 thf(fact_1831_finite__nat__set__iff__bounded,axiom,
% 5.49/5.89 ( finite_finite_nat
% 5.49/5.89 = ( ^ [N6: set_nat] :
% 5.49/5.89 ? [M6: nat] :
% 5.49/5.89 ! [X2: nat] :
% 5.49/5.89 ( ( member_nat @ X2 @ N6 )
% 5.49/5.89 => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_nat_set_iff_bounded
% 5.49/5.89 thf(fact_1832_bounded__nat__set__is__finite,axiom,
% 5.49/5.89 ! [N5: set_nat,N: nat] :
% 5.49/5.89 ( ! [X3: nat] :
% 5.49/5.89 ( ( member_nat @ X3 @ N5 )
% 5.49/5.89 => ( ord_less_nat @ X3 @ N ) )
% 5.49/5.89 => ( finite_finite_nat @ N5 ) ) ).
% 5.49/5.89
% 5.49/5.89 % bounded_nat_set_is_finite
% 5.49/5.89 thf(fact_1833_finite__nat__set__iff__bounded__le,axiom,
% 5.49/5.89 ( finite_finite_nat
% 5.49/5.89 = ( ^ [N6: set_nat] :
% 5.49/5.89 ? [M6: nat] :
% 5.49/5.89 ! [X2: nat] :
% 5.49/5.89 ( ( member_nat @ X2 @ N6 )
% 5.49/5.89 => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_nat_set_iff_bounded_le
% 5.49/5.89 thf(fact_1834_finite__M__bounded__by__nat,axiom,
% 5.49/5.89 ! [P: nat > $o,I2: nat] :
% 5.49/5.89 ( finite_finite_nat
% 5.49/5.89 @ ( collect_nat
% 5.49/5.89 @ ^ [K3: nat] :
% 5.49/5.89 ( ( P @ K3 )
% 5.49/5.89 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_M_bounded_by_nat
% 5.49/5.89 thf(fact_1835_finite__less__ub,axiom,
% 5.49/5.89 ! [F: nat > nat,U: nat] :
% 5.49/5.89 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.49/5.89 => ( finite_finite_nat
% 5.49/5.89 @ ( collect_nat
% 5.49/5.89 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_less_ub
% 5.49/5.89 thf(fact_1836_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer] :
% 5.49/5.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.49/5.89 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.49/5.89 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.49/5.89 = A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less
% 5.49/5.89 thf(fact_1837_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.89 => ( ( ord_less_nat @ A @ B )
% 5.49/5.89 => ( ( modulo_modulo_nat @ A @ B )
% 5.49/5.89 = A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less
% 5.49/5.89 thf(fact_1838_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.89 => ( ( ord_less_int @ A @ B )
% 5.49/5.89 => ( ( modulo_modulo_int @ A @ B )
% 5.49/5.89 = A ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_less
% 5.49/5.89 thf(fact_1839_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.49/5.89 ! [B: code_integer,A: code_integer] :
% 5.49/5.89 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.89 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.49/5.89 thf(fact_1840_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.49/5.89 ! [B: nat,A: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.49/5.89 thf(fact_1841_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.49/5.89 ! [B: int,A: int] :
% 5.49/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.49/5.89 thf(fact_1842_cong__exp__iff__simps_I2_J,axiom,
% 5.49/5.89 ! [N: num,Q2: num] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(2)
% 5.49/5.89 thf(fact_1843_cong__exp__iff__simps_I2_J,axiom,
% 5.49/5.89 ! [N: num,Q2: num] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = zero_zero_int )
% 5.49/5.89 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.49/5.89 = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(2)
% 5.49/5.89 thf(fact_1844_cong__exp__iff__simps_I2_J,axiom,
% 5.49/5.89 ! [N: num,Q2: num] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = zero_z3403309356797280102nteger )
% 5.49/5.89 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.49/5.89 = zero_z3403309356797280102nteger ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(2)
% 5.49/5.89 thf(fact_1845_cong__exp__iff__simps_I1_J,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(1)
% 5.49/5.89 thf(fact_1846_cong__exp__iff__simps_I1_J,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.49/5.89 = zero_zero_int ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(1)
% 5.49/5.89 thf(fact_1847_cong__exp__iff__simps_I1_J,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.49/5.89 = zero_z3403309356797280102nteger ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(1)
% 5.49/5.89 thf(fact_1848_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.49/5.89 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.89 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.49/5.89 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.49/5.89 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ X3 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT_internal.naive_member.cases
% 5.49/5.89 thf(fact_1849_mod__le__divisor,axiom,
% 5.49/5.89 ! [N: nat,M: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_le_divisor
% 5.49/5.89 thf(fact_1850_invar__vebt_Ointros_I1_J,axiom,
% 5.49/5.89 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % invar_vebt.intros(1)
% 5.49/5.89 thf(fact_1851_max__add__distrib__left,axiom,
% 5.49/5.89 ! [X: real,Y2: real,Z: real] :
% 5.49/5.89 ( ( plus_plus_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_left
% 5.49/5.89 thf(fact_1852_max__add__distrib__left,axiom,
% 5.49/5.89 ! [X: rat,Y2: rat,Z: rat] :
% 5.49/5.89 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_left
% 5.49/5.89 thf(fact_1853_max__add__distrib__left,axiom,
% 5.49/5.89 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_left
% 5.49/5.89 thf(fact_1854_max__add__distrib__left,axiom,
% 5.49/5.89 ! [X: int,Y2: int,Z: int] :
% 5.49/5.89 ( ( plus_plus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_left
% 5.49/5.89 thf(fact_1855_max__add__distrib__right,axiom,
% 5.49/5.89 ! [X: real,Y2: real,Z: real] :
% 5.49/5.89 ( ( plus_plus_real @ X @ ( ord_max_real @ Y2 @ Z ) )
% 5.49/5.89 = ( ord_max_real @ ( plus_plus_real @ X @ Y2 ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_right
% 5.49/5.89 thf(fact_1856_max__add__distrib__right,axiom,
% 5.49/5.89 ! [X: rat,Y2: rat,Z: rat] :
% 5.49/5.89 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y2 @ Z ) )
% 5.49/5.89 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_right
% 5.49/5.89 thf(fact_1857_max__add__distrib__right,axiom,
% 5.49/5.89 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y2 @ Z ) )
% 5.49/5.89 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y2 ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_right
% 5.49/5.89 thf(fact_1858_max__add__distrib__right,axiom,
% 5.49/5.89 ! [X: int,Y2: int,Z: int] :
% 5.49/5.89 ( ( plus_plus_int @ X @ ( ord_max_int @ Y2 @ Z ) )
% 5.49/5.89 = ( ord_max_int @ ( plus_plus_int @ X @ Y2 ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_add_distrib_right
% 5.49/5.89 thf(fact_1859_max__diff__distrib__left,axiom,
% 5.49/5.89 ! [X: real,Y2: real,Z: real] :
% 5.49/5.89 ( ( minus_minus_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_diff_distrib_left
% 5.49/5.89 thf(fact_1860_max__diff__distrib__left,axiom,
% 5.49/5.89 ! [X: rat,Y2: rat,Z: rat] :
% 5.49/5.89 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_diff_distrib_left
% 5.49/5.89 thf(fact_1861_max__diff__distrib__left,axiom,
% 5.49/5.89 ! [X: int,Y2: int,Z: int] :
% 5.49/5.89 ( ( minus_minus_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 5.49/5.89 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y2 @ Z ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % max_diff_distrib_left
% 5.49/5.89 thf(fact_1862_power__0__left,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.49/5.89 = one_one_rat ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.49/5.89 = zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_0_left
% 5.49/5.89 thf(fact_1863_power__0__left,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.49/5.89 = one_one_nat ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.49/5.89 = zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_0_left
% 5.49/5.89 thf(fact_1864_power__0__left,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( ( power_power_real @ zero_zero_real @ N )
% 5.49/5.89 = one_one_real ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_real @ zero_zero_real @ N )
% 5.49/5.89 = zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_0_left
% 5.49/5.89 thf(fact_1865_power__0__left,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( ( power_power_int @ zero_zero_int @ N )
% 5.49/5.89 = one_one_int ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_int @ zero_zero_int @ N )
% 5.49/5.89 = zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_0_left
% 5.49/5.89 thf(fact_1866_power__0__left,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.49/5.89 = one_one_complex ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.49/5.89 = zero_zero_complex ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_0_left
% 5.49/5.89 thf(fact_1867_zero__power,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.49/5.89 = zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_power
% 5.49/5.89 thf(fact_1868_zero__power,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.49/5.89 = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_power
% 5.49/5.89 thf(fact_1869_zero__power,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( power_power_real @ zero_zero_real @ N )
% 5.49/5.89 = zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_power
% 5.49/5.89 thf(fact_1870_zero__power,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( power_power_int @ zero_zero_int @ N )
% 5.49/5.89 = zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_power
% 5.49/5.89 thf(fact_1871_zero__power,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.49/5.89 = zero_zero_complex ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_power
% 5.49/5.89 thf(fact_1872_mod__mult__right__eq,axiom,
% 5.49/5.89 ! [A: nat,B: nat,C: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_right_eq
% 5.49/5.89 thf(fact_1873_mod__mult__right__eq,axiom,
% 5.49/5.89 ! [A: int,B: int,C: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_right_eq
% 5.49/5.89 thf(fact_1874_mod__mult__right__eq,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_right_eq
% 5.49/5.89 thf(fact_1875_mod__mult__left__eq,axiom,
% 5.49/5.89 ! [A: nat,C: nat,B: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_left_eq
% 5.49/5.89 thf(fact_1876_mod__mult__left__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_left_eq
% 5.49/5.89 thf(fact_1877_mod__mult__left__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_left_eq
% 5.49/5.89 thf(fact_1878_mult__mod__right,axiom,
% 5.49/5.89 ! [C: nat,A: nat,B: nat] :
% 5.49/5.89 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.49/5.89 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_mod_right
% 5.49/5.89 thf(fact_1879_mult__mod__right,axiom,
% 5.49/5.89 ! [C: int,A: int,B: int] :
% 5.49/5.89 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.89 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_mod_right
% 5.49/5.89 thf(fact_1880_mult__mod__right,axiom,
% 5.49/5.89 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.49/5.89 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_mod_right
% 5.49/5.89 thf(fact_1881_mod__mult__mult2,axiom,
% 5.49/5.89 ! [A: nat,C: nat,B: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.49/5.89 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_mult2
% 5.49/5.89 thf(fact_1882_mod__mult__mult2,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.89 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_mult2
% 5.49/5.89 thf(fact_1883_mod__mult__mult2,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.49/5.89 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_mult2
% 5.49/5.89 thf(fact_1884_mod__mult__cong,axiom,
% 5.49/5.89 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ A @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_cong
% 5.49/5.89 thf(fact_1885_mod__mult__cong,axiom,
% 5.49/5.89 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ C )
% 5.49/5.89 = ( modulo_modulo_int @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo_modulo_int @ B @ C )
% 5.49/5.89 = ( modulo_modulo_int @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_cong
% 5.49/5.89 thf(fact_1886_mod__mult__cong,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_cong
% 5.49/5.89 thf(fact_1887_mod__mult__eq,axiom,
% 5.49/5.89 ! [A: nat,C: nat,B: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_eq
% 5.49/5.89 thf(fact_1888_mod__mult__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_eq
% 5.49/5.89 thf(fact_1889_mod__mult__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_mult_eq
% 5.49/5.89 thf(fact_1890_mod__add__right__eq,axiom,
% 5.49/5.89 ! [A: nat,B: nat,C: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_right_eq
% 5.49/5.89 thf(fact_1891_mod__add__right__eq,axiom,
% 5.49/5.89 ! [A: int,B: int,C: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_right_eq
% 5.49/5.89 thf(fact_1892_mod__add__right__eq,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_right_eq
% 5.49/5.89 thf(fact_1893_mod__add__left__eq,axiom,
% 5.49/5.89 ! [A: nat,C: nat,B: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_left_eq
% 5.49/5.89 thf(fact_1894_mod__add__left__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_left_eq
% 5.49/5.89 thf(fact_1895_mod__add__left__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_left_eq
% 5.49/5.89 thf(fact_1896_mod__add__cong,axiom,
% 5.49/5.89 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ A @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_cong
% 5.49/5.89 thf(fact_1897_mod__add__cong,axiom,
% 5.49/5.89 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ C )
% 5.49/5.89 = ( modulo_modulo_int @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo_modulo_int @ B @ C )
% 5.49/5.89 = ( modulo_modulo_int @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_cong
% 5.49/5.89 thf(fact_1898_mod__add__cong,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_cong
% 5.49/5.89 thf(fact_1899_mod__add__eq,axiom,
% 5.49/5.89 ! [A: nat,C: nat,B: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_eq
% 5.49/5.89 thf(fact_1900_mod__add__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_eq
% 5.49/5.89 thf(fact_1901_mod__add__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_add_eq
% 5.49/5.89 thf(fact_1902_mod__diff__right__eq,axiom,
% 5.49/5.89 ! [A: int,B: int,C: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_right_eq
% 5.49/5.89 thf(fact_1903_mod__diff__right__eq,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_right_eq
% 5.49/5.89 thf(fact_1904_mod__diff__left__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_left_eq
% 5.49/5.89 thf(fact_1905_mod__diff__left__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_left_eq
% 5.49/5.89 thf(fact_1906_mod__diff__cong,axiom,
% 5.49/5.89 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ C )
% 5.49/5.89 = ( modulo_modulo_int @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo_modulo_int @ B @ C )
% 5.49/5.89 = ( modulo_modulo_int @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_cong
% 5.49/5.89 thf(fact_1907_mod__diff__cong,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.49/5.89 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.49/5.89 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_cong
% 5.49/5.89 thf(fact_1908_mod__diff__eq,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_eq
% 5.49/5.89 thf(fact_1909_mod__diff__eq,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_diff_eq
% 5.49/5.89 thf(fact_1910_power__mod,axiom,
% 5.49/5.89 ! [A: nat,B: nat,N: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.49/5.89 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mod
% 5.49/5.89 thf(fact_1911_power__mod,axiom,
% 5.49/5.89 ! [A: int,B: int,N: nat] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.49/5.89 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mod
% 5.49/5.89 thf(fact_1912_power__mod,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer,N: nat] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_mod
% 5.49/5.89 thf(fact_1913_nat__add__max__left,axiom,
% 5.49/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.49/5.89 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_add_max_left
% 5.49/5.89 thf(fact_1914_nat__add__max__right,axiom,
% 5.49/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.49/5.89 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_add_max_right
% 5.49/5.89 thf(fact_1915_vebt__member_Osimps_I1_J,axiom,
% 5.49/5.89 ! [A: $o,B: $o,X: nat] :
% 5.49/5.89 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.49/5.89 = ( ( ( X = zero_zero_nat )
% 5.49/5.89 => A )
% 5.49/5.89 & ( ( X != zero_zero_nat )
% 5.49/5.89 => ( ( ( X = one_one_nat )
% 5.49/5.89 => B )
% 5.49/5.89 & ( X = one_one_nat ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % vebt_member.simps(1)
% 5.49/5.89 thf(fact_1916_nat__mult__max__left,axiom,
% 5.49/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.89 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.49/5.89 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_max_left
% 5.49/5.89 thf(fact_1917_nat__mult__max__right,axiom,
% 5.49/5.89 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.89 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.49/5.89 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_max_right
% 5.49/5.89 thf(fact_1918_VEBT_Odistinct_I1_J,axiom,
% 5.49/5.89 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.49/5.89 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.49/5.89 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT.distinct(1)
% 5.49/5.89 thf(fact_1919_VEBT_Oexhaust,axiom,
% 5.49/5.89 ! [Y2: vEBT_VEBT] :
% 5.49/5.89 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.49/5.89 ( Y2
% 5.49/5.89 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.49/5.89 => ~ ! [X212: $o,X223: $o] :
% 5.49/5.89 ( Y2
% 5.49/5.89 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT.exhaust
% 5.49/5.89 thf(fact_1920_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.49/5.89 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.89 ( ! [Uu3: $o,Uv2: $o,D3: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ D3 ) )
% 5.49/5.89 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT_internal.valid'.cases
% 5.49/5.89 thf(fact_1921_mod__Suc__Suc__eq,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_Suc_Suc_eq
% 5.49/5.89 thf(fact_1922_mod__Suc__eq,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.49/5.89 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_Suc_eq
% 5.49/5.89 thf(fact_1923_vebt__insert_Osimps_I1_J,axiom,
% 5.49/5.89 ! [X: nat,A: $o,B: $o] :
% 5.49/5.89 ( ( ( X = zero_zero_nat )
% 5.49/5.89 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.49/5.89 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.49/5.89 & ( ( X != zero_zero_nat )
% 5.49/5.89 => ( ( ( X = one_one_nat )
% 5.49/5.89 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.49/5.89 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.49/5.89 & ( ( X != one_one_nat )
% 5.49/5.89 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.49/5.89 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % vebt_insert.simps(1)
% 5.49/5.89 thf(fact_1924_mod__less__eq__dividend,axiom,
% 5.49/5.89 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.49/5.89
% 5.49/5.89 % mod_less_eq_dividend
% 5.49/5.89 thf(fact_1925_vebt__pred_Osimps_I1_J,axiom,
% 5.49/5.89 ! [Uu: $o,Uv: $o] :
% 5.49/5.89 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.49/5.89 = none_nat ) ).
% 5.49/5.89
% 5.49/5.89 % vebt_pred.simps(1)
% 5.49/5.89 thf(fact_1926_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 5.49/5.89 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member_real @ X @ A2 )
% 5.49/5.89 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1927_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 5.49/5.89 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member_complex @ X @ A2 )
% 5.49/5.89 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1928_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I2: nat] :
% 5.49/5.89 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.49/5.89 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1929_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 5.49/5.89 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member_nat @ X @ A2 )
% 5.49/5.89 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1930_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 5.49/5.89 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.49/5.89 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1931_set__update__subsetI,axiom,
% 5.49/5.89 ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 5.49/5.89 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.49/5.89 => ( ( member_int @ X @ A2 )
% 5.49/5.89 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % set_update_subsetI
% 5.49/5.89 thf(fact_1932_finite__list,axiom,
% 5.49/5.89 ! [A2: set_VEBT_VEBT] :
% 5.49/5.89 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.49/5.89 => ? [Xs3: list_VEBT_VEBT] :
% 5.49/5.89 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.49/5.89 = A2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_list
% 5.49/5.89 thf(fact_1933_finite__list,axiom,
% 5.49/5.89 ! [A2: set_nat] :
% 5.49/5.89 ( ( finite_finite_nat @ A2 )
% 5.49/5.89 => ? [Xs3: list_nat] :
% 5.49/5.89 ( ( set_nat2 @ Xs3 )
% 5.49/5.89 = A2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_list
% 5.49/5.89 thf(fact_1934_finite__list,axiom,
% 5.49/5.89 ! [A2: set_int] :
% 5.49/5.89 ( ( finite_finite_int @ A2 )
% 5.49/5.89 => ? [Xs3: list_int] :
% 5.49/5.89 ( ( set_int2 @ Xs3 )
% 5.49/5.89 = A2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_list
% 5.49/5.89 thf(fact_1935_finite__list,axiom,
% 5.49/5.89 ! [A2: set_complex] :
% 5.49/5.89 ( ( finite3207457112153483333omplex @ A2 )
% 5.49/5.89 => ? [Xs3: list_complex] :
% 5.49/5.89 ( ( set_complex2 @ Xs3 )
% 5.49/5.89 = A2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_list
% 5.49/5.89 thf(fact_1936_finite__lists__length__eq,axiom,
% 5.49/5.89 ! [A2: set_complex,N: nat] :
% 5.49/5.89 ( ( finite3207457112153483333omplex @ A2 )
% 5.49/5.89 => ( finite8712137658972009173omplex
% 5.49/5.89 @ ( collect_list_complex
% 5.49/5.89 @ ^ [Xs: list_complex] :
% 5.49/5.89 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.49/5.89 = N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_eq
% 5.49/5.89 thf(fact_1937_finite__lists__length__eq,axiom,
% 5.49/5.89 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.49/5.89 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.49/5.89 => ( finite3004134309566078307T_VEBT
% 5.49/5.89 @ ( collec5608196760682091941T_VEBT
% 5.49/5.89 @ ^ [Xs: list_VEBT_VEBT] :
% 5.49/5.89 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.49/5.89 = N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_eq
% 5.49/5.89 thf(fact_1938_finite__lists__length__eq,axiom,
% 5.49/5.89 ! [A2: set_o,N: nat] :
% 5.49/5.89 ( ( finite_finite_o @ A2 )
% 5.49/5.89 => ( finite_finite_list_o
% 5.49/5.89 @ ( collect_list_o
% 5.49/5.89 @ ^ [Xs: list_o] :
% 5.49/5.89 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ( size_size_list_o @ Xs )
% 5.49/5.89 = N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_eq
% 5.49/5.89 thf(fact_1939_finite__lists__length__eq,axiom,
% 5.49/5.89 ! [A2: set_nat,N: nat] :
% 5.49/5.89 ( ( finite_finite_nat @ A2 )
% 5.49/5.89 => ( finite8100373058378681591st_nat
% 5.49/5.89 @ ( collect_list_nat
% 5.49/5.89 @ ^ [Xs: list_nat] :
% 5.49/5.89 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ( size_size_list_nat @ Xs )
% 5.49/5.89 = N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_eq
% 5.49/5.89 thf(fact_1940_finite__lists__length__eq,axiom,
% 5.49/5.89 ! [A2: set_int,N: nat] :
% 5.49/5.89 ( ( finite_finite_int @ A2 )
% 5.49/5.89 => ( finite3922522038869484883st_int
% 5.49/5.89 @ ( collect_list_int
% 5.49/5.89 @ ^ [Xs: list_int] :
% 5.49/5.89 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ( size_size_list_int @ Xs )
% 5.49/5.89 = N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_eq
% 5.49/5.89 thf(fact_1941_zero__le,axiom,
% 5.49/5.89 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.49/5.89
% 5.49/5.89 % zero_le
% 5.49/5.89 thf(fact_1942_le__numeral__extra_I3_J,axiom,
% 5.49/5.89 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.49/5.89
% 5.49/5.89 % le_numeral_extra(3)
% 5.49/5.89 thf(fact_1943_le__numeral__extra_I3_J,axiom,
% 5.49/5.89 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.49/5.89
% 5.49/5.89 % le_numeral_extra(3)
% 5.49/5.89 thf(fact_1944_le__numeral__extra_I3_J,axiom,
% 5.49/5.89 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.49/5.89
% 5.49/5.89 % le_numeral_extra(3)
% 5.49/5.89 thf(fact_1945_le__numeral__extra_I3_J,axiom,
% 5.49/5.89 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.49/5.89
% 5.49/5.89 % le_numeral_extra(3)
% 5.49/5.89 thf(fact_1946_zero__less__iff__neq__zero,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 = ( N != zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_less_iff_neq_zero
% 5.49/5.89 thf(fact_1947_gr__implies__not__zero,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ M @ N )
% 5.49/5.89 => ( N != zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % gr_implies_not_zero
% 5.49/5.89 thf(fact_1948_not__less__zero,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % not_less_zero
% 5.49/5.89 thf(fact_1949_gr__zeroI,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % gr_zeroI
% 5.49/5.89 thf(fact_1950_field__lbound__gt__zero,axiom,
% 5.49/5.89 ! [D1: real,D22: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.49/5.89 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.49/5.89 => ? [E2: real] :
% 5.49/5.89 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.49/5.89 & ( ord_less_real @ E2 @ D1 )
% 5.49/5.89 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % field_lbound_gt_zero
% 5.49/5.89 thf(fact_1951_field__lbound__gt__zero,axiom,
% 5.49/5.89 ! [D1: rat,D22: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.49/5.89 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.49/5.89 => ? [E2: rat] :
% 5.49/5.89 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.49/5.89 & ( ord_less_rat @ E2 @ D1 )
% 5.49/5.89 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % field_lbound_gt_zero
% 5.49/5.89 thf(fact_1952_less__numeral__extra_I3_J,axiom,
% 5.49/5.89 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.49/5.89
% 5.49/5.89 % less_numeral_extra(3)
% 5.49/5.89 thf(fact_1953_less__numeral__extra_I3_J,axiom,
% 5.49/5.89 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.49/5.89
% 5.49/5.89 % less_numeral_extra(3)
% 5.49/5.89 thf(fact_1954_less__numeral__extra_I3_J,axiom,
% 5.49/5.89 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % less_numeral_extra(3)
% 5.49/5.89 thf(fact_1955_less__numeral__extra_I3_J,axiom,
% 5.49/5.89 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.49/5.89
% 5.49/5.89 % less_numeral_extra(3)
% 5.49/5.89 thf(fact_1956_zero__neq__numeral,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( zero_zero_complex
% 5.49/5.89 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_neq_numeral
% 5.49/5.89 thf(fact_1957_zero__neq__numeral,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( zero_zero_real
% 5.49/5.89 != ( numeral_numeral_real @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_neq_numeral
% 5.49/5.89 thf(fact_1958_zero__neq__numeral,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( zero_zero_rat
% 5.49/5.89 != ( numeral_numeral_rat @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_neq_numeral
% 5.49/5.89 thf(fact_1959_zero__neq__numeral,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( zero_zero_nat
% 5.49/5.89 != ( numeral_numeral_nat @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_neq_numeral
% 5.49/5.89 thf(fact_1960_zero__neq__numeral,axiom,
% 5.49/5.89 ! [N: num] :
% 5.49/5.89 ( zero_zero_int
% 5.49/5.89 != ( numeral_numeral_int @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_neq_numeral
% 5.49/5.89 thf(fact_1961_mult__not__zero,axiom,
% 5.49/5.89 ! [A: complex,B: complex] :
% 5.49/5.89 ( ( ( times_times_complex @ A @ B )
% 5.49/5.89 != zero_zero_complex )
% 5.49/5.89 => ( ( A != zero_zero_complex )
% 5.49/5.89 & ( B != zero_zero_complex ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_not_zero
% 5.49/5.89 thf(fact_1962_mult__not__zero,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ( times_times_real @ A @ B )
% 5.49/5.89 != zero_zero_real )
% 5.49/5.89 => ( ( A != zero_zero_real )
% 5.49/5.89 & ( B != zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_not_zero
% 5.49/5.89 thf(fact_1963_mult__not__zero,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ( times_times_rat @ A @ B )
% 5.49/5.89 != zero_zero_rat )
% 5.49/5.89 => ( ( A != zero_zero_rat )
% 5.49/5.89 & ( B != zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_not_zero
% 5.49/5.89 thf(fact_1964_mult__not__zero,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( ( times_times_nat @ A @ B )
% 5.49/5.89 != zero_zero_nat )
% 5.49/5.89 => ( ( A != zero_zero_nat )
% 5.49/5.89 & ( B != zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_not_zero
% 5.49/5.89 thf(fact_1965_mult__not__zero,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( ( times_times_int @ A @ B )
% 5.49/5.89 != zero_zero_int )
% 5.49/5.89 => ( ( A != zero_zero_int )
% 5.49/5.89 & ( B != zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_not_zero
% 5.49/5.89 thf(fact_1966_divisors__zero,axiom,
% 5.49/5.89 ! [A: complex,B: complex] :
% 5.49/5.89 ( ( ( times_times_complex @ A @ B )
% 5.49/5.89 = zero_zero_complex )
% 5.49/5.89 => ( ( A = zero_zero_complex )
% 5.49/5.89 | ( B = zero_zero_complex ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divisors_zero
% 5.49/5.89 thf(fact_1967_divisors__zero,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( ( times_times_real @ A @ B )
% 5.49/5.89 = zero_zero_real )
% 5.49/5.89 => ( ( A = zero_zero_real )
% 5.49/5.89 | ( B = zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divisors_zero
% 5.49/5.89 thf(fact_1968_divisors__zero,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( ( times_times_rat @ A @ B )
% 5.49/5.89 = zero_zero_rat )
% 5.49/5.89 => ( ( A = zero_zero_rat )
% 5.49/5.89 | ( B = zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divisors_zero
% 5.49/5.89 thf(fact_1969_divisors__zero,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( ( times_times_nat @ A @ B )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 => ( ( A = zero_zero_nat )
% 5.49/5.89 | ( B = zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divisors_zero
% 5.49/5.89 thf(fact_1970_divisors__zero,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( ( times_times_int @ A @ B )
% 5.49/5.89 = zero_zero_int )
% 5.49/5.89 => ( ( A = zero_zero_int )
% 5.49/5.89 | ( B = zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % divisors_zero
% 5.49/5.89 thf(fact_1971_no__zero__divisors,axiom,
% 5.49/5.89 ! [A: complex,B: complex] :
% 5.49/5.89 ( ( A != zero_zero_complex )
% 5.49/5.89 => ( ( B != zero_zero_complex )
% 5.49/5.89 => ( ( times_times_complex @ A @ B )
% 5.49/5.89 != zero_zero_complex ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % no_zero_divisors
% 5.49/5.89 thf(fact_1972_no__zero__divisors,axiom,
% 5.49/5.89 ! [A: real,B: real] :
% 5.49/5.89 ( ( A != zero_zero_real )
% 5.49/5.89 => ( ( B != zero_zero_real )
% 5.49/5.89 => ( ( times_times_real @ A @ B )
% 5.49/5.89 != zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % no_zero_divisors
% 5.49/5.89 thf(fact_1973_no__zero__divisors,axiom,
% 5.49/5.89 ! [A: rat,B: rat] :
% 5.49/5.89 ( ( A != zero_zero_rat )
% 5.49/5.89 => ( ( B != zero_zero_rat )
% 5.49/5.89 => ( ( times_times_rat @ A @ B )
% 5.49/5.89 != zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % no_zero_divisors
% 5.49/5.89 thf(fact_1974_no__zero__divisors,axiom,
% 5.49/5.89 ! [A: nat,B: nat] :
% 5.49/5.89 ( ( A != zero_zero_nat )
% 5.49/5.89 => ( ( B != zero_zero_nat )
% 5.49/5.89 => ( ( times_times_nat @ A @ B )
% 5.49/5.89 != zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % no_zero_divisors
% 5.49/5.89 thf(fact_1975_no__zero__divisors,axiom,
% 5.49/5.89 ! [A: int,B: int] :
% 5.49/5.89 ( ( A != zero_zero_int )
% 5.49/5.89 => ( ( B != zero_zero_int )
% 5.49/5.89 => ( ( times_times_int @ A @ B )
% 5.49/5.89 != zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % no_zero_divisors
% 5.49/5.89 thf(fact_1976_mult__left__cancel,axiom,
% 5.49/5.89 ! [C: complex,A: complex,B: complex] :
% 5.49/5.89 ( ( C != zero_zero_complex )
% 5.49/5.89 => ( ( ( times_times_complex @ C @ A )
% 5.49/5.89 = ( times_times_complex @ C @ B ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_left_cancel
% 5.49/5.89 thf(fact_1977_mult__left__cancel,axiom,
% 5.49/5.89 ! [C: real,A: real,B: real] :
% 5.49/5.89 ( ( C != zero_zero_real )
% 5.49/5.89 => ( ( ( times_times_real @ C @ A )
% 5.49/5.89 = ( times_times_real @ C @ B ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_left_cancel
% 5.49/5.89 thf(fact_1978_mult__left__cancel,axiom,
% 5.49/5.89 ! [C: rat,A: rat,B: rat] :
% 5.49/5.89 ( ( C != zero_zero_rat )
% 5.49/5.89 => ( ( ( times_times_rat @ C @ A )
% 5.49/5.89 = ( times_times_rat @ C @ B ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_left_cancel
% 5.49/5.89 thf(fact_1979_mult__left__cancel,axiom,
% 5.49/5.89 ! [C: nat,A: nat,B: nat] :
% 5.49/5.89 ( ( C != zero_zero_nat )
% 5.49/5.89 => ( ( ( times_times_nat @ C @ A )
% 5.49/5.89 = ( times_times_nat @ C @ B ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_left_cancel
% 5.49/5.89 thf(fact_1980_mult__left__cancel,axiom,
% 5.49/5.89 ! [C: int,A: int,B: int] :
% 5.49/5.89 ( ( C != zero_zero_int )
% 5.49/5.89 => ( ( ( times_times_int @ C @ A )
% 5.49/5.89 = ( times_times_int @ C @ B ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_left_cancel
% 5.49/5.89 thf(fact_1981_mult__right__cancel,axiom,
% 5.49/5.89 ! [C: complex,A: complex,B: complex] :
% 5.49/5.89 ( ( C != zero_zero_complex )
% 5.49/5.89 => ( ( ( times_times_complex @ A @ C )
% 5.49/5.89 = ( times_times_complex @ B @ C ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_right_cancel
% 5.49/5.89 thf(fact_1982_mult__right__cancel,axiom,
% 5.49/5.89 ! [C: real,A: real,B: real] :
% 5.49/5.89 ( ( C != zero_zero_real )
% 5.49/5.89 => ( ( ( times_times_real @ A @ C )
% 5.49/5.89 = ( times_times_real @ B @ C ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_right_cancel
% 5.49/5.89 thf(fact_1983_mult__right__cancel,axiom,
% 5.49/5.89 ! [C: rat,A: rat,B: rat] :
% 5.49/5.89 ( ( C != zero_zero_rat )
% 5.49/5.89 => ( ( ( times_times_rat @ A @ C )
% 5.49/5.89 = ( times_times_rat @ B @ C ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_right_cancel
% 5.49/5.89 thf(fact_1984_mult__right__cancel,axiom,
% 5.49/5.89 ! [C: nat,A: nat,B: nat] :
% 5.49/5.89 ( ( C != zero_zero_nat )
% 5.49/5.89 => ( ( ( times_times_nat @ A @ C )
% 5.49/5.89 = ( times_times_nat @ B @ C ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_right_cancel
% 5.49/5.89 thf(fact_1985_mult__right__cancel,axiom,
% 5.49/5.89 ! [C: int,A: int,B: int] :
% 5.49/5.89 ( ( C != zero_zero_int )
% 5.49/5.89 => ( ( ( times_times_int @ A @ C )
% 5.49/5.89 = ( times_times_int @ B @ C ) )
% 5.49/5.89 = ( A = B ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mult_right_cancel
% 5.49/5.89 thf(fact_1986_comm__monoid__add__class_Oadd__0,axiom,
% 5.49/5.89 ! [A: complex] :
% 5.49/5.89 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % comm_monoid_add_class.add_0
% 5.49/5.89 thf(fact_1987_comm__monoid__add__class_Oadd__0,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % comm_monoid_add_class.add_0
% 5.49/5.89 thf(fact_1988_comm__monoid__add__class_Oadd__0,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % comm_monoid_add_class.add_0
% 5.49/5.89 thf(fact_1989_comm__monoid__add__class_Oadd__0,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % comm_monoid_add_class.add_0
% 5.49/5.89 thf(fact_1990_comm__monoid__add__class_Oadd__0,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % comm_monoid_add_class.add_0
% 5.49/5.89 thf(fact_1991_add_Ocomm__neutral,axiom,
% 5.49/5.89 ! [A: complex] :
% 5.49/5.89 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.comm_neutral
% 5.49/5.89 thf(fact_1992_add_Ocomm__neutral,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.comm_neutral
% 5.49/5.89 thf(fact_1993_add_Ocomm__neutral,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.comm_neutral
% 5.49/5.89 thf(fact_1994_add_Ocomm__neutral,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.comm_neutral
% 5.49/5.89 thf(fact_1995_add_Ocomm__neutral,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.comm_neutral
% 5.49/5.89 thf(fact_1996_add_Ogroup__left__neutral,axiom,
% 5.49/5.89 ! [A: complex] :
% 5.49/5.89 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.group_left_neutral
% 5.49/5.89 thf(fact_1997_add_Ogroup__left__neutral,axiom,
% 5.49/5.89 ! [A: real] :
% 5.49/5.89 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.group_left_neutral
% 5.49/5.89 thf(fact_1998_add_Ogroup__left__neutral,axiom,
% 5.49/5.89 ! [A: rat] :
% 5.49/5.89 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.group_left_neutral
% 5.49/5.89 thf(fact_1999_add_Ogroup__left__neutral,axiom,
% 5.49/5.89 ! [A: int] :
% 5.49/5.89 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.49/5.89 = A ) ).
% 5.49/5.89
% 5.49/5.89 % add.group_left_neutral
% 5.49/5.89 thf(fact_2000_eq__iff__diff__eq__0,axiom,
% 5.49/5.89 ( ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 ) )
% 5.49/5.89 = ( ^ [A4: complex,B3: complex] :
% 5.49/5.89 ( ( minus_minus_complex @ A4 @ B3 )
% 5.49/5.89 = zero_zero_complex ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_iff_diff_eq_0
% 5.49/5.89 thf(fact_2001_eq__iff__diff__eq__0,axiom,
% 5.49/5.89 ( ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) )
% 5.49/5.89 = ( ^ [A4: real,B3: real] :
% 5.49/5.89 ( ( minus_minus_real @ A4 @ B3 )
% 5.49/5.89 = zero_zero_real ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_iff_diff_eq_0
% 5.49/5.89 thf(fact_2002_eq__iff__diff__eq__0,axiom,
% 5.49/5.89 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.49/5.89 = ( ^ [A4: rat,B3: rat] :
% 5.49/5.89 ( ( minus_minus_rat @ A4 @ B3 )
% 5.49/5.89 = zero_zero_rat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_iff_diff_eq_0
% 5.49/5.89 thf(fact_2003_eq__iff__diff__eq__0,axiom,
% 5.49/5.89 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.49/5.89 = ( ^ [A4: int,B3: int] :
% 5.49/5.89 ( ( minus_minus_int @ A4 @ B3 )
% 5.49/5.89 = zero_zero_int ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % eq_iff_diff_eq_0
% 5.49/5.89 thf(fact_2004_power__not__zero,axiom,
% 5.49/5.89 ! [A: rat,N: nat] :
% 5.49/5.89 ( ( A != zero_zero_rat )
% 5.49/5.89 => ( ( power_power_rat @ A @ N )
% 5.49/5.89 != zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_not_zero
% 5.49/5.89 thf(fact_2005_power__not__zero,axiom,
% 5.49/5.89 ! [A: nat,N: nat] :
% 5.49/5.89 ( ( A != zero_zero_nat )
% 5.49/5.89 => ( ( power_power_nat @ A @ N )
% 5.49/5.89 != zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_not_zero
% 5.49/5.89 thf(fact_2006_power__not__zero,axiom,
% 5.49/5.89 ! [A: real,N: nat] :
% 5.49/5.89 ( ( A != zero_zero_real )
% 5.49/5.89 => ( ( power_power_real @ A @ N )
% 5.49/5.89 != zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_not_zero
% 5.49/5.89 thf(fact_2007_power__not__zero,axiom,
% 5.49/5.89 ! [A: int,N: nat] :
% 5.49/5.89 ( ( A != zero_zero_int )
% 5.49/5.89 => ( ( power_power_int @ A @ N )
% 5.49/5.89 != zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_not_zero
% 5.49/5.89 thf(fact_2008_power__not__zero,axiom,
% 5.49/5.89 ! [A: complex,N: nat] :
% 5.49/5.89 ( ( A != zero_zero_complex )
% 5.49/5.89 => ( ( power_power_complex @ A @ N )
% 5.49/5.89 != zero_zero_complex ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_not_zero
% 5.49/5.89 thf(fact_2009_num_Osize_I4_J,axiom,
% 5.49/5.89 ( ( size_size_num @ one )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % num.size(4)
% 5.49/5.89 thf(fact_2010_nat_Odistinct_I1_J,axiom,
% 5.49/5.89 ! [X22: nat] :
% 5.49/5.89 ( zero_zero_nat
% 5.49/5.89 != ( suc @ X22 ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat.distinct(1)
% 5.49/5.89 thf(fact_2011_old_Onat_Odistinct_I2_J,axiom,
% 5.49/5.89 ! [Nat2: nat] :
% 5.49/5.89 ( ( suc @ Nat2 )
% 5.49/5.89 != zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % old.nat.distinct(2)
% 5.49/5.89 thf(fact_2012_old_Onat_Odistinct_I1_J,axiom,
% 5.49/5.89 ! [Nat2: nat] :
% 5.49/5.89 ( zero_zero_nat
% 5.49/5.89 != ( suc @ Nat2 ) ) ).
% 5.49/5.89
% 5.49/5.89 % old.nat.distinct(1)
% 5.49/5.89 thf(fact_2013_nat_OdiscI,axiom,
% 5.49/5.89 ! [Nat: nat,X22: nat] :
% 5.49/5.89 ( ( Nat
% 5.49/5.89 = ( suc @ X22 ) )
% 5.49/5.89 => ( Nat != zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat.discI
% 5.49/5.89 thf(fact_2014_old_Onat_Oexhaust,axiom,
% 5.49/5.89 ! [Y2: nat] :
% 5.49/5.89 ( ( Y2 != zero_zero_nat )
% 5.49/5.89 => ~ ! [Nat3: nat] :
% 5.49/5.89 ( Y2
% 5.49/5.89 != ( suc @ Nat3 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % old.nat.exhaust
% 5.49/5.89 thf(fact_2015_nat__induct,axiom,
% 5.49/5.89 ! [P: nat > $o,N: nat] :
% 5.49/5.89 ( ( P @ zero_zero_nat )
% 5.49/5.89 => ( ! [N3: nat] :
% 5.49/5.89 ( ( P @ N3 )
% 5.49/5.89 => ( P @ ( suc @ N3 ) ) )
% 5.49/5.89 => ( P @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_induct
% 5.49/5.89 thf(fact_2016_diff__induct,axiom,
% 5.49/5.89 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.49/5.89 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.49/5.89 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.49/5.89 => ( ! [X3: nat,Y3: nat] :
% 5.49/5.89 ( ( P @ X3 @ Y3 )
% 5.49/5.89 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.49/5.89 => ( P @ M @ N ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % diff_induct
% 5.49/5.89 thf(fact_2017_zero__induct,axiom,
% 5.49/5.89 ! [P: nat > $o,K: nat] :
% 5.49/5.89 ( ( P @ K )
% 5.49/5.89 => ( ! [N3: nat] :
% 5.49/5.89 ( ( P @ ( suc @ N3 ) )
% 5.49/5.89 => ( P @ N3 ) )
% 5.49/5.89 => ( P @ zero_zero_nat ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % zero_induct
% 5.49/5.89 thf(fact_2018_Suc__neq__Zero,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( suc @ M )
% 5.49/5.89 != zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_neq_Zero
% 5.49/5.89 thf(fact_2019_Zero__neq__Suc,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( zero_zero_nat
% 5.49/5.89 != ( suc @ M ) ) ).
% 5.49/5.89
% 5.49/5.89 % Zero_neq_Suc
% 5.49/5.89 thf(fact_2020_Zero__not__Suc,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( zero_zero_nat
% 5.49/5.89 != ( suc @ M ) ) ).
% 5.49/5.89
% 5.49/5.89 % Zero_not_Suc
% 5.49/5.89 thf(fact_2021_not0__implies__Suc,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( N != zero_zero_nat )
% 5.49/5.89 => ? [M5: nat] :
% 5.49/5.89 ( N
% 5.49/5.89 = ( suc @ M5 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % not0_implies_Suc
% 5.49/5.89 thf(fact_2022_vebt__buildup_Ocases,axiom,
% 5.49/5.89 ! [X: nat] :
% 5.49/5.89 ( ( X != zero_zero_nat )
% 5.49/5.89 => ( ( X
% 5.49/5.89 != ( suc @ zero_zero_nat ) )
% 5.49/5.89 => ~ ! [Va3: nat] :
% 5.49/5.89 ( X
% 5.49/5.89 != ( suc @ ( suc @ Va3 ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % vebt_buildup.cases
% 5.49/5.89 thf(fact_2023_infinite__descent0,axiom,
% 5.49/5.89 ! [P: nat > $o,N: nat] :
% 5.49/5.89 ( ( P @ zero_zero_nat )
% 5.49/5.89 => ( ! [N3: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.49/5.89 => ( ~ ( P @ N3 )
% 5.49/5.89 => ? [M2: nat] :
% 5.49/5.89 ( ( ord_less_nat @ M2 @ N3 )
% 5.49/5.89 & ~ ( P @ M2 ) ) ) )
% 5.49/5.89 => ( P @ N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % infinite_descent0
% 5.49/5.89 thf(fact_2024_gr__implies__not0,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ M @ N )
% 5.49/5.89 => ( N != zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % gr_implies_not0
% 5.49/5.89 thf(fact_2025_less__zeroE,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % less_zeroE
% 5.49/5.89 thf(fact_2026_not__less0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % not_less0
% 5.49/5.89 thf(fact_2027_not__gr0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.49/5.89 = ( N = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % not_gr0
% 5.49/5.89 thf(fact_2028_gr0I,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( N != zero_zero_nat )
% 5.49/5.89 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.49/5.89
% 5.49/5.89 % gr0I
% 5.49/5.89 thf(fact_2029_bot__nat__0_Oextremum__strict,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % bot_nat_0.extremum_strict
% 5.49/5.89 thf(fact_2030_less__eq__nat_Osimps_I1_J,axiom,
% 5.49/5.89 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.49/5.89
% 5.49/5.89 % less_eq_nat.simps(1)
% 5.49/5.89 thf(fact_2031_bot__nat__0_Oextremum__unique,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.89 = ( A = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % bot_nat_0.extremum_unique
% 5.49/5.89 thf(fact_2032_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.49/5.89 ! [A: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.89 => ( A = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % bot_nat_0.extremum_uniqueI
% 5.49/5.89 thf(fact_2033_le__0__eq,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.49/5.89 = ( N = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % le_0_eq
% 5.49/5.89 thf(fact_2034_plus__nat_Oadd__0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.49/5.89 = N ) ).
% 5.49/5.89
% 5.49/5.89 % plus_nat.add_0
% 5.49/5.89 thf(fact_2035_add__eq__self__zero,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ( plus_plus_nat @ M @ N )
% 5.49/5.89 = M )
% 5.49/5.89 => ( N = zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % add_eq_self_zero
% 5.49/5.89 thf(fact_2036_diffs0__imp__equal,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ( minus_minus_nat @ M @ N )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 => ( ( ( minus_minus_nat @ N @ M )
% 5.49/5.89 = zero_zero_nat )
% 5.49/5.89 => ( M = N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % diffs0_imp_equal
% 5.49/5.89 thf(fact_2037_minus__nat_Odiff__0,axiom,
% 5.49/5.89 ! [M: nat] :
% 5.49/5.89 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.49/5.89 = M ) ).
% 5.49/5.89
% 5.49/5.89 % minus_nat.diff_0
% 5.49/5.89 thf(fact_2038_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.49/5.89 ! [Uu: $o] :
% 5.49/5.89 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT_internal.minNull.simps(3)
% 5.49/5.89 thf(fact_2039_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.49/5.89 ! [Uv: $o] :
% 5.49/5.89 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT_internal.minNull.simps(2)
% 5.49/5.89 thf(fact_2040_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.49/5.89 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.49/5.89
% 5.49/5.89 % VEBT_internal.minNull.simps(1)
% 5.49/5.89 thf(fact_2041_nat__mult__eq__cancel__disj,axiom,
% 5.49/5.89 ! [K: nat,M: nat,N: nat] :
% 5.49/5.89 ( ( ( times_times_nat @ K @ M )
% 5.49/5.89 = ( times_times_nat @ K @ N ) )
% 5.49/5.89 = ( ( K = zero_zero_nat )
% 5.49/5.89 | ( M = N ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_mult_eq_cancel_disj
% 5.49/5.89 thf(fact_2042_mult__0,axiom,
% 5.49/5.89 ! [N: nat] :
% 5.49/5.89 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.49/5.89 = zero_zero_nat ) ).
% 5.49/5.89
% 5.49/5.89 % mult_0
% 5.49/5.89 thf(fact_2043_split__mod,axiom,
% 5.49/5.89 ! [P: nat > $o,M: nat,N: nat] :
% 5.49/5.89 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.49/5.89 = ( ( ( N = zero_zero_nat )
% 5.49/5.89 => ( P @ M ) )
% 5.49/5.89 & ( ( N != zero_zero_nat )
% 5.49/5.89 => ! [I3: nat,J3: nat] :
% 5.49/5.89 ( ( ord_less_nat @ J3 @ N )
% 5.49/5.89 => ( ( M
% 5.49/5.89 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 5.49/5.89 => ( P @ J3 ) ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % split_mod
% 5.49/5.89 thf(fact_2044_power__eq__iff__eq__base,axiom,
% 5.49/5.89 ! [N: nat,A: real,B: real] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.89 => ( ( ( power_power_real @ A @ N )
% 5.49/5.89 = ( power_power_real @ B @ N ) )
% 5.49/5.89 = ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_iff_eq_base
% 5.49/5.89 thf(fact_2045_power__eq__iff__eq__base,axiom,
% 5.49/5.89 ! [N: nat,A: rat,B: rat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.89 => ( ( ( power_power_rat @ A @ N )
% 5.49/5.89 = ( power_power_rat @ B @ N ) )
% 5.49/5.89 = ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_iff_eq_base
% 5.49/5.89 thf(fact_2046_power__eq__iff__eq__base,axiom,
% 5.49/5.89 ! [N: nat,A: nat,B: nat] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ( ( power_power_nat @ A @ N )
% 5.49/5.89 = ( power_power_nat @ B @ N ) )
% 5.49/5.89 = ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_iff_eq_base
% 5.49/5.89 thf(fact_2047_power__eq__iff__eq__base,axiom,
% 5.49/5.89 ! [N: nat,A: int,B: int] :
% 5.49/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ( ( power_power_int @ A @ N )
% 5.49/5.89 = ( power_power_int @ B @ N ) )
% 5.49/5.89 = ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_iff_eq_base
% 5.49/5.89 thf(fact_2048_power__eq__imp__eq__base,axiom,
% 5.49/5.89 ! [A: real,N: nat,B: real] :
% 5.49/5.89 ( ( ( power_power_real @ A @ N )
% 5.49/5.89 = ( power_power_real @ B @ N ) )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_imp_eq_base
% 5.49/5.89 thf(fact_2049_power__eq__imp__eq__base,axiom,
% 5.49/5.89 ! [A: rat,N: nat,B: rat] :
% 5.49/5.89 ( ( ( power_power_rat @ A @ N )
% 5.49/5.89 = ( power_power_rat @ B @ N ) )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_imp_eq_base
% 5.49/5.89 thf(fact_2050_power__eq__imp__eq__base,axiom,
% 5.49/5.89 ! [A: nat,N: nat,B: nat] :
% 5.49/5.89 ( ( ( power_power_nat @ A @ N )
% 5.49/5.89 = ( power_power_nat @ B @ N ) )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_imp_eq_base
% 5.49/5.89 thf(fact_2051_power__eq__imp__eq__base,axiom,
% 5.49/5.89 ! [A: int,N: nat,B: int] :
% 5.49/5.89 ( ( ( power_power_int @ A @ N )
% 5.49/5.89 = ( power_power_int @ B @ N ) )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.89 => ( A = B ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % power_eq_imp_eq_base
% 5.49/5.89 thf(fact_2052_lambda__zero,axiom,
% 5.49/5.89 ( ( ^ [H: complex] : zero_zero_complex )
% 5.49/5.89 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.49/5.89
% 5.49/5.89 % lambda_zero
% 5.49/5.89 thf(fact_2053_lambda__zero,axiom,
% 5.49/5.89 ( ( ^ [H: real] : zero_zero_real )
% 5.49/5.89 = ( times_times_real @ zero_zero_real ) ) ).
% 5.49/5.89
% 5.49/5.89 % lambda_zero
% 5.49/5.89 thf(fact_2054_lambda__zero,axiom,
% 5.49/5.89 ( ( ^ [H: rat] : zero_zero_rat )
% 5.49/5.89 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.49/5.89
% 5.49/5.89 % lambda_zero
% 5.49/5.89 thf(fact_2055_lambda__zero,axiom,
% 5.49/5.89 ( ( ^ [H: nat] : zero_zero_nat )
% 5.49/5.89 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % lambda_zero
% 5.49/5.89 thf(fact_2056_lambda__zero,axiom,
% 5.49/5.89 ( ( ^ [H: int] : zero_zero_int )
% 5.49/5.89 = ( times_times_int @ zero_zero_int ) ) ).
% 5.49/5.89
% 5.49/5.89 % lambda_zero
% 5.49/5.89 thf(fact_2057_finite__lists__length__le,axiom,
% 5.49/5.89 ! [A2: set_complex,N: nat] :
% 5.49/5.89 ( ( finite3207457112153483333omplex @ A2 )
% 5.49/5.89 => ( finite8712137658972009173omplex
% 5.49/5.89 @ ( collect_list_complex
% 5.49/5.89 @ ^ [Xs: list_complex] :
% 5.49/5.89 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_le
% 5.49/5.89 thf(fact_2058_finite__lists__length__le,axiom,
% 5.49/5.89 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.49/5.89 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.49/5.89 => ( finite3004134309566078307T_VEBT
% 5.49/5.89 @ ( collec5608196760682091941T_VEBT
% 5.49/5.89 @ ^ [Xs: list_VEBT_VEBT] :
% 5.49/5.89 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_le
% 5.49/5.89 thf(fact_2059_finite__lists__length__le,axiom,
% 5.49/5.89 ! [A2: set_o,N: nat] :
% 5.49/5.89 ( ( finite_finite_o @ A2 )
% 5.49/5.89 => ( finite_finite_list_o
% 5.49/5.89 @ ( collect_list_o
% 5.49/5.89 @ ^ [Xs: list_o] :
% 5.49/5.89 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_le
% 5.49/5.89 thf(fact_2060_finite__lists__length__le,axiom,
% 5.49/5.89 ! [A2: set_nat,N: nat] :
% 5.49/5.89 ( ( finite_finite_nat @ A2 )
% 5.49/5.89 => ( finite8100373058378681591st_nat
% 5.49/5.89 @ ( collect_list_nat
% 5.49/5.89 @ ^ [Xs: list_nat] :
% 5.49/5.89 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_le
% 5.49/5.89 thf(fact_2061_finite__lists__length__le,axiom,
% 5.49/5.89 ! [A2: set_int,N: nat] :
% 5.49/5.89 ( ( finite_finite_int @ A2 )
% 5.49/5.89 => ( finite3922522038869484883st_int
% 5.49/5.89 @ ( collect_list_int
% 5.49/5.89 @ ^ [Xs: list_int] :
% 5.49/5.89 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.49/5.89 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % finite_lists_length_le
% 5.49/5.89 thf(fact_2062_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.49/5.89 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.49/5.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.49/5.89 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.49/5.89 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.49/5.89 thf(fact_2063_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.49/5.89 ! [C: nat,A: nat,B: nat] :
% 5.49/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.89 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.49/5.89 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.49/5.89 thf(fact_2064_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.49/5.89 ! [C: int,A: int,B: int] :
% 5.49/5.89 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.89 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.49/5.89 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.49/5.89 thf(fact_2065_cong__exp__iff__simps_I9_J,axiom,
% 5.49/5.89 ! [M: num,Q2: num,N: num] :
% 5.49/5.89 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.49/5.89 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.49/5.89 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(9)
% 5.49/5.89 thf(fact_2066_cong__exp__iff__simps_I9_J,axiom,
% 5.49/5.89 ! [M: num,Q2: num,N: num] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.49/5.89 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.49/5.89 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(9)
% 5.49/5.89 thf(fact_2067_cong__exp__iff__simps_I9_J,axiom,
% 5.49/5.89 ! [M: num,Q2: num,N: num] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.49/5.89 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(9)
% 5.49/5.89 thf(fact_2068_cong__exp__iff__simps_I4_J,axiom,
% 5.49/5.89 ! [M: num,N: num] :
% 5.49/5.89 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.49/5.89 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(4)
% 5.49/5.89 thf(fact_2069_cong__exp__iff__simps_I4_J,axiom,
% 5.49/5.89 ! [M: num,N: num] :
% 5.49/5.89 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.49/5.89 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(4)
% 5.49/5.89 thf(fact_2070_cong__exp__iff__simps_I4_J,axiom,
% 5.49/5.89 ! [M: num,N: num] :
% 5.49/5.89 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.49/5.89 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % cong_exp_iff_simps(4)
% 5.49/5.89 thf(fact_2071_mod__eqE,axiom,
% 5.49/5.89 ! [A: int,C: int,B: int] :
% 5.49/5.89 ( ( ( modulo_modulo_int @ A @ C )
% 5.49/5.89 = ( modulo_modulo_int @ B @ C ) )
% 5.49/5.89 => ~ ! [D3: int] :
% 5.49/5.89 ( B
% 5.49/5.89 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eqE
% 5.49/5.89 thf(fact_2072_mod__eqE,axiom,
% 5.49/5.89 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.49/5.89 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.49/5.89 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.49/5.89 => ~ ! [D3: code_integer] :
% 5.49/5.89 ( B
% 5.49/5.89 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_eqE
% 5.49/5.89 thf(fact_2073_div__add1__eq,axiom,
% 5.49/5.89 ! [A: nat,B: nat,C: nat] :
% 5.49/5.89 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.49/5.89 = ( 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 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_add1_eq
% 5.49/5.89 thf(fact_2074_div__add1__eq,axiom,
% 5.49/5.89 ! [A: int,B: int,C: int] :
% 5.49/5.89 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.49/5.89 = ( 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 ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_add1_eq
% 5.49/5.89 thf(fact_2075_div__add1__eq,axiom,
% 5.49/5.89 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.89 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.49/5.89 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % div_add1_eq
% 5.49/5.89 thf(fact_2076_nat__minus__add__max,axiom,
% 5.49/5.89 ! [N: nat,M: nat] :
% 5.49/5.89 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.49/5.89 = ( ord_max_nat @ N @ M ) ) ).
% 5.49/5.89
% 5.49/5.89 % nat_minus_add_max
% 5.49/5.89 thf(fact_2077_Suc__times__mod__eq,axiom,
% 5.49/5.89 ! [M: nat,N: nat] :
% 5.49/5.89 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.49/5.89 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.49/5.89 = one_one_nat ) ) ).
% 5.49/5.89
% 5.49/5.89 % Suc_times_mod_eq
% 5.49/5.89 thf(fact_2078_mod__induct,axiom,
% 5.49/5.89 ! [P: nat > $o,N: nat,P4: nat,M: nat] :
% 5.49/5.89 ( ( P @ N )
% 5.49/5.89 => ( ( ord_less_nat @ N @ P4 )
% 5.49/5.89 => ( ( ord_less_nat @ M @ P4 )
% 5.49/5.89 => ( ! [N3: nat] :
% 5.49/5.89 ( ( ord_less_nat @ N3 @ P4 )
% 5.49/5.89 => ( ( P @ N3 )
% 5.49/5.89 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P4 ) ) ) )
% 5.49/5.89 => ( P @ M ) ) ) ) ) ).
% 5.49/5.89
% 5.49/5.89 % mod_induct
% 5.49/5.89 thf(fact_2079_mod__Suc__le__divisor,axiom,
% 5.49/5.89 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.49/5.89
% 5.49/5.89 % mod_Suc_le_divisor
% 5.49/5.89 thf(fact_2080_power__strict__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,N: nat] :
% 5.49/5.90 ( ( ord_less_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_strict_mono
% 5.49/5.90 thf(fact_2081_power__strict__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,N: nat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_strict_mono
% 5.49/5.90 thf(fact_2082_power__strict__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_strict_mono
% 5.49/5.90 thf(fact_2083_power__strict__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,N: nat] :
% 5.49/5.90 ( ( ord_less_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_strict_mono
% 5.49/5.90 thf(fact_2084_mod__if,axiom,
% 5.49/5.90 ( modulo_modulo_nat
% 5.49/5.90 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_if
% 5.49/5.90 thf(fact_2085_mod__geq,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ~ ( ord_less_nat @ M @ N )
% 5.49/5.90 => ( ( modulo_modulo_nat @ M @ N )
% 5.49/5.90 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_geq
% 5.49/5.90 thf(fact_2086_le__mod__geq,axiom,
% 5.49/5.90 ! [N: nat,M: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.90 => ( ( modulo_modulo_nat @ M @ N )
% 5.49/5.90 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % le_mod_geq
% 5.49/5.90 thf(fact_2087_nat__mod__eq__iff,axiom,
% 5.49/5.90 ! [X: nat,N: nat,Y2: nat] :
% 5.49/5.90 ( ( ( modulo_modulo_nat @ X @ N )
% 5.49/5.90 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.49/5.90 = ( ? [Q1: nat,Q22: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 5.49/5.90 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nat_mod_eq_iff
% 5.49/5.90 thf(fact_2088_vebt__pred_Osimps_I2_J,axiom,
% 5.49/5.90 ! [A: $o,Uw: $o] :
% 5.49/5.90 ( ( A
% 5.49/5.90 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.49/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.90 & ( ~ A
% 5.49/5.90 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.49/5.90 = none_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_pred.simps(2)
% 5.49/5.90 thf(fact_2089_vebt__mint_Osimps_I1_J,axiom,
% 5.49/5.90 ! [A: $o,B: $o] :
% 5.49/5.90 ( ( A
% 5.49/5.90 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.90 & ( ~ A
% 5.49/5.90 => ( ( B
% 5.49/5.90 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.90 & ( ~ B
% 5.49/5.90 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = none_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_mint.simps(1)
% 5.49/5.90 thf(fact_2090_not__numeral__le__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_le_zero
% 5.49/5.90 thf(fact_2091_not__numeral__le__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_le_zero
% 5.49/5.90 thf(fact_2092_not__numeral__le__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_le_zero
% 5.49/5.90 thf(fact_2093_not__numeral__le__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_le_zero
% 5.49/5.90 thf(fact_2094_zero__le__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_numeral
% 5.49/5.90 thf(fact_2095_zero__le__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_numeral
% 5.49/5.90 thf(fact_2096_zero__le__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_numeral
% 5.49/5.90 thf(fact_2097_zero__le__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_numeral
% 5.49/5.90 thf(fact_2098_mult__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono
% 5.49/5.90 thf(fact_2099_mult__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono
% 5.49/5.90 thf(fact_2100_mult__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono
% 5.49/5.90 thf(fact_2101_mult__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono
% 5.49/5.90 thf(fact_2102_mult__mono_H,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono'
% 5.49/5.90 thf(fact_2103_mult__mono_H,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono'
% 5.49/5.90 thf(fact_2104_mult__mono_H,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono'
% 5.49/5.90 thf(fact_2105_mult__mono_H,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ C @ D )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_mono'
% 5.49/5.90 thf(fact_2106_zero__le__square,axiom,
% 5.49/5.90 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_square
% 5.49/5.90 thf(fact_2107_zero__le__square,axiom,
% 5.49/5.90 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_square
% 5.49/5.90 thf(fact_2108_zero__le__square,axiom,
% 5.49/5.90 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_square
% 5.49/5.90 thf(fact_2109_split__mult__pos__le,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_pos_le
% 5.49/5.90 thf(fact_2110_split__mult__pos__le,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_pos_le
% 5.49/5.90 thf(fact_2111_split__mult__pos__le,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.49/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_pos_le
% 5.49/5.90 thf(fact_2112_mult__left__mono__neg,axiom,
% 5.49/5.90 ! [B: real,A: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono_neg
% 5.49/5.90 thf(fact_2113_mult__left__mono__neg,axiom,
% 5.49/5.90 ! [B: rat,A: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono_neg
% 5.49/5.90 thf(fact_2114_mult__left__mono__neg,axiom,
% 5.49/5.90 ! [B: int,A: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono_neg
% 5.49/5.90 thf(fact_2115_mult__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonpos
% 5.49/5.90 thf(fact_2116_mult__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonpos
% 5.49/5.90 thf(fact_2117_mult__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonpos
% 5.49/5.90 thf(fact_2118_mult__left__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono
% 5.49/5.90 thf(fact_2119_mult__left__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono
% 5.49/5.90 thf(fact_2120_mult__left__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono
% 5.49/5.90 thf(fact_2121_mult__left__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_left_mono
% 5.49/5.90 thf(fact_2122_mult__right__mono__neg,axiom,
% 5.49/5.90 ! [B: real,A: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono_neg
% 5.49/5.90 thf(fact_2123_mult__right__mono__neg,axiom,
% 5.49/5.90 ! [B: rat,A: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono_neg
% 5.49/5.90 thf(fact_2124_mult__right__mono__neg,axiom,
% 5.49/5.90 ! [B: int,A: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono_neg
% 5.49/5.90 thf(fact_2125_mult__right__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono
% 5.49/5.90 thf(fact_2126_mult__right__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono
% 5.49/5.90 thf(fact_2127_mult__right__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono
% 5.49/5.90 thf(fact_2128_mult__right__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_right_mono
% 5.49/5.90 thf(fact_2129_mult__le__0__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.49/5.90 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_le_0_iff
% 5.49/5.90 thf(fact_2130_mult__le__0__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.49/5.90 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_le_0_iff
% 5.49/5.90 thf(fact_2131_mult__le__0__iff,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.49/5.90 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.49/5.90 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_le_0_iff
% 5.49/5.90 thf(fact_2132_split__mult__neg__le,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_neg_le
% 5.49/5.90 thf(fact_2133_split__mult__neg__le,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_neg_le
% 5.49/5.90 thf(fact_2134_split__mult__neg__le,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.49/5.90 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.90 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_neg_le
% 5.49/5.90 thf(fact_2135_split__mult__neg__le,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.49/5.90 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.49/5.90
% 5.49/5.90 % split_mult_neg_le
% 5.49/5.90 thf(fact_2136_mult__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonneg
% 5.49/5.90 thf(fact_2137_mult__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonneg
% 5.49/5.90 thf(fact_2138_mult__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonneg
% 5.49/5.90 thf(fact_2139_mult__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonneg
% 5.49/5.90 thf(fact_2140_mult__nonneg__nonpos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos
% 5.49/5.90 thf(fact_2141_mult__nonneg__nonpos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos
% 5.49/5.90 thf(fact_2142_mult__nonneg__nonpos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos
% 5.49/5.90 thf(fact_2143_mult__nonneg__nonpos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos
% 5.49/5.90 thf(fact_2144_mult__nonpos__nonneg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonneg
% 5.49/5.90 thf(fact_2145_mult__nonpos__nonneg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonneg
% 5.49/5.90 thf(fact_2146_mult__nonpos__nonneg,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonneg
% 5.49/5.90 thf(fact_2147_mult__nonpos__nonneg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonpos_nonneg
% 5.49/5.90 thf(fact_2148_mult__nonneg__nonpos2,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos2
% 5.49/5.90 thf(fact_2149_mult__nonneg__nonpos2,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos2
% 5.49/5.90 thf(fact_2150_mult__nonneg__nonpos2,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos2
% 5.49/5.90 thf(fact_2151_mult__nonneg__nonpos2,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_nonneg_nonpos2
% 5.49/5.90 thf(fact_2152_zero__le__mult__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_mult_iff
% 5.49/5.90 thf(fact_2153_zero__le__mult__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_mult_iff
% 5.49/5.90 thf(fact_2154_zero__le__mult__iff,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_mult_iff
% 5.49/5.90 thf(fact_2155_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.49/5.90 thf(fact_2156_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.49/5.90 thf(fact_2157_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.49/5.90 thf(fact_2158_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.49/5.90 thf(fact_2159_not__numeral__less__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_less_zero
% 5.49/5.90 thf(fact_2160_not__numeral__less__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_less_zero
% 5.49/5.90 thf(fact_2161_not__numeral__less__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_less_zero
% 5.49/5.90 thf(fact_2162_not__numeral__less__zero,axiom,
% 5.49/5.90 ! [N: num] :
% 5.49/5.90 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.49/5.90
% 5.49/5.90 % not_numeral_less_zero
% 5.49/5.90 thf(fact_2163_zero__less__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_numeral
% 5.49/5.90 thf(fact_2164_zero__less__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_numeral
% 5.49/5.90 thf(fact_2165_zero__less__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_numeral
% 5.49/5.90 thf(fact_2166_zero__less__numeral,axiom,
% 5.49/5.90 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_numeral
% 5.49/5.90 thf(fact_2167_zero__less__one__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one_class.zero_le_one
% 5.49/5.90 thf(fact_2168_zero__less__one__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one_class.zero_le_one
% 5.49/5.90 thf(fact_2169_zero__less__one__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one_class.zero_le_one
% 5.49/5.90 thf(fact_2170_zero__less__one__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one_class.zero_le_one
% 5.49/5.90 thf(fact_2171_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.49/5.90
% 5.49/5.90 % linordered_nonzero_semiring_class.zero_le_one
% 5.49/5.90 thf(fact_2172_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.49/5.90
% 5.49/5.90 % linordered_nonzero_semiring_class.zero_le_one
% 5.49/5.90 thf(fact_2173_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.49/5.90
% 5.49/5.90 % linordered_nonzero_semiring_class.zero_le_one
% 5.49/5.90 thf(fact_2174_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.49/5.90 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.49/5.90
% 5.49/5.90 % linordered_nonzero_semiring_class.zero_le_one
% 5.49/5.90 thf(fact_2175_not__one__le__zero,axiom,
% 5.49/5.90 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_le_zero
% 5.49/5.90 thf(fact_2176_not__one__le__zero,axiom,
% 5.49/5.90 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_le_zero
% 5.49/5.90 thf(fact_2177_not__one__le__zero,axiom,
% 5.49/5.90 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_le_zero
% 5.49/5.90 thf(fact_2178_not__one__le__zero,axiom,
% 5.49/5.90 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_le_zero
% 5.49/5.90 thf(fact_2179_add__nonpos__eq__0__iff,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.49/5.90 => ( ( ( plus_plus_real @ X @ Y2 )
% 5.49/5.90 = zero_zero_real )
% 5.49/5.90 = ( ( X = zero_zero_real )
% 5.49/5.90 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_eq_0_iff
% 5.49/5.90 thf(fact_2180_add__nonpos__eq__0__iff,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.49/5.90 => ( ( ( plus_plus_rat @ X @ Y2 )
% 5.49/5.90 = zero_zero_rat )
% 5.49/5.90 = ( ( X = zero_zero_rat )
% 5.49/5.90 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_eq_0_iff
% 5.49/5.90 thf(fact_2181_add__nonpos__eq__0__iff,axiom,
% 5.49/5.90 ! [X: nat,Y2: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_eq_nat @ Y2 @ zero_zero_nat )
% 5.49/5.90 => ( ( ( plus_plus_nat @ X @ Y2 )
% 5.49/5.90 = zero_zero_nat )
% 5.49/5.90 = ( ( X = zero_zero_nat )
% 5.49/5.90 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_eq_0_iff
% 5.49/5.90 thf(fact_2182_add__nonpos__eq__0__iff,axiom,
% 5.49/5.90 ! [X: int,Y2: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 5.49/5.90 => ( ( ( plus_plus_int @ X @ Y2 )
% 5.49/5.90 = zero_zero_int )
% 5.49/5.90 = ( ( X = zero_zero_int )
% 5.49/5.90 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_eq_0_iff
% 5.49/5.90 thf(fact_2183_add__nonneg__eq__0__iff,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.90 => ( ( ( plus_plus_real @ X @ Y2 )
% 5.49/5.90 = zero_zero_real )
% 5.49/5.90 = ( ( X = zero_zero_real )
% 5.49/5.90 & ( Y2 = zero_zero_real ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_eq_0_iff
% 5.49/5.90 thf(fact_2184_add__nonneg__eq__0__iff,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.90 => ( ( ( plus_plus_rat @ X @ Y2 )
% 5.49/5.90 = zero_zero_rat )
% 5.49/5.90 = ( ( X = zero_zero_rat )
% 5.49/5.90 & ( Y2 = zero_zero_rat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_eq_0_iff
% 5.49/5.90 thf(fact_2185_add__nonneg__eq__0__iff,axiom,
% 5.49/5.90 ! [X: nat,Y2: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.49/5.90 => ( ( ( plus_plus_nat @ X @ Y2 )
% 5.49/5.90 = zero_zero_nat )
% 5.49/5.90 = ( ( X = zero_zero_nat )
% 5.49/5.90 & ( Y2 = zero_zero_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_eq_0_iff
% 5.49/5.90 thf(fact_2186_add__nonneg__eq__0__iff,axiom,
% 5.49/5.90 ! [X: int,Y2: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.90 => ( ( ( plus_plus_int @ X @ Y2 )
% 5.49/5.90 = zero_zero_int )
% 5.49/5.90 = ( ( X = zero_zero_int )
% 5.49/5.90 & ( Y2 = zero_zero_int ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_eq_0_iff
% 5.49/5.90 thf(fact_2187_add__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_nonpos
% 5.49/5.90 thf(fact_2188_add__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_nonpos
% 5.49/5.90 thf(fact_2189_add__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_nonpos
% 5.49/5.90 thf(fact_2190_add__nonpos__nonpos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonpos_nonpos
% 5.49/5.90 thf(fact_2191_add__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_nonneg
% 5.49/5.90 thf(fact_2192_add__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_nonneg
% 5.49/5.90 thf(fact_2193_add__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_nonneg
% 5.49/5.90 thf(fact_2194_add__nonneg__nonneg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_nonneg_nonneg
% 5.49/5.90 thf(fact_2195_add__increasing2,axiom,
% 5.49/5.90 ! [C: real,B: real,A: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ A )
% 5.49/5.90 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing2
% 5.49/5.90 thf(fact_2196_add__increasing2,axiom,
% 5.49/5.90 ! [C: rat,B: rat,A: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.90 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing2
% 5.49/5.90 thf(fact_2197_add__increasing2,axiom,
% 5.49/5.90 ! [C: nat,B: nat,A: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.90 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing2
% 5.49/5.90 thf(fact_2198_add__increasing2,axiom,
% 5.49/5.90 ! [C: int,B: int,A: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ A )
% 5.49/5.90 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing2
% 5.49/5.90 thf(fact_2199_add__decreasing2,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing2
% 5.49/5.90 thf(fact_2200_add__decreasing2,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing2
% 5.49/5.90 thf(fact_2201_add__decreasing2,axiom,
% 5.49/5.90 ! [C: nat,A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing2
% 5.49/5.90 thf(fact_2202_add__decreasing2,axiom,
% 5.49/5.90 ! [C: int,A: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing2
% 5.49/5.90 thf(fact_2203_add__increasing,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_eq_real @ B @ C )
% 5.49/5.90 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing
% 5.49/5.90 thf(fact_2204_add__increasing,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_eq_rat @ B @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing
% 5.49/5.90 thf(fact_2205_add__increasing,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_eq_nat @ B @ C )
% 5.49/5.90 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing
% 5.49/5.90 thf(fact_2206_add__increasing,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_eq_int @ B @ C )
% 5.49/5.90 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_increasing
% 5.49/5.90 thf(fact_2207_add__decreasing,axiom,
% 5.49/5.90 ! [A: real,C: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ B )
% 5.49/5.90 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing
% 5.49/5.90 thf(fact_2208_add__decreasing,axiom,
% 5.49/5.90 ! [A: rat,C: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ B )
% 5.49/5.90 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing
% 5.49/5.90 thf(fact_2209_add__decreasing,axiom,
% 5.49/5.90 ! [A: nat,C: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_eq_nat @ C @ B )
% 5.49/5.90 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing
% 5.49/5.90 thf(fact_2210_add__decreasing,axiom,
% 5.49/5.90 ! [A: int,C: int,B: int] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_eq_int @ C @ B )
% 5.49/5.90 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_decreasing
% 5.49/5.90 thf(fact_2211_mult__neg__neg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_neg
% 5.49/5.90 thf(fact_2212_mult__neg__neg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_neg
% 5.49/5.90 thf(fact_2213_mult__neg__neg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_neg
% 5.49/5.90 thf(fact_2214_not__square__less__zero,axiom,
% 5.49/5.90 ! [A: real] :
% 5.49/5.90 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.49/5.90
% 5.49/5.90 % not_square_less_zero
% 5.49/5.90 thf(fact_2215_not__square__less__zero,axiom,
% 5.49/5.90 ! [A: rat] :
% 5.49/5.90 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.49/5.90
% 5.49/5.90 % not_square_less_zero
% 5.49/5.90 thf(fact_2216_not__square__less__zero,axiom,
% 5.49/5.90 ! [A: int] :
% 5.49/5.90 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.49/5.90
% 5.49/5.90 % not_square_less_zero
% 5.49/5.90 thf(fact_2217_mult__less__0__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.49/5.90 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_0_iff
% 5.49/5.90 thf(fact_2218_mult__less__0__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.49/5.90 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_0_iff
% 5.49/5.90 thf(fact_2219_mult__less__0__iff,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.49/5.90 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.49/5.90 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_0_iff
% 5.49/5.90 thf(fact_2220_mult__neg__pos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_pos
% 5.49/5.90 thf(fact_2221_mult__neg__pos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_pos
% 5.49/5.90 thf(fact_2222_mult__neg__pos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_pos
% 5.49/5.90 thf(fact_2223_mult__neg__pos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_neg_pos
% 5.49/5.90 thf(fact_2224_mult__pos__neg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg
% 5.49/5.90 thf(fact_2225_mult__pos__neg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg
% 5.49/5.90 thf(fact_2226_mult__pos__neg,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg
% 5.49/5.90 thf(fact_2227_mult__pos__neg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg
% 5.49/5.90 thf(fact_2228_mult__pos__pos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_pos
% 5.49/5.90 thf(fact_2229_mult__pos__pos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_pos
% 5.49/5.90 thf(fact_2230_mult__pos__pos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_pos
% 5.49/5.90 thf(fact_2231_mult__pos__pos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_pos
% 5.49/5.90 thf(fact_2232_mult__pos__neg2,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg2
% 5.49/5.90 thf(fact_2233_mult__pos__neg2,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg2
% 5.49/5.90 thf(fact_2234_mult__pos__neg2,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg2
% 5.49/5.90 thf(fact_2235_mult__pos__neg2,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_pos_neg2
% 5.49/5.90 thf(fact_2236_zero__less__mult__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.49/5.90 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_iff
% 5.49/5.90 thf(fact_2237_zero__less__mult__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.49/5.90 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_iff
% 5.49/5.90 thf(fact_2238_zero__less__mult__iff,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.49/5.90 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.90 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_iff
% 5.49/5.90 thf(fact_2239_zero__less__mult__pos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos
% 5.49/5.90 thf(fact_2240_zero__less__mult__pos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos
% 5.49/5.90 thf(fact_2241_zero__less__mult__pos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos
% 5.49/5.90 thf(fact_2242_zero__less__mult__pos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos
% 5.49/5.90 thf(fact_2243_zero__less__mult__pos2,axiom,
% 5.49/5.90 ! [B: real,A: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos2
% 5.49/5.90 thf(fact_2244_zero__less__mult__pos2,axiom,
% 5.49/5.90 ! [B: rat,A: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos2
% 5.49/5.90 thf(fact_2245_zero__less__mult__pos2,axiom,
% 5.49/5.90 ! [B: nat,A: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos2
% 5.49/5.90 thf(fact_2246_zero__less__mult__pos2,axiom,
% 5.49/5.90 ! [B: int,A: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_mult_pos2
% 5.49/5.90 thf(fact_2247_mult__less__cancel__left__neg,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.90 = ( ord_less_real @ B @ A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_neg
% 5.49/5.90 thf(fact_2248_mult__less__cancel__left__neg,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.90 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_neg
% 5.49/5.90 thf(fact_2249_mult__less__cancel__left__neg,axiom,
% 5.49/5.90 ! [C: int,A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.90 = ( ord_less_int @ B @ A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_neg
% 5.49/5.90 thf(fact_2250_mult__less__cancel__left__pos,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.90 = ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_pos
% 5.49/5.90 thf(fact_2251_mult__less__cancel__left__pos,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.90 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_pos
% 5.49/5.90 thf(fact_2252_mult__less__cancel__left__pos,axiom,
% 5.49/5.90 ! [C: int,A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.90 = ( ord_less_int @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_pos
% 5.49/5.90 thf(fact_2253_mult__strict__left__mono__neg,axiom,
% 5.49/5.90 ! [B: real,A: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ B @ A )
% 5.49/5.90 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono_neg
% 5.49/5.90 thf(fact_2254_mult__strict__left__mono__neg,axiom,
% 5.49/5.90 ! [B: rat,A: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ B @ A )
% 5.49/5.90 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono_neg
% 5.49/5.90 thf(fact_2255_mult__strict__left__mono__neg,axiom,
% 5.49/5.90 ! [B: int,A: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ B @ A )
% 5.49/5.90 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono_neg
% 5.49/5.90 thf(fact_2256_mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono
% 5.49/5.90 thf(fact_2257_mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono
% 5.49/5.90 thf(fact_2258_mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono
% 5.49/5.90 thf(fact_2259_mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_left_mono
% 5.49/5.90 thf(fact_2260_mult__less__cancel__left__disj,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 & ( ord_less_real @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_disj
% 5.49/5.90 thf(fact_2261_mult__less__cancel__left__disj,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 & ( ord_less_rat @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_disj
% 5.49/5.90 thf(fact_2262_mult__less__cancel__left__disj,axiom,
% 5.49/5.90 ! [C: int,A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.90 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 & ( ord_less_int @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.90 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_left_disj
% 5.49/5.90 thf(fact_2263_mult__strict__right__mono__neg,axiom,
% 5.49/5.90 ! [B: real,A: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ B @ A )
% 5.49/5.90 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono_neg
% 5.49/5.90 thf(fact_2264_mult__strict__right__mono__neg,axiom,
% 5.49/5.90 ! [B: rat,A: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ B @ A )
% 5.49/5.90 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono_neg
% 5.49/5.90 thf(fact_2265_mult__strict__right__mono__neg,axiom,
% 5.49/5.90 ! [B: int,A: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ B @ A )
% 5.49/5.90 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono_neg
% 5.49/5.90 thf(fact_2266_mult__strict__right__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono
% 5.49/5.90 thf(fact_2267_mult__strict__right__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono
% 5.49/5.90 thf(fact_2268_mult__strict__right__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono
% 5.49/5.90 thf(fact_2269_mult__strict__right__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_strict_right_mono
% 5.49/5.90 thf(fact_2270_mult__less__cancel__right__disj,axiom,
% 5.49/5.90 ! [A: real,C: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 & ( ord_less_real @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_right_disj
% 5.49/5.90 thf(fact_2271_mult__less__cancel__right__disj,axiom,
% 5.49/5.90 ! [A: rat,C: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 & ( ord_less_rat @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_right_disj
% 5.49/5.90 thf(fact_2272_mult__less__cancel__right__disj,axiom,
% 5.49/5.90 ! [A: int,C: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.90 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 & ( ord_less_int @ A @ B ) )
% 5.49/5.90 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.90 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_cancel_right_disj
% 5.49/5.90 thf(fact_2273_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.49/5.90 thf(fact_2274_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.49/5.90 thf(fact_2275_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.49/5.90 thf(fact_2276_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.90 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.49/5.90 thf(fact_2277_vebt__maxt_Osimps_I1_J,axiom,
% 5.49/5.90 ! [B: $o,A: $o] :
% 5.49/5.90 ( ( B
% 5.49/5.90 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.90 & ( ~ B
% 5.49/5.90 => ( ( A
% 5.49/5.90 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.90 & ( ~ A
% 5.49/5.90 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.49/5.90 = none_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_maxt.simps(1)
% 5.49/5.90 thf(fact_2278_le__iff__diff__le__0,axiom,
% 5.49/5.90 ( ord_less_eq_real
% 5.49/5.90 = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % le_iff_diff_le_0
% 5.49/5.90 thf(fact_2279_le__iff__diff__le__0,axiom,
% 5.49/5.90 ( ord_less_eq_rat
% 5.49/5.90 = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % le_iff_diff_le_0
% 5.49/5.90 thf(fact_2280_le__iff__diff__le__0,axiom,
% 5.49/5.90 ( ord_less_eq_int
% 5.49/5.90 = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % le_iff_diff_le_0
% 5.49/5.90 thf(fact_2281_zero__less__one,axiom,
% 5.49/5.90 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one
% 5.49/5.90 thf(fact_2282_zero__less__one,axiom,
% 5.49/5.90 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one
% 5.49/5.90 thf(fact_2283_zero__less__one,axiom,
% 5.49/5.90 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one
% 5.49/5.90 thf(fact_2284_zero__less__one,axiom,
% 5.49/5.90 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.49/5.90
% 5.49/5.90 % zero_less_one
% 5.49/5.90 thf(fact_2285_not__one__less__zero,axiom,
% 5.49/5.90 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_less_zero
% 5.49/5.90 thf(fact_2286_not__one__less__zero,axiom,
% 5.49/5.90 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_less_zero
% 5.49/5.90 thf(fact_2287_not__one__less__zero,axiom,
% 5.49/5.90 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_less_zero
% 5.49/5.90 thf(fact_2288_not__one__less__zero,axiom,
% 5.49/5.90 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.49/5.90
% 5.49/5.90 % not_one_less_zero
% 5.49/5.90 thf(fact_2289_less__numeral__extra_I1_J,axiom,
% 5.49/5.90 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.49/5.90
% 5.49/5.90 % less_numeral_extra(1)
% 5.49/5.90 thf(fact_2290_less__numeral__extra_I1_J,axiom,
% 5.49/5.90 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.49/5.90
% 5.49/5.90 % less_numeral_extra(1)
% 5.49/5.90 thf(fact_2291_less__numeral__extra_I1_J,axiom,
% 5.49/5.90 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.49/5.90
% 5.49/5.90 % less_numeral_extra(1)
% 5.49/5.90 thf(fact_2292_less__numeral__extra_I1_J,axiom,
% 5.49/5.90 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.49/5.90
% 5.49/5.90 % less_numeral_extra(1)
% 5.49/5.90 thf(fact_2293_add__less__zeroD,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.49/5.90 | ( ord_less_real @ Y2 @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_less_zeroD
% 5.49/5.90 thf(fact_2294_add__less__zeroD,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y2 ) @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.49/5.90 | ( ord_less_rat @ Y2 @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_less_zeroD
% 5.49/5.90 thf(fact_2295_add__less__zeroD,axiom,
% 5.49/5.90 ! [X: int,Y2: int] :
% 5.49/5.90 ( ( ord_less_int @ ( plus_plus_int @ X @ Y2 ) @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.49/5.90 | ( ord_less_int @ Y2 @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_less_zeroD
% 5.49/5.90 thf(fact_2296_pos__add__strict,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_real @ B @ C )
% 5.49/5.90 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % pos_add_strict
% 5.49/5.90 thf(fact_2297_pos__add__strict,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_rat @ B @ C )
% 5.49/5.90 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % pos_add_strict
% 5.49/5.90 thf(fact_2298_pos__add__strict,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ B @ C )
% 5.49/5.90 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % pos_add_strict
% 5.49/5.90 thf(fact_2299_pos__add__strict,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_int @ B @ C )
% 5.49/5.90 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % pos_add_strict
% 5.49/5.90 thf(fact_2300_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ B )
% 5.49/5.90 => ~ ! [C2: nat] :
% 5.49/5.90 ( ( B
% 5.49/5.90 = ( plus_plus_nat @ A @ C2 ) )
% 5.49/5.90 => ( C2 = zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % canonically_ordered_monoid_add_class.lessE
% 5.49/5.90 thf(fact_2301_add__pos__pos,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_pos_pos
% 5.49/5.90 thf(fact_2302_add__pos__pos,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_pos_pos
% 5.49/5.90 thf(fact_2303_add__pos__pos,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_pos_pos
% 5.49/5.90 thf(fact_2304_add__pos__pos,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_pos_pos
% 5.49/5.90 thf(fact_2305_add__neg__neg,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_neg_neg
% 5.49/5.90 thf(fact_2306_add__neg__neg,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_neg_neg
% 5.49/5.90 thf(fact_2307_add__neg__neg,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.49/5.90 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.49/5.90 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_neg_neg
% 5.49/5.90 thf(fact_2308_add__neg__neg,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.90 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_neg_neg
% 5.49/5.90 thf(fact_2309_divide__right__mono__neg,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_right_mono_neg
% 5.49/5.90 thf(fact_2310_divide__right__mono__neg,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_right_mono_neg
% 5.49/5.90 thf(fact_2311_divide__nonpos__nonpos,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonpos_nonpos
% 5.49/5.90 thf(fact_2312_divide__nonpos__nonpos,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonpos_nonpos
% 5.49/5.90 thf(fact_2313_divide__nonpos__nonneg,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.90 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonpos_nonneg
% 5.49/5.90 thf(fact_2314_divide__nonpos__nonneg,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.90 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonpos_nonneg
% 5.49/5.90 thf(fact_2315_divide__nonneg__nonpos,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.90 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.49/5.90 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonneg_nonpos
% 5.49/5.90 thf(fact_2316_divide__nonneg__nonpos,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.90 => ( ( ord_less_eq_rat @ Y2 @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonneg_nonpos
% 5.49/5.90 thf(fact_2317_divide__nonneg__nonneg,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonneg_nonneg
% 5.49/5.90 thf(fact_2318_divide__nonneg__nonneg,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_nonneg_nonneg
% 5.49/5.90 thf(fact_2319_zero__le__divide__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_divide_iff
% 5.49/5.90 thf(fact_2320_zero__le__divide__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_divide_iff
% 5.49/5.90 thf(fact_2321_divide__right__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_right_mono
% 5.49/5.90 thf(fact_2322_divide__right__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_right_mono
% 5.49/5.90 thf(fact_2323_divide__le__0__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.49/5.90 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.49/5.90 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_le_0_iff
% 5.49/5.90 thf(fact_2324_divide__le__0__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.49/5.90 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.49/5.90 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_le_0_iff
% 5.49/5.90 thf(fact_2325_less__iff__diff__less__0,axiom,
% 5.49/5.90 ( ord_less_real
% 5.49/5.90 = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % less_iff_diff_less_0
% 5.49/5.90 thf(fact_2326_less__iff__diff__less__0,axiom,
% 5.49/5.90 ( ord_less_rat
% 5.49/5.90 = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % less_iff_diff_less_0
% 5.49/5.90 thf(fact_2327_less__iff__diff__less__0,axiom,
% 5.49/5.90 ( ord_less_int
% 5.49/5.90 = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % less_iff_diff_less_0
% 5.49/5.90 thf(fact_2328_divide__strict__right__mono__neg,axiom,
% 5.49/5.90 ! [B: real,A: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ B @ A )
% 5.49/5.90 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_strict_right_mono_neg
% 5.49/5.90 thf(fact_2329_divide__strict__right__mono__neg,axiom,
% 5.49/5.90 ! [B: rat,A: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ B @ A )
% 5.49/5.90 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_strict_right_mono_neg
% 5.49/5.90 thf(fact_2330_divide__strict__right__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( ord_less_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_strict_right_mono
% 5.49/5.90 thf(fact_2331_divide__strict__right__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( ord_less_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_strict_right_mono
% 5.49/5.90 thf(fact_2332_zero__less__divide__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.49/5.90 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_divide_iff
% 5.49/5.90 thf(fact_2333_zero__less__divide__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.49/5.90 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_divide_iff
% 5.49/5.90 thf(fact_2334_divide__less__cancel,axiom,
% 5.49/5.90 ! [A: real,C: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.90 => ( ord_less_real @ A @ B ) )
% 5.49/5.90 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ B @ A ) )
% 5.49/5.90 & ( C != zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_less_cancel
% 5.49/5.90 thf(fact_2335_divide__less__cancel,axiom,
% 5.49/5.90 ! [A: rat,C: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.90 => ( ord_less_rat @ A @ B ) )
% 5.49/5.90 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ B @ A ) )
% 5.49/5.90 & ( C != zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_less_cancel
% 5.49/5.90 thf(fact_2336_divide__less__0__iff,axiom,
% 5.49/5.90 ! [A: real,B: real] :
% 5.49/5.90 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.49/5.90 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.49/5.90 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.90 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_less_0_iff
% 5.49/5.90 thf(fact_2337_divide__less__0__iff,axiom,
% 5.49/5.90 ! [A: rat,B: rat] :
% 5.49/5.90 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.49/5.90 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.49/5.90 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.90 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_less_0_iff
% 5.49/5.90 thf(fact_2338_divide__pos__pos,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ X )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_pos_pos
% 5.49/5.90 thf(fact_2339_divide__pos__pos,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_pos_pos
% 5.49/5.90 thf(fact_2340_divide__pos__neg,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ X )
% 5.49/5.90 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_pos_neg
% 5.49/5.90 thf(fact_2341_divide__pos__neg,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.49/5.90 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_pos_neg
% 5.49/5.90 thf(fact_2342_divide__neg__pos,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_real @ X @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.90 => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_neg_pos
% 5.49/5.90 thf(fact_2343_divide__neg__pos,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.90 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_neg_pos
% 5.49/5.90 thf(fact_2344_divide__neg__neg,axiom,
% 5.49/5.90 ! [X: real,Y2: real] :
% 5.49/5.90 ( ( ord_less_real @ X @ zero_zero_real )
% 5.49/5.90 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_neg_neg
% 5.49/5.90 thf(fact_2345_divide__neg__neg,axiom,
% 5.49/5.90 ! [X: rat,Y2: rat] :
% 5.49/5.90 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.49/5.90 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_neg_neg
% 5.49/5.90 thf(fact_2346_power__mono,axiom,
% 5.49/5.90 ! [A: real,B: real,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_mono
% 5.49/5.90 thf(fact_2347_power__mono,axiom,
% 5.49/5.90 ! [A: rat,B: rat,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_mono
% 5.49/5.90 thf(fact_2348_power__mono,axiom,
% 5.49/5.90 ! [A: nat,B: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_mono
% 5.49/5.90 thf(fact_2349_power__mono,axiom,
% 5.49/5.90 ! [A: int,B: int,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % power_mono
% 5.49/5.90 thf(fact_2350_zero__le__power,axiom,
% 5.49/5.90 ! [A: real,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_power
% 5.49/5.90 thf(fact_2351_zero__le__power,axiom,
% 5.49/5.90 ! [A: rat,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_power
% 5.49/5.90 thf(fact_2352_zero__le__power,axiom,
% 5.49/5.90 ! [A: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_power
% 5.49/5.90 thf(fact_2353_zero__le__power,axiom,
% 5.49/5.90 ! [A: int,N: nat] :
% 5.49/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_le_power
% 5.49/5.90 thf(fact_2354_zero__less__power,axiom,
% 5.49/5.90 ! [A: real,N: nat] :
% 5.49/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.90 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_power
% 5.49/5.90 thf(fact_2355_zero__less__power,axiom,
% 5.49/5.90 ! [A: rat,N: nat] :
% 5.49/5.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.90 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_power
% 5.49/5.90 thf(fact_2356_zero__less__power,axiom,
% 5.49/5.90 ! [A: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.90 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_power
% 5.49/5.90 thf(fact_2357_zero__less__power,axiom,
% 5.49/5.90 ! [A: int,N: nat] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.90 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % zero_less_power
% 5.49/5.90 thf(fact_2358_nonzero__eq__divide__eq,axiom,
% 5.49/5.90 ! [C: complex,A: complex,B: complex] :
% 5.49/5.90 ( ( C != zero_zero_complex )
% 5.49/5.90 => ( ( A
% 5.49/5.90 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.90 = ( ( times_times_complex @ A @ C )
% 5.49/5.90 = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_eq_divide_eq
% 5.49/5.90 thf(fact_2359_nonzero__eq__divide__eq,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( C != zero_zero_real )
% 5.49/5.90 => ( ( A
% 5.49/5.90 = ( divide_divide_real @ B @ C ) )
% 5.49/5.90 = ( ( times_times_real @ A @ C )
% 5.49/5.90 = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_eq_divide_eq
% 5.49/5.90 thf(fact_2360_nonzero__eq__divide__eq,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( C != zero_zero_rat )
% 5.49/5.90 => ( ( A
% 5.49/5.90 = ( divide_divide_rat @ B @ C ) )
% 5.49/5.90 = ( ( times_times_rat @ A @ C )
% 5.49/5.90 = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_eq_divide_eq
% 5.49/5.90 thf(fact_2361_nonzero__divide__eq__eq,axiom,
% 5.49/5.90 ! [C: complex,B: complex,A: complex] :
% 5.49/5.90 ( ( C != zero_zero_complex )
% 5.49/5.90 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( B
% 5.49/5.90 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_divide_eq_eq
% 5.49/5.90 thf(fact_2362_nonzero__divide__eq__eq,axiom,
% 5.49/5.90 ! [C: real,B: real,A: real] :
% 5.49/5.90 ( ( C != zero_zero_real )
% 5.49/5.90 => ( ( ( divide_divide_real @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( B
% 5.49/5.90 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_divide_eq_eq
% 5.49/5.90 thf(fact_2363_nonzero__divide__eq__eq,axiom,
% 5.49/5.90 ! [C: rat,B: rat,A: rat] :
% 5.49/5.90 ( ( C != zero_zero_rat )
% 5.49/5.90 => ( ( ( divide_divide_rat @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( B
% 5.49/5.90 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nonzero_divide_eq_eq
% 5.49/5.90 thf(fact_2364_eq__divide__imp,axiom,
% 5.49/5.90 ! [C: complex,A: complex,B: complex] :
% 5.49/5.90 ( ( C != zero_zero_complex )
% 5.49/5.90 => ( ( ( times_times_complex @ A @ C )
% 5.49/5.90 = B )
% 5.49/5.90 => ( A
% 5.49/5.90 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_imp
% 5.49/5.90 thf(fact_2365_eq__divide__imp,axiom,
% 5.49/5.90 ! [C: real,A: real,B: real] :
% 5.49/5.90 ( ( C != zero_zero_real )
% 5.49/5.90 => ( ( ( times_times_real @ A @ C )
% 5.49/5.90 = B )
% 5.49/5.90 => ( A
% 5.49/5.90 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_imp
% 5.49/5.90 thf(fact_2366_eq__divide__imp,axiom,
% 5.49/5.90 ! [C: rat,A: rat,B: rat] :
% 5.49/5.90 ( ( C != zero_zero_rat )
% 5.49/5.90 => ( ( ( times_times_rat @ A @ C )
% 5.49/5.90 = B )
% 5.49/5.90 => ( A
% 5.49/5.90 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_imp
% 5.49/5.90 thf(fact_2367_divide__eq__imp,axiom,
% 5.49/5.90 ! [C: complex,B: complex,A: complex] :
% 5.49/5.90 ( ( C != zero_zero_complex )
% 5.49/5.90 => ( ( B
% 5.49/5.90 = ( times_times_complex @ A @ C ) )
% 5.49/5.90 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.49/5.90 = A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_imp
% 5.49/5.90 thf(fact_2368_divide__eq__imp,axiom,
% 5.49/5.90 ! [C: real,B: real,A: real] :
% 5.49/5.90 ( ( C != zero_zero_real )
% 5.49/5.90 => ( ( B
% 5.49/5.90 = ( times_times_real @ A @ C ) )
% 5.49/5.90 => ( ( divide_divide_real @ B @ C )
% 5.49/5.90 = A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_imp
% 5.49/5.90 thf(fact_2369_divide__eq__imp,axiom,
% 5.49/5.90 ! [C: rat,B: rat,A: rat] :
% 5.49/5.90 ( ( C != zero_zero_rat )
% 5.49/5.90 => ( ( B
% 5.49/5.90 = ( times_times_rat @ A @ C ) )
% 5.49/5.90 => ( ( divide_divide_rat @ B @ C )
% 5.49/5.90 = A ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_imp
% 5.49/5.90 thf(fact_2370_eq__divide__eq,axiom,
% 5.49/5.90 ! [A: complex,B: complex,C: complex] :
% 5.49/5.90 ( ( A
% 5.49/5.90 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.90 = ( ( ( C != zero_zero_complex )
% 5.49/5.90 => ( ( times_times_complex @ A @ C )
% 5.49/5.90 = B ) )
% 5.49/5.90 & ( ( C = zero_zero_complex )
% 5.49/5.90 => ( A = zero_zero_complex ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_eq
% 5.49/5.90 thf(fact_2371_eq__divide__eq,axiom,
% 5.49/5.90 ! [A: real,B: real,C: real] :
% 5.49/5.90 ( ( A
% 5.49/5.90 = ( divide_divide_real @ B @ C ) )
% 5.49/5.90 = ( ( ( C != zero_zero_real )
% 5.49/5.90 => ( ( times_times_real @ A @ C )
% 5.49/5.90 = B ) )
% 5.49/5.90 & ( ( C = zero_zero_real )
% 5.49/5.90 => ( A = zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_eq
% 5.49/5.90 thf(fact_2372_eq__divide__eq,axiom,
% 5.49/5.90 ! [A: rat,B: rat,C: rat] :
% 5.49/5.90 ( ( A
% 5.49/5.90 = ( divide_divide_rat @ B @ C ) )
% 5.49/5.90 = ( ( ( C != zero_zero_rat )
% 5.49/5.90 => ( ( times_times_rat @ A @ C )
% 5.49/5.90 = B ) )
% 5.49/5.90 & ( ( C = zero_zero_rat )
% 5.49/5.90 => ( A = zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % eq_divide_eq
% 5.49/5.90 thf(fact_2373_divide__eq__eq,axiom,
% 5.49/5.90 ! [B: complex,C: complex,A: complex] :
% 5.49/5.90 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( ( ( C != zero_zero_complex )
% 5.49/5.90 => ( B
% 5.49/5.90 = ( times_times_complex @ A @ C ) ) )
% 5.49/5.90 & ( ( C = zero_zero_complex )
% 5.49/5.90 => ( A = zero_zero_complex ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_eq
% 5.49/5.90 thf(fact_2374_divide__eq__eq,axiom,
% 5.49/5.90 ! [B: real,C: real,A: real] :
% 5.49/5.90 ( ( ( divide_divide_real @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( ( ( C != zero_zero_real )
% 5.49/5.90 => ( B
% 5.49/5.90 = ( times_times_real @ A @ C ) ) )
% 5.49/5.90 & ( ( C = zero_zero_real )
% 5.49/5.90 => ( A = zero_zero_real ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_eq
% 5.49/5.90 thf(fact_2375_divide__eq__eq,axiom,
% 5.49/5.90 ! [B: rat,C: rat,A: rat] :
% 5.49/5.90 ( ( ( divide_divide_rat @ B @ C )
% 5.49/5.90 = A )
% 5.49/5.90 = ( ( ( C != zero_zero_rat )
% 5.49/5.90 => ( B
% 5.49/5.90 = ( times_times_rat @ A @ C ) ) )
% 5.49/5.90 & ( ( C = zero_zero_rat )
% 5.49/5.90 => ( A = zero_zero_rat ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divide_eq_eq
% 5.49/5.90 thf(fact_2376_frac__eq__eq,axiom,
% 5.49/5.90 ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 5.49/5.90 ( ( Y2 != zero_zero_complex )
% 5.49/5.90 => ( ( Z != zero_zero_complex )
% 5.49/5.90 => ( ( ( divide1717551699836669952omplex @ X @ Y2 )
% 5.49/5.90 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.49/5.90 = ( ( times_times_complex @ X @ Z )
% 5.49/5.90 = ( times_times_complex @ W @ Y2 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % frac_eq_eq
% 5.49/5.90 thf(fact_2377_frac__eq__eq,axiom,
% 5.49/5.90 ! [Y2: real,Z: real,X: real,W: real] :
% 5.49/5.90 ( ( Y2 != zero_zero_real )
% 5.49/5.90 => ( ( Z != zero_zero_real )
% 5.49/5.90 => ( ( ( divide_divide_real @ X @ Y2 )
% 5.49/5.90 = ( divide_divide_real @ W @ Z ) )
% 5.49/5.90 = ( ( times_times_real @ X @ Z )
% 5.49/5.90 = ( times_times_real @ W @ Y2 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % frac_eq_eq
% 5.49/5.90 thf(fact_2378_frac__eq__eq,axiom,
% 5.49/5.90 ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 5.49/5.90 ( ( Y2 != zero_zero_rat )
% 5.49/5.90 => ( ( Z != zero_zero_rat )
% 5.49/5.90 => ( ( ( divide_divide_rat @ X @ Y2 )
% 5.49/5.90 = ( divide_divide_rat @ W @ Z ) )
% 5.49/5.90 = ( ( times_times_rat @ X @ Z )
% 5.49/5.90 = ( times_times_rat @ W @ Y2 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % frac_eq_eq
% 5.49/5.90 thf(fact_2379_right__inverse__eq,axiom,
% 5.49/5.90 ! [B: complex,A: complex] :
% 5.49/5.90 ( ( B != zero_zero_complex )
% 5.49/5.90 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.49/5.90 = one_one_complex )
% 5.49/5.90 = ( A = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % right_inverse_eq
% 5.49/5.90 thf(fact_2380_right__inverse__eq,axiom,
% 5.49/5.90 ! [B: real,A: real] :
% 5.49/5.90 ( ( B != zero_zero_real )
% 5.49/5.90 => ( ( ( divide_divide_real @ A @ B )
% 5.49/5.90 = one_one_real )
% 5.49/5.90 = ( A = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % right_inverse_eq
% 5.49/5.90 thf(fact_2381_right__inverse__eq,axiom,
% 5.49/5.90 ! [B: rat,A: rat] :
% 5.49/5.90 ( ( B != zero_zero_rat )
% 5.49/5.90 => ( ( ( divide_divide_rat @ A @ B )
% 5.49/5.90 = one_one_rat )
% 5.49/5.90 = ( A = B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % right_inverse_eq
% 5.49/5.90 thf(fact_2382_power__0,axiom,
% 5.49/5.90 ! [A: rat] :
% 5.49/5.90 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.49/5.90 = one_one_rat ) ).
% 5.49/5.90
% 5.49/5.90 % power_0
% 5.49/5.90 thf(fact_2383_power__0,axiom,
% 5.49/5.90 ! [A: nat] :
% 5.49/5.90 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.49/5.90 = one_one_nat ) ).
% 5.49/5.90
% 5.49/5.90 % power_0
% 5.49/5.90 thf(fact_2384_power__0,axiom,
% 5.49/5.90 ! [A: real] :
% 5.49/5.90 ( ( power_power_real @ A @ zero_zero_nat )
% 5.49/5.90 = one_one_real ) ).
% 5.49/5.90
% 5.49/5.90 % power_0
% 5.49/5.90 thf(fact_2385_power__0,axiom,
% 5.49/5.90 ! [A: int] :
% 5.49/5.90 ( ( power_power_int @ A @ zero_zero_nat )
% 5.49/5.90 = one_one_int ) ).
% 5.49/5.90
% 5.49/5.90 % power_0
% 5.49/5.90 thf(fact_2386_power__0,axiom,
% 5.49/5.90 ! [A: complex] :
% 5.49/5.90 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.49/5.90 = one_one_complex ) ).
% 5.49/5.90
% 5.49/5.90 % power_0
% 5.49/5.90 thf(fact_2387_Ex__less__Suc2,axiom,
% 5.49/5.90 ! [N: nat,P: nat > $o] :
% 5.49/5.90 ( ( ? [I3: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.49/5.90 & ( P @ I3 ) ) )
% 5.49/5.90 = ( ( P @ zero_zero_nat )
% 5.49/5.90 | ? [I3: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I3 @ N )
% 5.49/5.90 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % Ex_less_Suc2
% 5.49/5.90 thf(fact_2388_gr0__conv__Suc,axiom,
% 5.49/5.90 ! [N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 = ( ? [M6: nat] :
% 5.49/5.90 ( N
% 5.49/5.90 = ( suc @ M6 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % gr0_conv_Suc
% 5.49/5.90 thf(fact_2389_All__less__Suc2,axiom,
% 5.49/5.90 ! [N: nat,P: nat > $o] :
% 5.49/5.90 ( ( ! [I3: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 5.49/5.90 => ( P @ I3 ) ) )
% 5.49/5.90 = ( ( P @ zero_zero_nat )
% 5.49/5.90 & ! [I3: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I3 @ N )
% 5.49/5.90 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % All_less_Suc2
% 5.49/5.90 thf(fact_2390_gr0__implies__Suc,axiom,
% 5.49/5.90 ! [N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ? [M5: nat] :
% 5.49/5.90 ( N
% 5.49/5.90 = ( suc @ M5 ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % gr0_implies_Suc
% 5.49/5.90 thf(fact_2391_less__Suc__eq__0__disj,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.49/5.90 = ( ( M = zero_zero_nat )
% 5.49/5.90 | ? [J3: nat] :
% 5.49/5.90 ( ( M
% 5.49/5.90 = ( suc @ J3 ) )
% 5.49/5.90 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % less_Suc_eq_0_disj
% 5.49/5.90 thf(fact_2392_one__is__add,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ( ( suc @ zero_zero_nat )
% 5.49/5.90 = ( plus_plus_nat @ M @ N ) )
% 5.49/5.90 = ( ( ( M
% 5.49/5.90 = ( suc @ zero_zero_nat ) )
% 5.49/5.90 & ( N = zero_zero_nat ) )
% 5.49/5.90 | ( ( M = zero_zero_nat )
% 5.49/5.90 & ( N
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % one_is_add
% 5.49/5.90 thf(fact_2393_add__is__1,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ( ( plus_plus_nat @ M @ N )
% 5.49/5.90 = ( suc @ zero_zero_nat ) )
% 5.49/5.90 = ( ( ( M
% 5.49/5.90 = ( suc @ zero_zero_nat ) )
% 5.49/5.90 & ( N = zero_zero_nat ) )
% 5.49/5.90 | ( ( M = zero_zero_nat )
% 5.49/5.90 & ( N
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % add_is_1
% 5.49/5.90 thf(fact_2394_ex__least__nat__le,axiom,
% 5.49/5.90 ! [P: nat > $o,N: nat] :
% 5.49/5.90 ( ( P @ N )
% 5.49/5.90 => ( ~ ( P @ zero_zero_nat )
% 5.49/5.90 => ? [K2: nat] :
% 5.49/5.90 ( ( ord_less_eq_nat @ K2 @ N )
% 5.49/5.90 & ! [I: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I @ K2 )
% 5.49/5.90 => ~ ( P @ I ) )
% 5.49/5.90 & ( P @ K2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % ex_least_nat_le
% 5.49/5.90 thf(fact_2395_option_Osize_I4_J,axiom,
% 5.49/5.90 ! [X22: nat] :
% 5.49/5.90 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(4)
% 5.49/5.90 thf(fact_2396_option_Osize_I4_J,axiom,
% 5.49/5.90 ! [X22: product_prod_nat_nat] :
% 5.49/5.90 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(4)
% 5.49/5.90 thf(fact_2397_option_Osize_I4_J,axiom,
% 5.49/5.90 ! [X22: num] :
% 5.49/5.90 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(4)
% 5.49/5.90 thf(fact_2398_less__imp__add__positive,axiom,
% 5.49/5.90 ! [I2: nat,J: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.90 => ? [K2: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.49/5.90 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.49/5.90 = J ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % less_imp_add_positive
% 5.49/5.90 thf(fact_2399_option_Osize_I3_J,axiom,
% 5.49/5.90 ( ( size_size_option_nat @ none_nat )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(3)
% 5.49/5.90 thf(fact_2400_option_Osize_I3_J,axiom,
% 5.49/5.90 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(3)
% 5.49/5.90 thf(fact_2401_option_Osize_I3_J,axiom,
% 5.49/5.90 ( ( size_size_option_num @ none_num )
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % option.size(3)
% 5.49/5.90 thf(fact_2402_diff__less,axiom,
% 5.49/5.90 ! [N: nat,M: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.90 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % diff_less
% 5.49/5.90 thf(fact_2403_nat__mult__eq__cancel1,axiom,
% 5.49/5.90 ! [K: nat,M: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.90 => ( ( ( times_times_nat @ K @ M )
% 5.49/5.90 = ( times_times_nat @ K @ N ) )
% 5.49/5.90 = ( M = N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nat_mult_eq_cancel1
% 5.49/5.90 thf(fact_2404_nat__mult__less__cancel1,axiom,
% 5.49/5.90 ! [K: nat,M: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.90 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.90 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nat_mult_less_cancel1
% 5.49/5.90 thf(fact_2405_mult__less__mono1,axiom,
% 5.49/5.90 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_mono1
% 5.49/5.90 thf(fact_2406_mult__less__mono2,axiom,
% 5.49/5.90 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.90 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.90 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.90 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_less_mono2
% 5.49/5.90 thf(fact_2407_One__nat__def,axiom,
% 5.49/5.90 ( one_one_nat
% 5.49/5.90 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % One_nat_def
% 5.49/5.90 thf(fact_2408_divmod__digit__0_I2_J,axiom,
% 5.49/5.90 ! [B: nat,A: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.49/5.90 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(2)
% 5.49/5.90 thf(fact_2409_divmod__digit__0_I2_J,axiom,
% 5.49/5.90 ! [B: int,A: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.49/5.90 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(2)
% 5.49/5.90 thf(fact_2410_divmod__digit__0_I2_J,axiom,
% 5.49/5.90 ! [B: code_integer,A: code_integer] :
% 5.49/5.90 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.90 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.49/5.90 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(2)
% 5.49/5.90 thf(fact_2411_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ( ( divide_divide_nat @ M @ N )
% 5.49/5.90 = zero_zero_nat )
% 5.49/5.90 = ( ( ord_less_nat @ M @ N )
% 5.49/5.90 | ( N = zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % Euclidean_Division.div_eq_0_iff
% 5.49/5.90 thf(fact_2412_diff__add__0,axiom,
% 5.49/5.90 ! [N: nat,M: nat] :
% 5.49/5.90 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.49/5.90 = zero_zero_nat ) ).
% 5.49/5.90
% 5.49/5.90 % diff_add_0
% 5.49/5.90 thf(fact_2413_bits__stable__imp__add__self,axiom,
% 5.49/5.90 ! [A: nat] :
% 5.49/5.90 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.90 = A )
% 5.49/5.90 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.90 = zero_zero_nat ) ) ).
% 5.49/5.90
% 5.49/5.90 % bits_stable_imp_add_self
% 5.49/5.90 thf(fact_2414_bits__stable__imp__add__self,axiom,
% 5.49/5.90 ! [A: int] :
% 5.49/5.90 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.90 = A )
% 5.49/5.90 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.49/5.90 = zero_zero_int ) ) ).
% 5.49/5.90
% 5.49/5.90 % bits_stable_imp_add_self
% 5.49/5.90 thf(fact_2415_bits__stable__imp__add__self,axiom,
% 5.49/5.90 ! [A: code_integer] :
% 5.49/5.90 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.90 = A )
% 5.49/5.90 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.49/5.90 = zero_z3403309356797280102nteger ) ) ).
% 5.49/5.90
% 5.49/5.90 % bits_stable_imp_add_self
% 5.49/5.90 thf(fact_2416_nat__power__less__imp__less,axiom,
% 5.49/5.90 ! [I2: nat,M: nat,N: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.49/5.90 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.49/5.90 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nat_power_less_imp_less
% 5.49/5.90 thf(fact_2417_mult__eq__self__implies__10,axiom,
% 5.49/5.90 ! [M: nat,N: nat] :
% 5.49/5.90 ( ( M
% 5.49/5.90 = ( times_times_nat @ M @ N ) )
% 5.49/5.90 => ( ( N = one_one_nat )
% 5.49/5.90 | ( M = zero_zero_nat ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mult_eq_self_implies_10
% 5.49/5.90 thf(fact_2418_vebt__insert_Ocases,axiom,
% 5.49/5.90 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.90 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.49/5.90 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ X3 ) )
% 5.49/5.90 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 ) )
% 5.49/5.90 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) )
% 5.49/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_insert.cases
% 5.49/5.90 thf(fact_2419_vebt__pred_Ocases,axiom,
% 5.49/5.90 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.90 ( ! [Uu3: $o,Uv2: $o] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ zero_zero_nat ) )
% 5.49/5.90 => ( ! [A3: $o,Uw2: $o] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.49/5.90 => ( ! [A3: $o,B2: $o,Va3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.49/5.90 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.49/5.90 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.49/5.90 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.49/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_pred.cases
% 5.49/5.90 thf(fact_2420_VEBT__internal_Omembermima_Ocases,axiom,
% 5.49/5.90 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.90 ( ! [Uu3: $o,Uv2: $o,Uw2: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Uw2 ) )
% 5.49/5.90 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.49/5.90 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 5.49/5.90 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X3 ) )
% 5.49/5.90 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % VEBT_internal.membermima.cases
% 5.49/5.90 thf(fact_2421_vebt__member_Ocases,axiom,
% 5.49/5.90 ! [X: produc9072475918466114483BT_nat] :
% 5.49/5.90 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.49/5.90 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.49/5.90 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 5.49/5.90 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.49/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_member.cases
% 5.49/5.90 thf(fact_2422_vebt__insert_Osimps_I2_J,axiom,
% 5.49/5.90 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.49/5.90 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) @ X )
% 5.49/5.90 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_insert.simps(2)
% 5.49/5.90 thf(fact_2423_vebt__pred_Osimps_I3_J,axiom,
% 5.49/5.90 ! [B: $o,A: $o,Va: nat] :
% 5.49/5.90 ( ( B
% 5.49/5.90 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.49/5.90 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.90 & ( ~ B
% 5.49/5.90 => ( ( A
% 5.49/5.90 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.49/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.90 & ( ~ A
% 5.49/5.90 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.49/5.90 = none_nat ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % vebt_pred.simps(3)
% 5.49/5.90 thf(fact_2424_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.49/5.90 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.49/5.90 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.49/5.90
% 5.49/5.90 % VEBT_internal.naive_member.simps(2)
% 5.49/5.90 thf(fact_2425_divmod__digit__0_I1_J,axiom,
% 5.49/5.90 ! [B: nat,A: nat] :
% 5.49/5.90 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.90 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.90 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(1)
% 5.49/5.90 thf(fact_2426_divmod__digit__0_I1_J,axiom,
% 5.49/5.90 ! [B: int,A: int] :
% 5.49/5.90 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.90 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.90 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(1)
% 5.49/5.90 thf(fact_2427_divmod__digit__0_I1_J,axiom,
% 5.49/5.90 ! [B: code_integer,A: code_integer] :
% 5.49/5.90 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.90 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.90 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.90 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % divmod_digit_0(1)
% 5.49/5.90 thf(fact_2428_cong__exp__iff__simps_I6_J,axiom,
% 5.49/5.90 ! [Q2: num,N: num] :
% 5.49/5.90 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(6)
% 5.49/5.90 thf(fact_2429_cong__exp__iff__simps_I6_J,axiom,
% 5.49/5.90 ! [Q2: num,N: num] :
% 5.49/5.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(6)
% 5.49/5.90 thf(fact_2430_cong__exp__iff__simps_I6_J,axiom,
% 5.49/5.90 ! [Q2: num,N: num] :
% 5.49/5.90 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(6)
% 5.49/5.90 thf(fact_2431_cong__exp__iff__simps_I8_J,axiom,
% 5.49/5.90 ! [M: num,Q2: num] :
% 5.49/5.90 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(8)
% 5.49/5.90 thf(fact_2432_cong__exp__iff__simps_I8_J,axiom,
% 5.49/5.90 ! [M: num,Q2: num] :
% 5.49/5.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(8)
% 5.49/5.90 thf(fact_2433_cong__exp__iff__simps_I8_J,axiom,
% 5.49/5.90 ! [M: num,Q2: num] :
% 5.49/5.90 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.49/5.90 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % cong_exp_iff_simps(8)
% 5.49/5.90 thf(fact_2434_mult__div__mod__eq,axiom,
% 5.49/5.90 ! [B: nat,A: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mult_div_mod_eq
% 5.49/5.90 thf(fact_2435_mult__div__mod__eq,axiom,
% 5.49/5.90 ! [B: int,A: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mult_div_mod_eq
% 5.49/5.90 thf(fact_2436_mult__div__mod__eq,axiom,
% 5.49/5.90 ! [B: code_integer,A: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mult_div_mod_eq
% 5.49/5.90 thf(fact_2437_mod__mult__div__eq,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_mult_div_eq
% 5.49/5.90 thf(fact_2438_mod__mult__div__eq,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_mult_div_eq
% 5.49/5.90 thf(fact_2439_mod__mult__div__eq,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_mult_div_eq
% 5.49/5.90 thf(fact_2440_mod__div__mult__eq,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_mult_eq
% 5.49/5.90 thf(fact_2441_mod__div__mult__eq,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_mult_eq
% 5.49/5.90 thf(fact_2442_mod__div__mult__eq,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_mult_eq
% 5.49/5.90 thf(fact_2443_div__mult__mod__eq,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult_mod_eq
% 5.49/5.90 thf(fact_2444_div__mult__mod__eq,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult_mod_eq
% 5.49/5.90 thf(fact_2445_div__mult__mod__eq,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.49/5.90 = A ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult_mod_eq
% 5.49/5.90 thf(fact_2446_mod__div__decomp,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( A
% 5.49/5.90 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_decomp
% 5.49/5.90 thf(fact_2447_mod__div__decomp,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( A
% 5.49/5.90 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_decomp
% 5.49/5.90 thf(fact_2448_mod__div__decomp,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( A
% 5.49/5.90 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_div_decomp
% 5.49/5.90 thf(fact_2449_cancel__div__mod__rules_I1_J,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_plus_nat @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(1)
% 5.49/5.90 thf(fact_2450_cancel__div__mod__rules_I1_J,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_plus_int @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(1)
% 5.49/5.90 thf(fact_2451_cancel__div__mod__rules_I1_J,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(1)
% 5.49/5.90 thf(fact_2452_cancel__div__mod__rules_I2_J,axiom,
% 5.49/5.90 ! [B: nat,A: nat,C: nat] :
% 5.49/5.90 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_plus_nat @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(2)
% 5.49/5.90 thf(fact_2453_cancel__div__mod__rules_I2_J,axiom,
% 5.49/5.90 ! [B: int,A: int,C: int] :
% 5.49/5.90 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_plus_int @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(2)
% 5.49/5.90 thf(fact_2454_cancel__div__mod__rules_I2_J,axiom,
% 5.49/5.90 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.49/5.90 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.49/5.90 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.49/5.90
% 5.49/5.90 % cancel_div_mod_rules(2)
% 5.49/5.90 thf(fact_2455_div__mult1__eq,axiom,
% 5.49/5.90 ! [A: nat,B: nat,C: nat] :
% 5.49/5.90 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.49/5.90 = ( 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 ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult1_eq
% 5.49/5.90 thf(fact_2456_div__mult1__eq,axiom,
% 5.49/5.90 ! [A: int,B: int,C: int] :
% 5.49/5.90 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.49/5.90 = ( 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 ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult1_eq
% 5.49/5.90 thf(fact_2457_div__mult1__eq,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.49/5.90 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.49/5.90 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % div_mult1_eq
% 5.49/5.90 thf(fact_2458_minus__mult__div__eq__mod,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.49/5.90 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mult_div_eq_mod
% 5.49/5.90 thf(fact_2459_minus__mult__div__eq__mod,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.49/5.90 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mult_div_eq_mod
% 5.49/5.90 thf(fact_2460_minus__mult__div__eq__mod,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.49/5.90 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mult_div_eq_mod
% 5.49/5.90 thf(fact_2461_minus__mod__eq__mult__div,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.49/5.90 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_mult_div
% 5.49/5.90 thf(fact_2462_minus__mod__eq__mult__div,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.90 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_mult_div
% 5.49/5.90 thf(fact_2463_minus__mod__eq__mult__div,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.49/5.90 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_mult_div
% 5.49/5.90 thf(fact_2464_minus__mod__eq__div__mult,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.49/5.90 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_div_mult
% 5.49/5.90 thf(fact_2465_minus__mod__eq__div__mult,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.90 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_div_mult
% 5.49/5.90 thf(fact_2466_minus__mod__eq__div__mult,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.49/5.90 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_mod_eq_div_mult
% 5.49/5.90 thf(fact_2467_minus__div__mult__eq__mod,axiom,
% 5.49/5.90 ! [A: nat,B: nat] :
% 5.49/5.90 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.49/5.90 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_div_mult_eq_mod
% 5.49/5.90 thf(fact_2468_minus__div__mult__eq__mod,axiom,
% 5.49/5.90 ! [A: int,B: int] :
% 5.49/5.90 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.49/5.90 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_div_mult_eq_mod
% 5.49/5.90 thf(fact_2469_minus__div__mult__eq__mod,axiom,
% 5.49/5.90 ! [A: code_integer,B: code_integer] :
% 5.49/5.90 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.49/5.90 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.49/5.90
% 5.49/5.90 % minus_div_mult_eq_mod
% 5.49/5.90 thf(fact_2470_nat__mod__eq__lemma,axiom,
% 5.49/5.90 ! [X: nat,N: nat,Y2: nat] :
% 5.49/5.90 ( ( ( modulo_modulo_nat @ X @ N )
% 5.49/5.90 = ( modulo_modulo_nat @ Y2 @ N ) )
% 5.49/5.90 => ( ( ord_less_eq_nat @ Y2 @ X )
% 5.49/5.90 => ? [Q3: nat] :
% 5.49/5.90 ( X
% 5.49/5.90 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % nat_mod_eq_lemma
% 5.49/5.90 thf(fact_2471_mod__eq__nat2E,axiom,
% 5.49/5.90 ! [M: nat,Q2: nat,N: nat] :
% 5.49/5.90 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.49/5.90 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.49/5.90 => ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.90 => ~ ! [S: nat] :
% 5.49/5.90 ( N
% 5.49/5.90 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_eq_nat2E
% 5.49/5.90 thf(fact_2472_mod__eq__nat1E,axiom,
% 5.49/5.90 ! [M: nat,Q2: nat,N: nat] :
% 5.49/5.90 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.49/5.90 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.49/5.90 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.90 => ~ ! [S: nat] :
% 5.49/5.90 ( M
% 5.49/5.90 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_eq_nat1E
% 5.49/5.90 thf(fact_2473_mod__mult2__eq,axiom,
% 5.49/5.90 ! [M: nat,N: nat,Q2: nat] :
% 5.49/5.90 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.49/5.90 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.49/5.90
% 5.49/5.90 % mod_mult2_eq
% 5.49/5.90 thf(fact_2474_modulo__nat__def,axiom,
% 5.49/5.90 ( modulo_modulo_nat
% 5.49/5.90 = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % modulo_nat_def
% 5.49/5.91 thf(fact_2475_VEBT__internal_OminNull_Ocases,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT] :
% 5.49/5.91 ( ( X
% 5.49/5.91 != ( vEBT_Leaf @ $false @ $false ) )
% 5.49/5.91 => ( ! [Uv2: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.49/5.91 => ( ! [Uu3: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.49/5.91 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.49/5.91 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % VEBT_internal.minNull.cases
% 5.49/5.91 thf(fact_2476_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_real,X: real] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.49/5.91 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2477_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_complex,X: complex] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.49/5.91 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2478_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.49/5.91 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2479_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.91 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2480_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_o,X: $o] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.91 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2481_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_nat,X: nat] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.91 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2482_set__update__memI,axiom,
% 5.49/5.91 ! [N: nat,Xs2: list_int,X: int] :
% 5.49/5.91 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.91 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % set_update_memI
% 5.49/5.91 thf(fact_2483_list__update__same__conv,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.91 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.49/5.91 = Xs2 )
% 5.49/5.91 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.49/5.91 = X ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % list_update_same_conv
% 5.49/5.91 thf(fact_2484_list__update__same__conv,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.91 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.49/5.91 = Xs2 )
% 5.49/5.91 = ( ( nth_o @ Xs2 @ I2 )
% 5.49/5.91 = X ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % list_update_same_conv
% 5.49/5.91 thf(fact_2485_list__update__same__conv,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.91 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.49/5.91 = Xs2 )
% 5.49/5.91 = ( ( nth_nat @ Xs2 @ I2 )
% 5.49/5.91 = X ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % list_update_same_conv
% 5.49/5.91 thf(fact_2486_list__update__same__conv,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_int,X: int] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.91 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.49/5.91 = Xs2 )
% 5.49/5.91 = ( ( nth_int @ Xs2 @ I2 )
% 5.49/5.91 = X ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % list_update_same_conv
% 5.49/5.91 thf(fact_2487_nth__list__update,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.49/5.91 => ( ( ( I2 = J )
% 5.49/5.91 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = X ) )
% 5.49/5.91 & ( ( I2 != J )
% 5.49/5.91 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nth_list_update
% 5.49/5.91 thf(fact_2488_nth__list__update,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.49/5.91 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = ( ( ( I2 = J )
% 5.49/5.91 => X )
% 5.49/5.91 & ( ( I2 != J )
% 5.49/5.91 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nth_list_update
% 5.49/5.91 thf(fact_2489_nth__list__update,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.49/5.91 => ( ( ( I2 = J )
% 5.49/5.91 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = X ) )
% 5.49/5.91 & ( ( I2 != J )
% 5.49/5.91 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nth_list_update
% 5.49/5.91 thf(fact_2490_nth__list__update,axiom,
% 5.49/5.91 ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 5.49/5.91 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.49/5.91 => ( ( ( I2 = J )
% 5.49/5.91 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = X ) )
% 5.49/5.91 & ( ( I2 != J )
% 5.49/5.91 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.49/5.91 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nth_list_update
% 5.49/5.91 thf(fact_2491_mult__le__cancel__left,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left
% 5.49/5.91 thf(fact_2492_mult__le__cancel__left,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left
% 5.49/5.91 thf(fact_2493_mult__le__cancel__left,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left
% 5.49/5.91 thf(fact_2494_mult__le__cancel__right,axiom,
% 5.49/5.91 ! [A: real,C: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right
% 5.49/5.91 thf(fact_2495_mult__le__cancel__right,axiom,
% 5.49/5.91 ! [A: rat,C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right
% 5.49/5.91 thf(fact_2496_mult__le__cancel__right,axiom,
% 5.49/5.91 ! [A: int,C: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right
% 5.49/5.91 thf(fact_2497_mult__left__less__imp__less,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_less_imp_less
% 5.49/5.91 thf(fact_2498_mult__left__less__imp__less,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_less_imp_less
% 5.49/5.91 thf(fact_2499_mult__left__less__imp__less,axiom,
% 5.49/5.91 ! [C: nat,A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_less_imp_less
% 5.49/5.91 thf(fact_2500_mult__left__less__imp__less,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_less_imp_less
% 5.49/5.91 thf(fact_2501_mult__strict__mono,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_real @ C @ D )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono
% 5.49/5.91 thf(fact_2502_mult__strict__mono,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_rat @ C @ D )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono
% 5.49/5.91 thf(fact_2503_mult__strict__mono,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.91 ( ( ord_less_nat @ A @ B )
% 5.49/5.91 => ( ( ord_less_nat @ C @ D )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono
% 5.49/5.91 thf(fact_2504_mult__strict__mono,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.91 ( ( ord_less_int @ A @ B )
% 5.49/5.91 => ( ( ord_less_int @ C @ D )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono
% 5.49/5.91 thf(fact_2505_mult__less__cancel__left,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left
% 5.49/5.91 thf(fact_2506_mult__less__cancel__left,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left
% 5.49/5.91 thf(fact_2507_mult__less__cancel__left,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left
% 5.49/5.91 thf(fact_2508_mult__right__less__imp__less,axiom,
% 5.49/5.91 ! [A: real,C: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_less_imp_less
% 5.49/5.91 thf(fact_2509_mult__right__less__imp__less,axiom,
% 5.49/5.91 ! [A: rat,C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_less_imp_less
% 5.49/5.91 thf(fact_2510_mult__right__less__imp__less,axiom,
% 5.49/5.91 ! [A: nat,C: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_less_imp_less
% 5.49/5.91 thf(fact_2511_mult__right__less__imp__less,axiom,
% 5.49/5.91 ! [A: int,C: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_less_imp_less
% 5.49/5.91 thf(fact_2512_mult__strict__mono_H,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_real @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono'
% 5.49/5.91 thf(fact_2513_mult__strict__mono_H,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_rat @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono'
% 5.49/5.91 thf(fact_2514_mult__strict__mono_H,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.91 ( ( ord_less_nat @ A @ B )
% 5.49/5.91 => ( ( ord_less_nat @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono'
% 5.49/5.91 thf(fact_2515_mult__strict__mono_H,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.91 ( ( ord_less_int @ A @ B )
% 5.49/5.91 => ( ( ord_less_int @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_strict_mono'
% 5.49/5.91 thf(fact_2516_mult__less__cancel__right,axiom,
% 5.49/5.91 ! [A: real,C: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right
% 5.49/5.91 thf(fact_2517_mult__less__cancel__right,axiom,
% 5.49/5.91 ! [A: rat,C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right
% 5.49/5.91 thf(fact_2518_mult__less__cancel__right,axiom,
% 5.49/5.91 ! [A: int,C: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right
% 5.49/5.91 thf(fact_2519_mult__le__cancel__left__neg,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_neg
% 5.49/5.91 thf(fact_2520_mult__le__cancel__left__neg,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_neg
% 5.49/5.91 thf(fact_2521_mult__le__cancel__left__neg,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_neg
% 5.49/5.91 thf(fact_2522_mult__le__cancel__left__pos,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_pos
% 5.49/5.91 thf(fact_2523_mult__le__cancel__left__pos,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_pos
% 5.49/5.91 thf(fact_2524_mult__le__cancel__left__pos,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left_pos
% 5.49/5.91 thf(fact_2525_mult__left__le__imp__le,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_imp_le
% 5.49/5.91 thf(fact_2526_mult__left__le__imp__le,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_imp_le
% 5.49/5.91 thf(fact_2527_mult__left__le__imp__le,axiom,
% 5.49/5.91 ! [C: nat,A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_imp_le
% 5.49/5.91 thf(fact_2528_mult__left__le__imp__le,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_imp_le
% 5.49/5.91 thf(fact_2529_mult__right__le__imp__le,axiom,
% 5.49/5.91 ! [A: real,C: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_imp_le
% 5.49/5.91 thf(fact_2530_mult__right__le__imp__le,axiom,
% 5.49/5.91 ! [A: rat,C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_imp_le
% 5.49/5.91 thf(fact_2531_mult__right__le__imp__le,axiom,
% 5.49/5.91 ! [A: nat,C: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_imp_le
% 5.49/5.91 thf(fact_2532_mult__right__le__imp__le,axiom,
% 5.49/5.91 ! [A: int,C: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_imp_le
% 5.49/5.91 thf(fact_2533_mult__le__less__imp__less,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_real @ C @ D )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_less_imp_less
% 5.49/5.91 thf(fact_2534_mult__le__less__imp__less,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_rat @ C @ D )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_less_imp_less
% 5.49/5.91 thf(fact_2535_mult__le__less__imp__less,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.91 => ( ( ord_less_nat @ C @ D )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_less_imp_less
% 5.49/5.91 thf(fact_2536_mult__le__less__imp__less,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.91 => ( ( ord_less_int @ C @ D )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_less_imp_less
% 5.49/5.91 thf(fact_2537_mult__less__le__imp__less,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_real @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_le_imp_less
% 5.49/5.91 thf(fact_2538_mult__less__le__imp__less,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_rat @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_le_imp_less
% 5.49/5.91 thf(fact_2539_mult__less__le__imp__less,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.91 ( ( ord_less_nat @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_le_imp_less
% 5.49/5.91 thf(fact_2540_mult__less__le__imp__less,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.91 ( ( ord_less_int @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ C @ D )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_le_imp_less
% 5.49/5.91 thf(fact_2541_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT] :
% 5.49/5.91 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.49/5.91 => ( ! [Uv2: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.49/5.91 => ( ! [Uu3: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.49/5.91 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % VEBT_internal.minNull.elims(3)
% 5.49/5.91 thf(fact_2542_field__le__epsilon,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ! [E2: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.49/5.91 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y2 @ E2 ) ) )
% 5.49/5.91 => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.49/5.91
% 5.49/5.91 % field_le_epsilon
% 5.49/5.91 thf(fact_2543_field__le__epsilon,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ! [E2: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.49/5.91 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y2 @ E2 ) ) )
% 5.49/5.91 => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.49/5.91
% 5.49/5.91 % field_le_epsilon
% 5.49/5.91 thf(fact_2544_add__neg__nonpos,axiom,
% 5.49/5.91 ! [A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_neg_nonpos
% 5.49/5.91 thf(fact_2545_add__neg__nonpos,axiom,
% 5.49/5.91 ! [A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_neg_nonpos
% 5.49/5.91 thf(fact_2546_add__neg__nonpos,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.49/5.91 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_neg_nonpos
% 5.49/5.91 thf(fact_2547_add__neg__nonpos,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_neg_nonpos
% 5.49/5.91 thf(fact_2548_add__nonneg__pos,axiom,
% 5.49/5.91 ! [A: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonneg_pos
% 5.49/5.91 thf(fact_2549_add__nonneg__pos,axiom,
% 5.49/5.91 ! [A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonneg_pos
% 5.49/5.91 thf(fact_2550_add__nonneg__pos,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonneg_pos
% 5.49/5.91 thf(fact_2551_add__nonneg__pos,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonneg_pos
% 5.49/5.91 thf(fact_2552_add__nonpos__neg,axiom,
% 5.49/5.91 ! [A: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonpos_neg
% 5.49/5.91 thf(fact_2553_add__nonpos__neg,axiom,
% 5.49/5.91 ! [A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonpos_neg
% 5.49/5.91 thf(fact_2554_add__nonpos__neg,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.49/5.91 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.49/5.91 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonpos_neg
% 5.49/5.91 thf(fact_2555_add__nonpos__neg,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.91 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_nonpos_neg
% 5.49/5.91 thf(fact_2556_add__pos__nonneg,axiom,
% 5.49/5.91 ! [A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_pos_nonneg
% 5.49/5.91 thf(fact_2557_add__pos__nonneg,axiom,
% 5.49/5.91 ! [A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_pos_nonneg
% 5.49/5.91 thf(fact_2558_add__pos__nonneg,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_pos_nonneg
% 5.49/5.91 thf(fact_2559_add__pos__nonneg,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_pos_nonneg
% 5.49/5.91 thf(fact_2560_add__strict__increasing,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ B @ C )
% 5.49/5.91 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing
% 5.49/5.91 thf(fact_2561_add__strict__increasing,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ B @ C )
% 5.49/5.91 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing
% 5.49/5.91 thf(fact_2562_add__strict__increasing,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ C )
% 5.49/5.91 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing
% 5.49/5.91 thf(fact_2563_add__strict__increasing,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ C )
% 5.49/5.91 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing
% 5.49/5.91 thf(fact_2564_add__strict__increasing2,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ B @ C )
% 5.49/5.91 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing2
% 5.49/5.91 thf(fact_2565_add__strict__increasing2,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ B @ C )
% 5.49/5.91 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing2
% 5.49/5.91 thf(fact_2566_add__strict__increasing2,axiom,
% 5.49/5.91 ! [A: nat,B: nat,C: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ B @ C )
% 5.49/5.91 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing2
% 5.49/5.91 thf(fact_2567_add__strict__increasing2,axiom,
% 5.49/5.91 ! [A: int,B: int,C: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ B @ C )
% 5.49/5.91 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_strict_increasing2
% 5.49/5.91 thf(fact_2568_divide__nonpos__pos,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonpos_pos
% 5.49/5.91 thf(fact_2569_divide__nonpos__pos,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonpos_pos
% 5.49/5.91 thf(fact_2570_divide__nonpos__neg,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonpos_neg
% 5.49/5.91 thf(fact_2571_divide__nonpos__neg,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonpos_neg
% 5.49/5.91 thf(fact_2572_divide__nonneg__pos,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonneg_pos
% 5.49/5.91 thf(fact_2573_divide__nonneg__pos,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonneg_pos
% 5.49/5.91 thf(fact_2574_divide__nonneg__neg,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_real @ Y2 @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonneg_neg
% 5.49/5.91 thf(fact_2575_divide__nonneg__neg,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_rat @ Y2 @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_nonneg_neg
% 5.49/5.91 thf(fact_2576_divide__le__cancel,axiom,
% 5.49/5.91 ! [A: real,C: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_cancel
% 5.49/5.91 thf(fact_2577_divide__le__cancel,axiom,
% 5.49/5.91 ! [A: rat,C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_cancel
% 5.49/5.91 thf(fact_2578_frac__less2,axiom,
% 5.49/5.91 ! [X: real,Y2: real,W: real,Z: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.49/5.91 => ( ( ord_less_real @ W @ Z )
% 5.49/5.91 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less2
% 5.49/5.91 thf(fact_2579_frac__less2,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_eq_rat @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.49/5.91 => ( ( ord_less_rat @ W @ Z )
% 5.49/5.91 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less2
% 5.49/5.91 thf(fact_2580_frac__less,axiom,
% 5.49/5.91 ! [X: real,Y2: real,W: real,Z: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_real @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.49/5.91 => ( ( ord_less_eq_real @ W @ Z )
% 5.49/5.91 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less
% 5.49/5.91 thf(fact_2581_frac__less,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat,W: rat,Z: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_rat @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.49/5.91 => ( ( ord_less_eq_rat @ W @ Z )
% 5.49/5.91 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less
% 5.49/5.91 thf(fact_2582_frac__le,axiom,
% 5.49/5.91 ! [Y2: real,X: real,W: real,Z: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.49/5.91 => ( ( ord_less_eq_real @ W @ Z )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_le
% 5.49/5.91 thf(fact_2583_frac__le,axiom,
% 5.49/5.91 ! [Y2: rat,X: rat,W: rat,Z: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_rat @ X @ Y2 )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.49/5.91 => ( ( ord_less_eq_rat @ W @ Z )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y2 @ W ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_le
% 5.49/5.91 thf(fact_2584_div__positive,axiom,
% 5.49/5.91 ! [B: nat,A: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_positive
% 5.49/5.91 thf(fact_2585_div__positive,axiom,
% 5.49/5.91 ! [B: int,A: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ A )
% 5.49/5.91 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_positive
% 5.49/5.91 thf(fact_2586_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ A @ B )
% 5.49/5.91 => ( ( divide_divide_nat @ A @ B )
% 5.49/5.91 = zero_zero_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % unique_euclidean_semiring_numeral_class.div_less
% 5.49/5.91 thf(fact_2587_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ A @ B )
% 5.49/5.91 => ( ( divide_divide_int @ A @ B )
% 5.49/5.91 = zero_zero_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % unique_euclidean_semiring_numeral_class.div_less
% 5.49/5.91 thf(fact_2588_mult__left__le__one__le,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ Y2 @ X ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_one_le
% 5.49/5.91 thf(fact_2589_mult__left__le__one__le,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ Y2 @ X ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_one_le
% 5.49/5.91 thf(fact_2590_mult__left__le__one__le,axiom,
% 5.49/5.91 ! [X: int,Y2: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( times_times_int @ Y2 @ X ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le_one_le
% 5.49/5.91 thf(fact_2591_mult__right__le__one__le,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ X @ Y2 ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_one_le
% 5.49/5.91 thf(fact_2592_mult__right__le__one__le,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_rat @ Y2 @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y2 ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_one_le
% 5.49/5.91 thf(fact_2593_mult__right__le__one__le,axiom,
% 5.49/5.91 ! [X: int,Y2: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_int @ Y2 @ one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( times_times_int @ X @ Y2 ) @ X ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_right_le_one_le
% 5.49/5.91 thf(fact_2594_mult__le__one,axiom,
% 5.49/5.91 ! [A: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_one
% 5.49/5.91 thf(fact_2595_mult__le__one,axiom,
% 5.49/5.91 ! [A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_one
% 5.49/5.91 thf(fact_2596_mult__le__one,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.49/5.91 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_one
% 5.49/5.91 thf(fact_2597_mult__le__one,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_one
% 5.49/5.91 thf(fact_2598_mult__left__le,axiom,
% 5.49/5.91 ! [C: real,A: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le
% 5.49/5.91 thf(fact_2599_mult__left__le,axiom,
% 5.49/5.91 ! [C: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le
% 5.49/5.91 thf(fact_2600_mult__left__le,axiom,
% 5.49/5.91 ! [C: nat,A: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le
% 5.49/5.91 thf(fact_2601_mult__left__le,axiom,
% 5.49/5.91 ! [C: int,A: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_left_le
% 5.49/5.91 thf(fact_2602_sum__squares__ge__zero,axiom,
% 5.49/5.91 ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_ge_zero
% 5.49/5.91 thf(fact_2603_sum__squares__ge__zero,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_ge_zero
% 5.49/5.91 thf(fact_2604_sum__squares__ge__zero,axiom,
% 5.49/5.91 ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_ge_zero
% 5.49/5.91 thf(fact_2605_sum__squares__le__zero__iff,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real )
% 5.49/5.91 = ( ( X = zero_zero_real )
% 5.49/5.91 & ( Y2 = zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_le_zero_iff
% 5.49/5.91 thf(fact_2606_sum__squares__le__zero__iff,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat )
% 5.49/5.91 = ( ( X = zero_zero_rat )
% 5.49/5.91 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_le_zero_iff
% 5.49/5.91 thf(fact_2607_sum__squares__le__zero__iff,axiom,
% 5.49/5.91 ! [X: int,Y2: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int )
% 5.49/5.91 = ( ( X = zero_zero_int )
% 5.49/5.91 & ( Y2 = zero_zero_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_le_zero_iff
% 5.49/5.91 thf(fact_2608_power__less__imp__less__base,axiom,
% 5.49/5.91 ! [A: real,N: nat,B: real] :
% 5.49/5.91 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ord_less_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_less_imp_less_base
% 5.49/5.91 thf(fact_2609_power__less__imp__less__base,axiom,
% 5.49/5.91 ! [A: rat,N: nat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_less_imp_less_base
% 5.49/5.91 thf(fact_2610_power__less__imp__less__base,axiom,
% 5.49/5.91 ! [A: nat,N: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_less_imp_less_base
% 5.49/5.91 thf(fact_2611_power__less__imp__less__base,axiom,
% 5.49/5.91 ! [A: int,N: nat,B: int] :
% 5.49/5.91 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ord_less_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_less_imp_less_base
% 5.49/5.91 thf(fact_2612_not__sum__squares__lt__zero,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) @ zero_zero_real ) ).
% 5.49/5.91
% 5.49/5.91 % not_sum_squares_lt_zero
% 5.49/5.91 thf(fact_2613_not__sum__squares__lt__zero,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) @ zero_zero_rat ) ).
% 5.49/5.91
% 5.49/5.91 % not_sum_squares_lt_zero
% 5.49/5.91 thf(fact_2614_not__sum__squares__lt__zero,axiom,
% 5.49/5.91 ! [X: int,Y2: int] :
% 5.49/5.91 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) @ zero_zero_int ) ).
% 5.49/5.91
% 5.49/5.91 % not_sum_squares_lt_zero
% 5.49/5.91 thf(fact_2615_sum__squares__gt__zero__iff,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) )
% 5.49/5.91 = ( ( X != zero_zero_real )
% 5.49/5.91 | ( Y2 != zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_gt_zero_iff
% 5.49/5.91 thf(fact_2616_sum__squares__gt__zero__iff,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y2 @ Y2 ) ) )
% 5.49/5.91 = ( ( X != zero_zero_rat )
% 5.49/5.91 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_gt_zero_iff
% 5.49/5.91 thf(fact_2617_sum__squares__gt__zero__iff,axiom,
% 5.49/5.91 ! [X: int,Y2: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y2 @ Y2 ) ) )
% 5.49/5.91 = ( ( X != zero_zero_int )
% 5.49/5.91 | ( Y2 != zero_zero_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % sum_squares_gt_zero_iff
% 5.49/5.91 thf(fact_2618_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.49/5.91 ! [C: nat,A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.49/5.91 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.49/5.91 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.49/5.91 thf(fact_2619_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.49/5.91 ! [C: int,A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.49/5.91 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.49/5.91 thf(fact_2620_zero__less__two,axiom,
% 5.49/5.91 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.49/5.91
% 5.49/5.91 % zero_less_two
% 5.49/5.91 thf(fact_2621_zero__less__two,axiom,
% 5.49/5.91 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.49/5.91
% 5.49/5.91 % zero_less_two
% 5.49/5.91 thf(fact_2622_zero__less__two,axiom,
% 5.49/5.91 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.49/5.91
% 5.49/5.91 % zero_less_two
% 5.49/5.91 thf(fact_2623_zero__less__two,axiom,
% 5.49/5.91 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.49/5.91
% 5.49/5.91 % zero_less_two
% 5.49/5.91 thf(fact_2624_divide__strict__left__mono__neg,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.91 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_strict_left_mono_neg
% 5.49/5.91 thf(fact_2625_divide__strict__left__mono__neg,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.91 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_strict_left_mono_neg
% 5.49/5.91 thf(fact_2626_divide__strict__left__mono,axiom,
% 5.49/5.91 ! [B: real,A: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ B @ A )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.91 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_strict_left_mono
% 5.49/5.91 thf(fact_2627_divide__strict__left__mono,axiom,
% 5.49/5.91 ! [B: rat,A: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ B @ A )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.91 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_strict_left_mono
% 5.49/5.91 thf(fact_2628_mult__imp__less__div__pos,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 5.49/5.91 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_less_div_pos
% 5.49/5.91 thf(fact_2629_mult__imp__less__div__pos,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 5.49/5.91 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_less_div_pos
% 5.49/5.91 thf(fact_2630_mult__imp__div__pos__less,axiom,
% 5.49/5.91 ! [Y2: real,X: real,Z: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 5.49/5.91 => ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_div_pos_less
% 5.49/5.91 thf(fact_2631_mult__imp__div__pos__less,axiom,
% 5.49/5.91 ! [Y2: rat,X: rat,Z: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 5.49/5.91 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_div_pos_less
% 5.49/5.91 thf(fact_2632_pos__less__divide__eq,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_less_divide_eq
% 5.49/5.91 thf(fact_2633_pos__less__divide__eq,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_less_divide_eq
% 5.49/5.91 thf(fact_2634_pos__divide__less__eq,axiom,
% 5.49/5.91 ! [C: real,B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_divide_less_eq
% 5.49/5.91 thf(fact_2635_pos__divide__less__eq,axiom,
% 5.49/5.91 ! [C: rat,B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_divide_less_eq
% 5.49/5.91 thf(fact_2636_neg__less__divide__eq,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_less_divide_eq
% 5.49/5.91 thf(fact_2637_neg__less__divide__eq,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_less_divide_eq
% 5.49/5.91 thf(fact_2638_neg__divide__less__eq,axiom,
% 5.49/5.91 ! [C: real,B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_divide_less_eq
% 5.49/5.91 thf(fact_2639_neg__divide__less__eq,axiom,
% 5.49/5.91 ! [C: rat,B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_divide_less_eq
% 5.49/5.91 thf(fact_2640_less__divide__eq,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq
% 5.49/5.91 thf(fact_2641_less__divide__eq,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq
% 5.49/5.91 thf(fact_2642_divide__less__eq,axiom,
% 5.49/5.91 ! [B: real,C: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq
% 5.49/5.91 thf(fact_2643_divide__less__eq,axiom,
% 5.49/5.91 ! [B: rat,C: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq
% 5.49/5.91 thf(fact_2644_less__divide__eq__1,axiom,
% 5.49/5.91 ! [B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 & ( ord_less_real @ A @ B ) )
% 5.49/5.91 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.91 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq_1
% 5.49/5.91 thf(fact_2645_less__divide__eq__1,axiom,
% 5.49/5.91 ! [B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 & ( ord_less_rat @ A @ B ) )
% 5.49/5.91 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.91 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq_1
% 5.49/5.91 thf(fact_2646_divide__less__eq__1,axiom,
% 5.49/5.91 ! [B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 & ( ord_less_real @ B @ A ) )
% 5.49/5.91 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.91 & ( ord_less_real @ A @ B ) )
% 5.49/5.91 | ( A = zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq_1
% 5.49/5.91 thf(fact_2647_divide__less__eq__1,axiom,
% 5.49/5.91 ! [B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 & ( ord_less_rat @ B @ A ) )
% 5.49/5.91 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.91 & ( ord_less_rat @ A @ B ) )
% 5.49/5.91 | ( A = zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq_1
% 5.49/5.91 thf(fact_2648_power__le__one,axiom,
% 5.49/5.91 ! [A: real,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_one
% 5.49/5.91 thf(fact_2649_power__le__one,axiom,
% 5.49/5.91 ! [A: rat,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_one
% 5.49/5.91 thf(fact_2650_power__le__one,axiom,
% 5.49/5.91 ! [A: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_one
% 5.49/5.91 thf(fact_2651_power__le__one,axiom,
% 5.49/5.91 ! [A: int,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_one
% 5.49/5.91 thf(fact_2652_eq__divide__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [W: num,B: complex,C: complex] :
% 5.49/5.91 ( ( ( numera6690914467698888265omplex @ W )
% 5.49/5.91 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.49/5.91 = ( ( ( C != zero_zero_complex )
% 5.49/5.91 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( C = zero_zero_complex )
% 5.49/5.91 => ( ( numera6690914467698888265omplex @ W )
% 5.49/5.91 = zero_zero_complex ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % eq_divide_eq_numeral(1)
% 5.49/5.91 thf(fact_2653_eq__divide__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [W: num,B: real,C: real] :
% 5.49/5.91 ( ( ( numeral_numeral_real @ W )
% 5.49/5.91 = ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ( ( C != zero_zero_real )
% 5.49/5.91 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( C = zero_zero_real )
% 5.49/5.91 => ( ( numeral_numeral_real @ W )
% 5.49/5.91 = zero_zero_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % eq_divide_eq_numeral(1)
% 5.49/5.91 thf(fact_2654_eq__divide__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [W: num,B: rat,C: rat] :
% 5.49/5.91 ( ( ( numeral_numeral_rat @ W )
% 5.49/5.91 = ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( C != zero_zero_rat )
% 5.49/5.91 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( C = zero_zero_rat )
% 5.49/5.91 => ( ( numeral_numeral_rat @ W )
% 5.49/5.91 = zero_zero_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % eq_divide_eq_numeral(1)
% 5.49/5.91 thf(fact_2655_divide__eq__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [B: complex,C: complex,W: num] :
% 5.49/5.91 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.49/5.91 = ( numera6690914467698888265omplex @ W ) )
% 5.49/5.91 = ( ( ( C != zero_zero_complex )
% 5.49/5.91 => ( B
% 5.49/5.91 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.49/5.91 & ( ( C = zero_zero_complex )
% 5.49/5.91 => ( ( numera6690914467698888265omplex @ W )
% 5.49/5.91 = zero_zero_complex ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_eq_eq_numeral(1)
% 5.49/5.91 thf(fact_2656_divide__eq__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [B: real,C: real,W: num] :
% 5.49/5.91 ( ( ( divide_divide_real @ B @ C )
% 5.49/5.91 = ( numeral_numeral_real @ W ) )
% 5.49/5.91 = ( ( ( C != zero_zero_real )
% 5.49/5.91 => ( B
% 5.49/5.91 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.49/5.91 & ( ( C = zero_zero_real )
% 5.49/5.91 => ( ( numeral_numeral_real @ W )
% 5.49/5.91 = zero_zero_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_eq_eq_numeral(1)
% 5.49/5.91 thf(fact_2657_divide__eq__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [B: rat,C: rat,W: num] :
% 5.49/5.91 ( ( ( divide_divide_rat @ B @ C )
% 5.49/5.91 = ( numeral_numeral_rat @ W ) )
% 5.49/5.91 = ( ( ( C != zero_zero_rat )
% 5.49/5.91 => ( B
% 5.49/5.91 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.49/5.91 & ( ( C = zero_zero_rat )
% 5.49/5.91 => ( ( numeral_numeral_rat @ W )
% 5.49/5.91 = zero_zero_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_eq_eq_numeral(1)
% 5.49/5.91 thf(fact_2658_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT] :
% 5.49/5.91 ( ( vEBT_VEBT_minNull @ X )
% 5.49/5.91 => ( ( X
% 5.49/5.91 != ( vEBT_Leaf @ $false @ $false ) )
% 5.49/5.91 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % VEBT_internal.minNull.elims(2)
% 5.49/5.91 thf(fact_2659_divide__add__eq__iff,axiom,
% 5.49/5.91 ! [Z: complex,X: complex,Y2: complex] :
% 5.49/5.91 ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_add_eq_iff
% 5.49/5.91 thf(fact_2660_divide__add__eq__iff,axiom,
% 5.49/5.91 ! [Z: real,X: real,Y2: real] :
% 5.49/5.91 ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_add_eq_iff
% 5.49/5.91 thf(fact_2661_divide__add__eq__iff,axiom,
% 5.49/5.91 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.91 ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_add_eq_iff
% 5.49/5.91 thf(fact_2662_add__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: complex,X: complex,Y2: complex] :
% 5.49/5.91 ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_iff
% 5.49/5.91 thf(fact_2663_add__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: real,X: real,Y2: real] :
% 5.49/5.91 ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_iff
% 5.49/5.91 thf(fact_2664_add__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.91 ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_iff
% 5.49/5.91 thf(fact_2665_add__num__frac,axiom,
% 5.49/5.91 ! [Y2: complex,Z: complex,X: complex] :
% 5.49/5.91 ( ( Y2 != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_num_frac
% 5.49/5.91 thf(fact_2666_add__num__frac,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y2 ) )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_num_frac
% 5.49/5.91 thf(fact_2667_add__num__frac,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_num_frac
% 5.49/5.91 thf(fact_2668_add__frac__num,axiom,
% 5.49/5.91 ! [Y2: complex,X: complex,Z: complex] :
% 5.49/5.91 ( ( Y2 != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ Z )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_num
% 5.49/5.91 thf(fact_2669_add__frac__num,axiom,
% 5.49/5.91 ! [Y2: real,X: real,Z: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ Z )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_num
% 5.49/5.91 thf(fact_2670_add__frac__num,axiom,
% 5.49/5.91 ! [Y2: rat,X: rat,Z: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y2 ) ) @ Y2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_num
% 5.49/5.91 thf(fact_2671_add__frac__eq,axiom,
% 5.49/5.91 ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 5.49/5.91 ( ( Y2 != zero_zero_complex )
% 5.49/5.91 => ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_eq
% 5.49/5.91 thf(fact_2672_add__frac__eq,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real,W: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_eq
% 5.49/5.91 thf(fact_2673_add__frac__eq,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_frac_eq
% 5.49/5.91 thf(fact_2674_add__divide__eq__if__simps_I1_J,axiom,
% 5.49/5.91 ! [Z: complex,A: complex,B: complex] :
% 5.49/5.91 ( ( ( Z = zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(1)
% 5.49/5.91 thf(fact_2675_add__divide__eq__if__simps_I1_J,axiom,
% 5.49/5.91 ! [Z: real,A: real,B: real] :
% 5.49/5.91 ( ( ( Z = zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(1)
% 5.49/5.91 thf(fact_2676_add__divide__eq__if__simps_I1_J,axiom,
% 5.49/5.91 ! [Z: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ( Z = zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(1)
% 5.49/5.91 thf(fact_2677_add__divide__eq__if__simps_I2_J,axiom,
% 5.49/5.91 ! [Z: complex,A: complex,B: complex] :
% 5.49/5.91 ( ( ( Z = zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(2)
% 5.49/5.91 thf(fact_2678_add__divide__eq__if__simps_I2_J,axiom,
% 5.49/5.91 ! [Z: real,A: real,B: real] :
% 5.49/5.91 ( ( ( Z = zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.49/5.91 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(2)
% 5.49/5.91 thf(fact_2679_add__divide__eq__if__simps_I2_J,axiom,
% 5.49/5.91 ! [Z: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ( Z = zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.49/5.91 = B ) )
% 5.49/5.91 & ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.49/5.91 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(2)
% 5.49/5.91 thf(fact_2680_power__inject__base,axiom,
% 5.49/5.91 ! [A: real,N: nat,B: real] :
% 5.49/5.91 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.49/5.91 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.91 => ( A = B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_inject_base
% 5.49/5.91 thf(fact_2681_power__inject__base,axiom,
% 5.49/5.91 ! [A: rat,N: nat,B: rat] :
% 5.49/5.91 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.49/5.91 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( A = B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_inject_base
% 5.49/5.91 thf(fact_2682_power__inject__base,axiom,
% 5.49/5.91 ! [A: nat,N: nat,B: nat] :
% 5.49/5.91 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.49/5.91 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( A = B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_inject_base
% 5.49/5.91 thf(fact_2683_power__inject__base,axiom,
% 5.49/5.91 ! [A: int,N: nat,B: int] :
% 5.49/5.91 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.49/5.91 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.91 => ( A = B ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_inject_base
% 5.49/5.91 thf(fact_2684_power__le__imp__le__base,axiom,
% 5.49/5.91 ! [A: real,N: nat,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.49/5.91 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_imp_le_base
% 5.49/5.91 thf(fact_2685_power__le__imp__le__base,axiom,
% 5.49/5.91 ! [A: rat,N: nat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_imp_le_base
% 5.49/5.91 thf(fact_2686_power__le__imp__le__base,axiom,
% 5.49/5.91 ! [A: nat,N: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_imp_le_base
% 5.49/5.91 thf(fact_2687_power__le__imp__le__base,axiom,
% 5.49/5.91 ! [A: int,N: nat,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_le_imp_le_base
% 5.49/5.91 thf(fact_2688_div__add__self2,axiom,
% 5.49/5.91 ! [B: nat,A: nat] :
% 5.49/5.91 ( ( B != zero_zero_nat )
% 5.49/5.91 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.49/5.91 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_add_self2
% 5.49/5.91 thf(fact_2689_div__add__self2,axiom,
% 5.49/5.91 ! [B: int,A: int] :
% 5.49/5.91 ( ( B != zero_zero_int )
% 5.49/5.91 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.49/5.91 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_add_self2
% 5.49/5.91 thf(fact_2690_div__add__self1,axiom,
% 5.49/5.91 ! [B: nat,A: nat] :
% 5.49/5.91 ( ( B != zero_zero_nat )
% 5.49/5.91 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.49/5.91 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_add_self1
% 5.49/5.91 thf(fact_2691_div__add__self1,axiom,
% 5.49/5.91 ! [B: int,A: int] :
% 5.49/5.91 ( ( B != zero_zero_int )
% 5.49/5.91 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.49/5.91 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_add_self1
% 5.49/5.91 thf(fact_2692_divide__diff__eq__iff,axiom,
% 5.49/5.91 ! [Z: complex,X: complex,Y2: complex] :
% 5.49/5.91 ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_diff_eq_iff
% 5.49/5.91 thf(fact_2693_divide__diff__eq__iff,axiom,
% 5.49/5.91 ! [Z: real,X: real,Y2: real] :
% 5.49/5.91 ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_diff_eq_iff
% 5.49/5.91 thf(fact_2694_divide__diff__eq__iff,axiom,
% 5.49/5.91 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.91 ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y2 )
% 5.49/5.91 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_diff_eq_iff
% 5.49/5.91 thf(fact_2695_diff__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: complex,X: complex,Y2: complex] :
% 5.49/5.91 ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y2 @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_divide_eq_iff
% 5.49/5.91 thf(fact_2696_diff__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: real,X: real,Y2: real] :
% 5.49/5.91 ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y2 @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_divide_eq_iff
% 5.49/5.91 thf(fact_2697_diff__divide__eq__iff,axiom,
% 5.49/5.91 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.91 ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y2 @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_divide_eq_iff
% 5.49/5.91 thf(fact_2698_diff__frac__eq,axiom,
% 5.49/5.91 ! [Y2: complex,Z: complex,X: complex,W: complex] :
% 5.49/5.91 ( ( Y2 != zero_zero_complex )
% 5.49/5.91 => ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y2 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y2 ) ) @ ( times_times_complex @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_frac_eq
% 5.49/5.91 thf(fact_2699_diff__frac__eq,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real,W: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_frac_eq
% 5.49/5.91 thf(fact_2700_diff__frac__eq,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_frac_eq
% 5.49/5.91 thf(fact_2701_add__divide__eq__if__simps_I4_J,axiom,
% 5.49/5.91 ! [Z: complex,A: complex,B: complex] :
% 5.49/5.91 ( ( ( Z = zero_zero_complex )
% 5.49/5.91 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_complex )
% 5.49/5.91 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.49/5.91 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(4)
% 5.49/5.91 thf(fact_2702_add__divide__eq__if__simps_I4_J,axiom,
% 5.49/5.91 ! [Z: real,A: real,B: real] :
% 5.49/5.91 ( ( ( Z = zero_zero_real )
% 5.49/5.91 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.49/5.91 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(4)
% 5.49/5.91 thf(fact_2703_add__divide__eq__if__simps_I4_J,axiom,
% 5.49/5.91 ! [Z: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ( Z = zero_zero_rat )
% 5.49/5.91 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.49/5.91 = A ) )
% 5.49/5.91 & ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.49/5.91 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % add_divide_eq_if_simps(4)
% 5.49/5.91 thf(fact_2704_mod__double__modulus,axiom,
% 5.49/5.91 ! [M: code_integer,X: code_integer] :
% 5.49/5.91 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.49/5.91 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.49/5.91 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.49/5.91 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mod_double_modulus
% 5.49/5.91 thf(fact_2705_mod__double__modulus,axiom,
% 5.49/5.91 ! [M: nat,X: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.91 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.49/5.91 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( modulo_modulo_nat @ X @ M ) )
% 5.49/5.91 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mod_double_modulus
% 5.49/5.91 thf(fact_2706_mod__double__modulus,axiom,
% 5.49/5.91 ! [M: int,X: int] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ M )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.91 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( modulo_modulo_int @ X @ M ) )
% 5.49/5.91 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.91 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mod_double_modulus
% 5.49/5.91 thf(fact_2707_divmod__digit__1_I2_J,axiom,
% 5.49/5.91 ! [A: code_integer,B: code_integer] :
% 5.49/5.91 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.49/5.91 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.91 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.91 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(2)
% 5.49/5.91 thf(fact_2708_divmod__digit__1_I2_J,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.91 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(2)
% 5.49/5.91 thf(fact_2709_divmod__digit__1_I2_J,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.49/5.91 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(2)
% 5.49/5.91 thf(fact_2710_bounded__Max__nat,axiom,
% 5.49/5.91 ! [P: nat > $o,X: nat,M7: nat] :
% 5.49/5.91 ( ( P @ X )
% 5.49/5.91 => ( ! [X3: nat] :
% 5.49/5.91 ( ( P @ X3 )
% 5.49/5.91 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.49/5.91 => ~ ! [M5: nat] :
% 5.49/5.91 ( ( P @ M5 )
% 5.49/5.91 => ~ ! [X5: nat] :
% 5.49/5.91 ( ( P @ X5 )
% 5.49/5.91 => ( ord_less_eq_nat @ X5 @ M5 ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % bounded_Max_nat
% 5.49/5.91 thf(fact_2711_numeral__1__eq__Suc__0,axiom,
% 5.49/5.91 ( ( numeral_numeral_nat @ one )
% 5.49/5.91 = ( suc @ zero_zero_nat ) ) ).
% 5.49/5.91
% 5.49/5.91 % numeral_1_eq_Suc_0
% 5.49/5.91 thf(fact_2712_num_Osize_I5_J,axiom,
% 5.49/5.91 ! [X22: num] :
% 5.49/5.91 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.49/5.91 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % num.size(5)
% 5.49/5.91 thf(fact_2713_ex__least__nat__less,axiom,
% 5.49/5.91 ! [P: nat > $o,N: nat] :
% 5.49/5.91 ( ( P @ N )
% 5.49/5.91 => ( ~ ( P @ zero_zero_nat )
% 5.49/5.91 => ? [K2: nat] :
% 5.49/5.91 ( ( ord_less_nat @ K2 @ N )
% 5.49/5.91 & ! [I: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ I @ K2 )
% 5.49/5.91 => ~ ( P @ I ) )
% 5.49/5.91 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % ex_least_nat_less
% 5.49/5.91 thf(fact_2714_diff__Suc__less,axiom,
% 5.49/5.91 ! [N: nat,I2: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.91 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 5.49/5.91
% 5.49/5.91 % diff_Suc_less
% 5.49/5.91 thf(fact_2715_one__less__mult,axiom,
% 5.49/5.91 ! [N: nat,M: nat] :
% 5.49/5.91 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.49/5.91 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.49/5.91 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % one_less_mult
% 5.49/5.91 thf(fact_2716_n__less__m__mult__n,axiom,
% 5.49/5.91 ! [N: nat,M: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.91 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.49/5.91 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % n_less_m_mult_n
% 5.49/5.91 thf(fact_2717_n__less__n__mult__m,axiom,
% 5.49/5.91 ! [N: nat,M: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.91 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.49/5.91 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % n_less_n_mult_m
% 5.49/5.91 thf(fact_2718_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: real,Xs2: list_real] :
% 5.49/5.91 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2719_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: complex,Xs2: list_complex] :
% 5.49/5.91 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2720_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.49/5.91 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2721_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.49/5.91 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2722_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: $o,Xs2: list_o] :
% 5.49/5.91 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2723_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: nat,Xs2: list_nat] :
% 5.49/5.91 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2724_length__pos__if__in__set,axiom,
% 5.49/5.91 ! [X: int,Xs2: list_int] :
% 5.49/5.91 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.49/5.91 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % length_pos_if_in_set
% 5.49/5.91 thf(fact_2725_nat__induct__non__zero,axiom,
% 5.49/5.91 ! [N: nat,P: nat > $o] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.91 => ( ( P @ one_one_nat )
% 5.49/5.91 => ( ! [N3: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.49/5.91 => ( ( P @ N3 )
% 5.49/5.91 => ( P @ ( suc @ N3 ) ) ) )
% 5.49/5.91 => ( P @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_induct_non_zero
% 5.49/5.91 thf(fact_2726_nat__mult__le__cancel1,axiom,
% 5.49/5.91 ! [K: nat,M: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.91 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.91 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_mult_le_cancel1
% 5.49/5.91 thf(fact_2727_nat__diff__split__asm,axiom,
% 5.49/5.91 ! [P: nat > $o,A: nat,B: nat] :
% 5.49/5.91 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.49/5.91 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.49/5.91 & ~ ( P @ zero_zero_nat ) )
% 5.49/5.91 | ? [D2: nat] :
% 5.49/5.91 ( ( A
% 5.49/5.91 = ( plus_plus_nat @ B @ D2 ) )
% 5.49/5.91 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_diff_split_asm
% 5.49/5.91 thf(fact_2728_nat__diff__split,axiom,
% 5.49/5.91 ! [P: nat > $o,A: nat,B: nat] :
% 5.49/5.91 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.49/5.91 = ( ( ( ord_less_nat @ A @ B )
% 5.49/5.91 => ( P @ zero_zero_nat ) )
% 5.49/5.91 & ! [D2: nat] :
% 5.49/5.91 ( ( A
% 5.49/5.91 = ( plus_plus_nat @ B @ D2 ) )
% 5.49/5.91 => ( P @ D2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_diff_split
% 5.49/5.91 thf(fact_2729_power__gt__expt,axiom,
% 5.49/5.91 ! [N: nat,K: nat] :
% 5.49/5.91 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.49/5.91 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_gt_expt
% 5.49/5.91 thf(fact_2730_div__greater__zero__iff,axiom,
% 5.49/5.91 ! [M: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.49/5.91 = ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.91 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_greater_zero_iff
% 5.49/5.91 thf(fact_2731_div__le__mono2,axiom,
% 5.49/5.91 ! [M: nat,N: nat,K: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.91 => ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.91 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_le_mono2
% 5.49/5.91 thf(fact_2732_nat__one__le__power,axiom,
% 5.49/5.91 ! [I2: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.49/5.91 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_one_le_power
% 5.49/5.91 thf(fact_2733_div__less__iff__less__mult,axiom,
% 5.49/5.91 ! [Q2: nat,M: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.49/5.91 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.49/5.91 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_less_iff_less_mult
% 5.49/5.91 thf(fact_2734_nat__mult__div__cancel1,axiom,
% 5.49/5.91 ! [K: nat,M: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.49/5.91 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.49/5.91 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % nat_mult_div_cancel1
% 5.49/5.91 thf(fact_2735_div__eq__dividend__iff,axiom,
% 5.49/5.91 ! [M: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.91 => ( ( ( divide_divide_nat @ M @ N )
% 5.49/5.91 = M )
% 5.49/5.91 = ( N = one_one_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_eq_dividend_iff
% 5.49/5.91 thf(fact_2736_div__less__dividend,axiom,
% 5.49/5.91 ! [N: nat,M: nat] :
% 5.49/5.91 ( ( ord_less_nat @ one_one_nat @ N )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.91 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % div_less_dividend
% 5.49/5.91 thf(fact_2737_vebt__insert_Osimps_I3_J,axiom,
% 5.49/5.91 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.49/5.91 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X )
% 5.49/5.91 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 5.49/5.91
% 5.49/5.91 % vebt_insert.simps(3)
% 5.49/5.91 thf(fact_2738_vebt__member_Osimps_I3_J,axiom,
% 5.49/5.91 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.49/5.91 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.49/5.91
% 5.49/5.91 % vebt_member.simps(3)
% 5.49/5.91 thf(fact_2739_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.49/5.91 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.49/5.91 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.49/5.91
% 5.49/5.91 % VEBT_internal.membermima.simps(2)
% 5.49/5.91 thf(fact_2740_vebt__mint_Ocases,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT] :
% 5.49/5.91 ( ! [A3: $o,B2: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.91 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.91 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % vebt_mint.cases
% 5.49/5.91 thf(fact_2741_mult__le__cancel__left1,axiom,
% 5.49/5.91 ! [C: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left1
% 5.49/5.91 thf(fact_2742_mult__le__cancel__left1,axiom,
% 5.49/5.91 ! [C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left1
% 5.49/5.91 thf(fact_2743_mult__le__cancel__left1,axiom,
% 5.49/5.91 ! [C: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left1
% 5.49/5.91 thf(fact_2744_mult__le__cancel__left2,axiom,
% 5.49/5.91 ! [C: real,A: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left2
% 5.49/5.91 thf(fact_2745_mult__le__cancel__left2,axiom,
% 5.49/5.91 ! [C: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left2
% 5.49/5.91 thf(fact_2746_mult__le__cancel__left2,axiom,
% 5.49/5.91 ! [C: int,A: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_left2
% 5.49/5.91 thf(fact_2747_mult__le__cancel__right1,axiom,
% 5.49/5.91 ! [C: real,B: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right1
% 5.49/5.91 thf(fact_2748_mult__le__cancel__right1,axiom,
% 5.49/5.91 ! [C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right1
% 5.49/5.91 thf(fact_2749_mult__le__cancel__right1,axiom,
% 5.49/5.91 ! [C: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right1
% 5.49/5.91 thf(fact_2750_mult__le__cancel__right2,axiom,
% 5.49/5.91 ! [A: real,C: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.49/5.91 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right2
% 5.49/5.91 thf(fact_2751_mult__le__cancel__right2,axiom,
% 5.49/5.91 ! [A: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.49/5.91 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right2
% 5.49/5.91 thf(fact_2752_mult__le__cancel__right2,axiom,
% 5.49/5.91 ! [A: int,C: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.49/5.91 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_le_cancel_right2
% 5.49/5.91 thf(fact_2753_mult__less__cancel__left1,axiom,
% 5.49/5.91 ! [C: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ one_one_real @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left1
% 5.49/5.91 thf(fact_2754_mult__less__cancel__left1,axiom,
% 5.49/5.91 ! [C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left1
% 5.49/5.91 thf(fact_2755_mult__less__cancel__left1,axiom,
% 5.49/5.91 ! [C: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ one_one_int @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left1
% 5.49/5.91 thf(fact_2756_mult__less__cancel__left2,axiom,
% 5.49/5.91 ! [C: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ one_one_real ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left2
% 5.49/5.91 thf(fact_2757_mult__less__cancel__left2,axiom,
% 5.49/5.91 ! [C: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left2
% 5.49/5.91 thf(fact_2758_mult__less__cancel__left2,axiom,
% 5.49/5.91 ! [C: int,A: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ one_one_int ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_left2
% 5.49/5.91 thf(fact_2759_mult__less__cancel__right1,axiom,
% 5.49/5.91 ! [C: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ one_one_real @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right1
% 5.49/5.91 thf(fact_2760_mult__less__cancel__right1,axiom,
% 5.49/5.91 ! [C: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right1
% 5.49/5.91 thf(fact_2761_mult__less__cancel__right1,axiom,
% 5.49/5.91 ! [C: int,B: int] :
% 5.49/5.91 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ one_one_int @ B ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right1
% 5.49/5.91 thf(fact_2762_mult__less__cancel__right2,axiom,
% 5.49/5.91 ! [A: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ A @ one_one_real ) )
% 5.49/5.91 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right2
% 5.49/5.91 thf(fact_2763_mult__less__cancel__right2,axiom,
% 5.49/5.91 ! [A: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.49/5.91 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right2
% 5.49/5.91 thf(fact_2764_mult__less__cancel__right2,axiom,
% 5.49/5.91 ! [A: int,C: int] :
% 5.49/5.91 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.49/5.91 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.91 => ( ord_less_int @ A @ one_one_int ) )
% 5.49/5.91 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.49/5.91 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_less_cancel_right2
% 5.49/5.91 thf(fact_2765_field__le__mult__one__interval,axiom,
% 5.49/5.91 ! [X: real,Y2: real] :
% 5.49/5.91 ( ! [Z3: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.49/5.91 => ( ( ord_less_real @ Z3 @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y2 ) ) )
% 5.49/5.91 => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.49/5.91
% 5.49/5.91 % field_le_mult_one_interval
% 5.49/5.91 thf(fact_2766_field__le__mult__one__interval,axiom,
% 5.49/5.91 ! [X: rat,Y2: rat] :
% 5.49/5.91 ( ! [Z3: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.49/5.91 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y2 ) ) )
% 5.49/5.91 => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.49/5.91
% 5.49/5.91 % field_le_mult_one_interval
% 5.49/5.91 thf(fact_2767_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT,Y2: $o] :
% 5.49/5.91 ( ( ( vEBT_VEBT_minNull @ X )
% 5.49/5.91 = Y2 )
% 5.49/5.91 => ( ( ( X
% 5.49/5.91 = ( vEBT_Leaf @ $false @ $false ) )
% 5.49/5.91 => ~ Y2 )
% 5.49/5.91 => ( ( ? [Uv2: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.49/5.91 => Y2 )
% 5.49/5.91 => ( ( ? [Uu3: $o] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.49/5.91 => Y2 )
% 5.49/5.91 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.49/5.91 => ~ Y2 )
% 5.49/5.91 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.49/5.91 => Y2 ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % VEBT_internal.minNull.elims(1)
% 5.49/5.91 thf(fact_2768_divide__left__mono__neg,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_left_mono_neg
% 5.49/5.91 thf(fact_2769_divide__left__mono__neg,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.91 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_left_mono_neg
% 5.49/5.91 thf(fact_2770_mult__imp__le__div__pos,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y2 ) @ X )
% 5.49/5.91 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_le_div_pos
% 5.49/5.91 thf(fact_2771_mult__imp__le__div__pos,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y2 ) @ X )
% 5.49/5.91 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_le_div_pos
% 5.49/5.91 thf(fact_2772_mult__imp__div__pos__le,axiom,
% 5.49/5.91 ! [Y2: real,X: real,Z: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y2 ) )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_div_pos_le
% 5.49/5.91 thf(fact_2773_mult__imp__div__pos__le,axiom,
% 5.49/5.91 ! [Y2: rat,X: rat,Z: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.49/5.91 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y2 ) )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ Z ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % mult_imp_div_pos_le
% 5.49/5.91 thf(fact_2774_pos__le__divide__eq,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_le_divide_eq
% 5.49/5.91 thf(fact_2775_pos__le__divide__eq,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_le_divide_eq
% 5.49/5.91 thf(fact_2776_pos__divide__le__eq,axiom,
% 5.49/5.91 ! [C: real,B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_divide_le_eq
% 5.49/5.91 thf(fact_2777_pos__divide__le__eq,axiom,
% 5.49/5.91 ! [C: rat,B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % pos_divide_le_eq
% 5.49/5.91 thf(fact_2778_neg__le__divide__eq,axiom,
% 5.49/5.91 ! [C: real,A: real,B: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_le_divide_eq
% 5.49/5.91 thf(fact_2779_neg__le__divide__eq,axiom,
% 5.49/5.91 ! [C: rat,A: rat,B: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_le_divide_eq
% 5.49/5.91 thf(fact_2780_neg__divide__le__eq,axiom,
% 5.49/5.91 ! [C: real,B: real,A: real] :
% 5.49/5.91 ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_divide_le_eq
% 5.49/5.91 thf(fact_2781_neg__divide__le__eq,axiom,
% 5.49/5.91 ! [C: rat,B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % neg_divide_le_eq
% 5.49/5.91 thf(fact_2782_divide__left__mono,axiom,
% 5.49/5.91 ! [B: real,A: real,C: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ B @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.49/5.91 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_left_mono
% 5.49/5.91 thf(fact_2783_divide__left__mono,axiom,
% 5.49/5.91 ! [B: rat,A: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.49/5.91 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_left_mono
% 5.49/5.91 thf(fact_2784_le__divide__eq,axiom,
% 5.49/5.91 ! [A: real,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % le_divide_eq
% 5.49/5.91 thf(fact_2785_le__divide__eq,axiom,
% 5.49/5.91 ! [A: rat,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % le_divide_eq
% 5.49/5.91 thf(fact_2786_divide__le__eq,axiom,
% 5.49/5.91 ! [B: real,C: real,A: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_eq
% 5.49/5.91 thf(fact_2787_divide__le__eq,axiom,
% 5.49/5.91 ! [B: rat,C: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_eq
% 5.49/5.91 thf(fact_2788_le__divide__eq__1,axiom,
% 5.49/5.91 ! [B: real,A: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 & ( ord_less_eq_real @ A @ B ) )
% 5.49/5.91 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.91 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % le_divide_eq_1
% 5.49/5.91 thf(fact_2789_le__divide__eq__1,axiom,
% 5.49/5.91 ! [B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 & ( ord_less_eq_rat @ A @ B ) )
% 5.49/5.91 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.91 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % le_divide_eq_1
% 5.49/5.91 thf(fact_2790_divide__le__eq__1,axiom,
% 5.49/5.91 ! [B: real,A: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 & ( ord_less_eq_real @ B @ A ) )
% 5.49/5.91 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.91 & ( ord_less_eq_real @ A @ B ) )
% 5.49/5.91 | ( A = zero_zero_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_eq_1
% 5.49/5.91 thf(fact_2791_divide__le__eq__1,axiom,
% 5.49/5.91 ! [B: rat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 & ( ord_less_eq_rat @ B @ A ) )
% 5.49/5.91 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.91 & ( ord_less_eq_rat @ A @ B ) )
% 5.49/5.91 | ( A = zero_zero_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_le_eq_1
% 5.49/5.91 thf(fact_2792_convex__bound__le,axiom,
% 5.49/5.91 ! [X: real,A: real,Y2: real,U: real,V: real] :
% 5.49/5.91 ( ( ord_less_eq_real @ X @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ Y2 @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.49/5.91 => ( ( ( plus_plus_real @ U @ V )
% 5.49/5.91 = one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % convex_bound_le
% 5.49/5.91 thf(fact_2793_convex__bound__le,axiom,
% 5.49/5.91 ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ X @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ Y2 @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.49/5.91 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.49/5.91 => ( ( ( plus_plus_rat @ U @ V )
% 5.49/5.91 = one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % convex_bound_le
% 5.49/5.91 thf(fact_2794_convex__bound__le,axiom,
% 5.49/5.91 ! [X: int,A: int,Y2: int,U: int,V: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ X @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ Y2 @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.49/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.49/5.91 => ( ( ( plus_plus_int @ U @ V )
% 5.49/5.91 = one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % convex_bound_le
% 5.49/5.91 thf(fact_2795_less__divide__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [W: num,B: real,C: real] :
% 5.49/5.91 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq_numeral(1)
% 5.49/5.91 thf(fact_2796_less__divide__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [W: num,B: rat,C: rat] :
% 5.49/5.91 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % less_divide_eq_numeral(1)
% 5.49/5.91 thf(fact_2797_divide__less__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [B: real,C: real,W: num] :
% 5.49/5.91 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.49/5.91 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.91 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.91 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq_numeral(1)
% 5.49/5.91 thf(fact_2798_divide__less__eq__numeral_I1_J,axiom,
% 5.49/5.91 ! [B: rat,C: rat,W: num] :
% 5.49/5.91 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.49/5.91 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.91 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.49/5.91 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.91 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divide_less_eq_numeral(1)
% 5.49/5.91 thf(fact_2799_frac__le__eq,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real,W: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.49/5.91 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_le_eq
% 5.49/5.91 thf(fact_2800_frac__le__eq,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.49/5.91 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_le_eq
% 5.49/5.91 thf(fact_2801_divmod__digit__1_I1_J,axiom,
% 5.49/5.91 ! [A: code_integer,B: code_integer] :
% 5.49/5.91 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.49/5.91 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.49/5.91 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.49/5.91 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(1)
% 5.49/5.91 thf(fact_2802_divmod__digit__1_I1_J,axiom,
% 5.49/5.91 ! [A: nat,B: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.49/5.91 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( 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 )
% 5.49/5.91 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(1)
% 5.49/5.91 thf(fact_2803_divmod__digit__1_I1_J,axiom,
% 5.49/5.91 ! [A: int,B: int] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.91 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.49/5.91 => ( ( 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 )
% 5.49/5.91 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % divmod_digit_1(1)
% 5.49/5.91 thf(fact_2804_frac__less__eq,axiom,
% 5.49/5.91 ! [Y2: real,Z: real,X: real,W: real] :
% 5.49/5.91 ( ( Y2 != zero_zero_real )
% 5.49/5.91 => ( ( Z != zero_zero_real )
% 5.49/5.91 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y2 ) @ ( divide_divide_real @ W @ Z ) )
% 5.49/5.91 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y2 ) ) @ ( times_times_real @ Y2 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less_eq
% 5.49/5.91 thf(fact_2805_frac__less__eq,axiom,
% 5.49/5.91 ! [Y2: rat,Z: rat,X: rat,W: rat] :
% 5.49/5.91 ( ( Y2 != zero_zero_rat )
% 5.49/5.91 => ( ( Z != zero_zero_rat )
% 5.49/5.91 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y2 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.49/5.91 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y2 ) ) @ ( times_times_rat @ Y2 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % frac_less_eq
% 5.49/5.91 thf(fact_2806_power__Suc__less,axiom,
% 5.49/5.91 ! [A: real,N: nat] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less
% 5.49/5.91 thf(fact_2807_power__Suc__less,axiom,
% 5.49/5.91 ! [A: rat,N: nat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less
% 5.49/5.91 thf(fact_2808_power__Suc__less,axiom,
% 5.49/5.91 ! [A: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less
% 5.49/5.91 thf(fact_2809_power__Suc__less,axiom,
% 5.49/5.91 ! [A: int,N: nat] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ A @ one_one_int )
% 5.49/5.91 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less
% 5.49/5.91 thf(fact_2810_power__Suc__le__self,axiom,
% 5.49/5.91 ! [A: real,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_le_self
% 5.49/5.91 thf(fact_2811_power__Suc__le__self,axiom,
% 5.49/5.91 ! [A: rat,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_le_self
% 5.49/5.91 thf(fact_2812_power__Suc__le__self,axiom,
% 5.49/5.91 ! [A: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_le_self
% 5.49/5.91 thf(fact_2813_power__Suc__le__self,axiom,
% 5.49/5.91 ! [A: int,N: nat] :
% 5.49/5.91 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.49/5.91 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_le_self
% 5.49/5.91 thf(fact_2814_power__Suc__less__one,axiom,
% 5.49/5.91 ! [A: real,N: nat] :
% 5.49/5.91 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less_one
% 5.49/5.91 thf(fact_2815_power__Suc__less__one,axiom,
% 5.49/5.91 ! [A: rat,N: nat] :
% 5.49/5.91 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less_one
% 5.49/5.91 thf(fact_2816_power__Suc__less__one,axiom,
% 5.49/5.91 ! [A: nat,N: nat] :
% 5.49/5.91 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less_one
% 5.49/5.91 thf(fact_2817_power__Suc__less__one,axiom,
% 5.49/5.91 ! [A: int,N: nat] :
% 5.49/5.91 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ A @ one_one_int )
% 5.49/5.91 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_Suc_less_one
% 5.49/5.91 thf(fact_2818_power__strict__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: real] :
% 5.49/5.91 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.91 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_strict_decreasing
% 5.49/5.91 thf(fact_2819_power__strict__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: rat] :
% 5.49/5.91 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.91 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.91 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.49/5.91 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_strict_decreasing
% 5.49/5.91 thf(fact_2820_power__strict__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: nat] :
% 5.49/5.91 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.91 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.49/5.91 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.49/5.91 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_strict_decreasing
% 5.49/5.91 thf(fact_2821_power__strict__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: int] :
% 5.49/5.91 ( ( ord_less_nat @ N @ N5 )
% 5.49/5.91 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.91 => ( ( ord_less_int @ A @ one_one_int )
% 5.49/5.91 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_strict_decreasing
% 5.49/5.91 thf(fact_2822_vebt__mint_Oelims,axiom,
% 5.49/5.91 ! [X: vEBT_VEBT,Y2: option_nat] :
% 5.49/5.91 ( ( ( vEBT_vebt_mint @ X )
% 5.49/5.91 = Y2 )
% 5.49/5.91 => ( ! [A3: $o,B2: $o] :
% 5.49/5.91 ( ( X
% 5.49/5.91 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.91 => ~ ( ( A3
% 5.49/5.91 => ( Y2
% 5.49/5.91 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.91 & ( ~ A3
% 5.49/5.91 => ( ( B2
% 5.49/5.91 => ( Y2
% 5.49/5.91 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.91 & ( ~ B2
% 5.49/5.91 => ( Y2 = none_nat ) ) ) ) ) )
% 5.49/5.91 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.91 => ( Y2 != none_nat ) )
% 5.49/5.91 => ~ ! [Mi2: nat] :
% 5.49/5.91 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.91 ( X
% 5.49/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.49/5.91 => ( Y2
% 5.49/5.91 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % vebt_mint.elims
% 5.49/5.91 thf(fact_2823_power__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: real] :
% 5.49/5.91 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.91 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.49/5.91 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.49/5.91 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.49/5.91
% 5.49/5.91 % power_decreasing
% 5.49/5.91 thf(fact_2824_power__decreasing,axiom,
% 5.49/5.91 ! [N: nat,N5: nat,A: rat] :
% 5.49/5.91 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.49/5.92 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.49/5.92 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_decreasing
% 5.49/5.92 thf(fact_2825_power__decreasing,axiom,
% 5.49/5.92 ! [N: nat,N5: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.92 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.49/5.92 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.49/5.92 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_decreasing
% 5.49/5.92 thf(fact_2826_power__decreasing,axiom,
% 5.49/5.92 ! [N: nat,N5: nat,A: int] :
% 5.49/5.92 ( ( ord_less_eq_nat @ N @ N5 )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.92 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.49/5.92 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_decreasing
% 5.49/5.92 thf(fact_2827_zero__power2,axiom,
% 5.49/5.92 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = zero_zero_rat ) ).
% 5.49/5.92
% 5.49/5.92 % zero_power2
% 5.49/5.92 thf(fact_2828_zero__power2,axiom,
% 5.49/5.92 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = zero_zero_nat ) ).
% 5.49/5.92
% 5.49/5.92 % zero_power2
% 5.49/5.92 thf(fact_2829_zero__power2,axiom,
% 5.49/5.92 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = zero_zero_real ) ).
% 5.49/5.92
% 5.49/5.92 % zero_power2
% 5.49/5.92 thf(fact_2830_zero__power2,axiom,
% 5.49/5.92 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = zero_zero_int ) ).
% 5.49/5.92
% 5.49/5.92 % zero_power2
% 5.49/5.92 thf(fact_2831_zero__power2,axiom,
% 5.49/5.92 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = zero_zero_complex ) ).
% 5.49/5.92
% 5.49/5.92 % zero_power2
% 5.49/5.92 thf(fact_2832_vebt__maxt_Oelims,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Y2: option_nat] :
% 5.49/5.92 ( ( ( vEBT_vebt_maxt @ X )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ~ ( ( B2
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.92 & ( ~ B2
% 5.49/5.92 => ( ( A3
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.92 & ( ~ A3
% 5.49/5.92 => ( Y2 = none_nat ) ) ) ) ) )
% 5.49/5.92 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.92 => ( Y2 != none_nat ) )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.49/5.92 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_maxt.elims
% 5.49/5.92 thf(fact_2833_self__le__power,axiom,
% 5.49/5.92 ! [A: real,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % self_le_power
% 5.49/5.92 thf(fact_2834_self__le__power,axiom,
% 5.49/5.92 ! [A: rat,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % self_le_power
% 5.49/5.92 thf(fact_2835_self__le__power,axiom,
% 5.49/5.92 ! [A: nat,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % self_le_power
% 5.49/5.92 thf(fact_2836_self__le__power,axiom,
% 5.49/5.92 ! [A: int,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % self_le_power
% 5.49/5.92 thf(fact_2837_vebt__insert_Oelims,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.49/5.92 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.49/5.92 & ( ( Xa2 != one_one_nat )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) ) )
% 5.49/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) ) )
% 5.49/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 5.49/5.92 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 != ( if_VEBT_VEBT
% 5.49/5.92 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 & ~ ( ( Xa2 = Mi2 )
% 5.49/5.92 | ( Xa2 = Ma2 ) ) )
% 5.49/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.49/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_insert.elims
% 5.49/5.92 thf(fact_2838_one__less__power,axiom,
% 5.49/5.92 ! [A: real,N: nat] :
% 5.49/5.92 ( ( ord_less_real @ one_one_real @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % one_less_power
% 5.49/5.92 thf(fact_2839_one__less__power,axiom,
% 5.49/5.92 ! [A: rat,N: nat] :
% 5.49/5.92 ( ( ord_less_rat @ one_one_rat @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % one_less_power
% 5.49/5.92 thf(fact_2840_one__less__power,axiom,
% 5.49/5.92 ! [A: nat,N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ one_one_nat @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % one_less_power
% 5.49/5.92 thf(fact_2841_one__less__power,axiom,
% 5.49/5.92 ! [A: int,N: nat] :
% 5.49/5.92 ( ( ord_less_int @ one_one_int @ A )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % one_less_power
% 5.49/5.92 thf(fact_2842_numeral__2__eq__2,axiom,
% 5.49/5.92 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.92 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % numeral_2_eq_2
% 5.49/5.92 thf(fact_2843_pos2,axiom,
% 5.49/5.92 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.49/5.92
% 5.49/5.92 % pos2
% 5.49/5.92 thf(fact_2844_power__diff,axiom,
% 5.49/5.92 ! [A: complex,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_complex )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.92 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff
% 5.49/5.92 thf(fact_2845_power__diff,axiom,
% 5.49/5.92 ! [A: real,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_real )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.92 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff
% 5.49/5.92 thf(fact_2846_power__diff,axiom,
% 5.49/5.92 ! [A: rat,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_rat )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.92 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff
% 5.49/5.92 thf(fact_2847_power__diff,axiom,
% 5.49/5.92 ! [A: nat,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_nat )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.92 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff
% 5.49/5.92 thf(fact_2848_power__diff,axiom,
% 5.49/5.92 ! [A: int,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_int )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.49/5.92 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff
% 5.49/5.92 thf(fact_2849_div__if,axiom,
% 5.49/5.92 ( divide_divide_nat
% 5.49/5.92 = ( ^ [M6: nat,N2: nat] :
% 5.49/5.92 ( if_nat
% 5.49/5.92 @ ( ( ord_less_nat @ M6 @ N2 )
% 5.49/5.92 | ( N2 = zero_zero_nat ) )
% 5.49/5.92 @ zero_zero_nat
% 5.49/5.92 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_if
% 5.49/5.92 thf(fact_2850_div__geq,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ~ ( ord_less_nat @ M @ N )
% 5.49/5.92 => ( ( divide_divide_nat @ M @ N )
% 5.49/5.92 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_geq
% 5.49/5.92 thf(fact_2851_Suc__pred_H,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( N
% 5.49/5.92 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Suc_pred'
% 5.49/5.92 thf(fact_2852_Suc__diff__eq__diff__pred,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.49/5.92 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Suc_diff_eq_diff_pred
% 5.49/5.92 thf(fact_2853_add__eq__if,axiom,
% 5.49/5.92 ( plus_plus_nat
% 5.49/5.92 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % add_eq_if
% 5.49/5.92 thf(fact_2854_less__eq__div__iff__mult__less__eq,axiom,
% 5.49/5.92 ! [Q2: nat,M: nat,N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.49/5.92 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.49/5.92 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % less_eq_div_iff_mult_less_eq
% 5.49/5.92 thf(fact_2855_dividend__less__times__div,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % dividend_less_times_div
% 5.49/5.92 thf(fact_2856_dividend__less__div__times,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % dividend_less_div_times
% 5.49/5.92 thf(fact_2857_split__div,axiom,
% 5.49/5.92 ! [P: nat > $o,M: nat,N: nat] :
% 5.49/5.92 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.49/5.92 = ( ( ( N = zero_zero_nat )
% 5.49/5.92 => ( P @ zero_zero_nat ) )
% 5.49/5.92 & ( ( N != zero_zero_nat )
% 5.49/5.92 => ! [I3: nat,J3: nat] :
% 5.49/5.92 ( ( ord_less_nat @ J3 @ N )
% 5.49/5.92 => ( ( M
% 5.49/5.92 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 5.49/5.92 => ( P @ I3 ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % split_div
% 5.49/5.92 thf(fact_2858_mult__eq__if,axiom,
% 5.49/5.92 ( times_times_nat
% 5.49/5.92 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % mult_eq_if
% 5.49/5.92 thf(fact_2859_vebt__member_Osimps_I4_J,axiom,
% 5.49/5.92 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.49/5.92 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_member.simps(4)
% 5.49/5.92 thf(fact_2860_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.49/5.92 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.49/5.92 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.49/5.92 = ( ( X = Mi )
% 5.49/5.92 | ( X = Ma ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.membermima.simps(3)
% 5.49/5.92 thf(fact_2861_vebt__pred_Osimps_I5_J,axiom,
% 5.49/5.92 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.49/5.92 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.49/5.92 = none_nat ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_pred.simps(5)
% 5.49/5.92 thf(fact_2862_convex__bound__lt,axiom,
% 5.49/5.92 ! [X: real,A: real,Y2: real,U: real,V: real] :
% 5.49/5.92 ( ( ord_less_real @ X @ A )
% 5.49/5.92 => ( ( ord_less_real @ Y2 @ A )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.49/5.92 => ( ( ( plus_plus_real @ U @ V )
% 5.49/5.92 = one_one_real )
% 5.49/5.92 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % convex_bound_lt
% 5.49/5.92 thf(fact_2863_convex__bound__lt,axiom,
% 5.49/5.92 ! [X: rat,A: rat,Y2: rat,U: rat,V: rat] :
% 5.49/5.92 ( ( ord_less_rat @ X @ A )
% 5.49/5.92 => ( ( ord_less_rat @ Y2 @ A )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.49/5.92 => ( ( ( plus_plus_rat @ U @ V )
% 5.49/5.92 = one_one_rat )
% 5.49/5.92 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % convex_bound_lt
% 5.49/5.92 thf(fact_2864_convex__bound__lt,axiom,
% 5.49/5.92 ! [X: int,A: int,Y2: int,U: int,V: int] :
% 5.49/5.92 ( ( ord_less_int @ X @ A )
% 5.49/5.92 => ( ( ord_less_int @ Y2 @ A )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.49/5.92 => ( ( ( plus_plus_int @ U @ V )
% 5.49/5.92 = one_one_int )
% 5.49/5.92 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y2 ) ) @ A ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % convex_bound_lt
% 5.49/5.92 thf(fact_2865_le__divide__eq__numeral_I1_J,axiom,
% 5.49/5.92 ! [W: num,B: real,C: real] :
% 5.49/5.92 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.49/5.92 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.92 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.49/5.92 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.92 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.92 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.49/5.92 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.92 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % le_divide_eq_numeral(1)
% 5.49/5.92 thf(fact_2866_le__divide__eq__numeral_I1_J,axiom,
% 5.49/5.92 ! [W: num,B: rat,C: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.49/5.92 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.92 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.49/5.92 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.92 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.92 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.49/5.92 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.92 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % le_divide_eq_numeral(1)
% 5.49/5.92 thf(fact_2867_divide__le__eq__numeral_I1_J,axiom,
% 5.49/5.92 ! [B: real,C: real,W: num] :
% 5.49/5.92 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.49/5.92 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.92 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.49/5.92 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.49/5.92 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.92 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.49/5.92 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.49/5.92 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % divide_le_eq_numeral(1)
% 5.49/5.92 thf(fact_2868_divide__le__eq__numeral_I1_J,axiom,
% 5.49/5.92 ! [B: rat,C: rat,W: num] :
% 5.49/5.92 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.49/5.92 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.92 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.49/5.92 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.49/5.92 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.92 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.49/5.92 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.49/5.92 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % divide_le_eq_numeral(1)
% 5.49/5.92 thf(fact_2869_half__gt__zero__iff,axiom,
% 5.49/5.92 ! [A: real] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.49/5.92 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_gt_zero_iff
% 5.49/5.92 thf(fact_2870_half__gt__zero__iff,axiom,
% 5.49/5.92 ! [A: rat] :
% 5.49/5.92 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_gt_zero_iff
% 5.49/5.92 thf(fact_2871_half__gt__zero,axiom,
% 5.49/5.92 ! [A: real] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.92 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_gt_zero
% 5.49/5.92 thf(fact_2872_half__gt__zero,axiom,
% 5.49/5.92 ! [A: rat] :
% 5.49/5.92 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.49/5.92 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_gt_zero
% 5.49/5.92 thf(fact_2873_scaling__mono,axiom,
% 5.49/5.92 ! [U: real,V: real,R2: real,S2: real] :
% 5.49/5.92 ( ( ord_less_eq_real @ U @ V )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.49/5.92 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.49/5.92 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % scaling_mono
% 5.49/5.92 thf(fact_2874_scaling__mono,axiom,
% 5.49/5.92 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ U @ V )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.49/5.92 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.49/5.92 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % scaling_mono
% 5.49/5.92 thf(fact_2875_power2__le__imp__le,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.92 => ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_le_imp_le
% 5.49/5.92 thf(fact_2876_power2__le__imp__le,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.92 => ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_le_imp_le
% 5.49/5.92 thf(fact_2877_power2__le__imp__le,axiom,
% 5.49/5.92 ! [X: nat,Y2: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.49/5.92 => ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_le_imp_le
% 5.49/5.92 thf(fact_2878_power2__le__imp__le,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.92 => ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_le_imp_le
% 5.49/5.92 thf(fact_2879_power2__eq__imp__eq,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.92 => ( X = Y2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_eq_imp_eq
% 5.49/5.92 thf(fact_2880_power2__eq__imp__eq,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.92 => ( X = Y2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_eq_imp_eq
% 5.49/5.92 thf(fact_2881_power2__eq__imp__eq,axiom,
% 5.49/5.92 ! [X: nat,Y2: nat] :
% 5.49/5.92 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.49/5.92 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.49/5.92 => ( X = Y2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_eq_imp_eq
% 5.49/5.92 thf(fact_2882_power2__eq__imp__eq,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.92 => ( X = Y2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_eq_imp_eq
% 5.49/5.92 thf(fact_2883_zero__le__power2,axiom,
% 5.49/5.92 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_power2
% 5.49/5.92 thf(fact_2884_zero__le__power2,axiom,
% 5.49/5.92 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_power2
% 5.49/5.92 thf(fact_2885_zero__le__power2,axiom,
% 5.49/5.92 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_power2
% 5.49/5.92 thf(fact_2886_power2__less__0,axiom,
% 5.49/5.92 ! [A: real] :
% 5.49/5.92 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_0
% 5.49/5.92 thf(fact_2887_power2__less__0,axiom,
% 5.49/5.92 ! [A: rat] :
% 5.49/5.92 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_0
% 5.49/5.92 thf(fact_2888_power2__less__0,axiom,
% 5.49/5.92 ! [A: int] :
% 5.49/5.92 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_0
% 5.49/5.92 thf(fact_2889_exp__add__not__zero__imp__right,axiom,
% 5.49/5.92 ! [M: nat,N: nat] :
% 5.49/5.92 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.92 != zero_zero_nat )
% 5.49/5.92 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.49/5.92 != zero_zero_nat ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_add_not_zero_imp_right
% 5.49/5.92 thf(fact_2890_exp__add__not__zero__imp__right,axiom,
% 5.49/5.92 ! [M: nat,N: nat] :
% 5.49/5.92 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.92 != zero_zero_int )
% 5.49/5.92 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.49/5.92 != zero_zero_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_add_not_zero_imp_right
% 5.49/5.92 thf(fact_2891_exp__add__not__zero__imp__left,axiom,
% 5.49/5.92 ! [M: nat,N: nat] :
% 5.49/5.92 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.92 != zero_zero_nat )
% 5.49/5.92 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.49/5.92 != zero_zero_nat ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_add_not_zero_imp_left
% 5.49/5.92 thf(fact_2892_exp__add__not__zero__imp__left,axiom,
% 5.49/5.92 ! [M: nat,N: nat] :
% 5.49/5.92 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.49/5.92 != zero_zero_int )
% 5.49/5.92 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.49/5.92 != zero_zero_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_add_not_zero_imp_left
% 5.49/5.92 thf(fact_2893_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.49/5.92 != zero_zero_nat )
% 5.49/5.92 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.49/5.92 != zero_zero_nat ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_not_zero_imp_exp_diff_not_zero
% 5.49/5.92 thf(fact_2894_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.49/5.92 != zero_zero_int )
% 5.49/5.92 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.49/5.92 != zero_zero_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % exp_not_zero_imp_exp_diff_not_zero
% 5.49/5.92 thf(fact_2895_power__diff__power__eq,axiom,
% 5.49/5.92 ! [A: nat,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_nat )
% 5.49/5.92 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.49/5.92 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.49/5.92 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.49/5.92 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff_power_eq
% 5.49/5.92 thf(fact_2896_power__diff__power__eq,axiom,
% 5.49/5.92 ! [A: int,N: nat,M: nat] :
% 5.49/5.92 ( ( A != zero_zero_int )
% 5.49/5.92 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.49/5.92 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.49/5.92 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.49/5.92 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_diff_power_eq
% 5.49/5.92 thf(fact_2897_less__2__cases__iff,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( ( N = zero_zero_nat )
% 5.49/5.92 | ( N
% 5.49/5.92 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % less_2_cases_iff
% 5.49/5.92 thf(fact_2898_less__2__cases,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 => ( ( N = zero_zero_nat )
% 5.49/5.92 | ( N
% 5.49/5.92 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % less_2_cases
% 5.49/5.92 thf(fact_2899_nat__induct2,axiom,
% 5.49/5.92 ! [P: nat > $o,N: nat] :
% 5.49/5.92 ( ( P @ zero_zero_nat )
% 5.49/5.92 => ( ( P @ one_one_nat )
% 5.49/5.92 => ( ! [N3: nat] :
% 5.49/5.92 ( ( P @ N3 )
% 5.49/5.92 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.92 => ( P @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % nat_induct2
% 5.49/5.92 thf(fact_2900_power__eq__if,axiom,
% 5.49/5.92 ( power_power_complex
% 5.49/5.92 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_eq_if
% 5.49/5.92 thf(fact_2901_power__eq__if,axiom,
% 5.49/5.92 ( power_power_real
% 5.49/5.92 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_eq_if
% 5.49/5.92 thf(fact_2902_power__eq__if,axiom,
% 5.49/5.92 ( power_power_rat
% 5.49/5.92 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_eq_if
% 5.49/5.92 thf(fact_2903_power__eq__if,axiom,
% 5.49/5.92 ( power_power_nat
% 5.49/5.92 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_eq_if
% 5.49/5.92 thf(fact_2904_power__eq__if,axiom,
% 5.49/5.92 ( power_power_int
% 5.49/5.92 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_eq_if
% 5.49/5.92 thf(fact_2905_power__minus__mult,axiom,
% 5.49/5.92 ! [N: nat,A: complex] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.49/5.92 = ( power_power_complex @ A @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_minus_mult
% 5.49/5.92 thf(fact_2906_power__minus__mult,axiom,
% 5.49/5.92 ! [N: nat,A: real] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.49/5.92 = ( power_power_real @ A @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_minus_mult
% 5.49/5.92 thf(fact_2907_power__minus__mult,axiom,
% 5.49/5.92 ! [N: nat,A: rat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.49/5.92 = ( power_power_rat @ A @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_minus_mult
% 5.49/5.92 thf(fact_2908_power__minus__mult,axiom,
% 5.49/5.92 ! [N: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.49/5.92 = ( power_power_nat @ A @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_minus_mult
% 5.49/5.92 thf(fact_2909_power__minus__mult,axiom,
% 5.49/5.92 ! [N: nat,A: int] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.49/5.92 = ( power_power_int @ A @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power_minus_mult
% 5.49/5.92 thf(fact_2910_le__div__geq,axiom,
% 5.49/5.92 ! [N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( ord_less_eq_nat @ N @ M )
% 5.49/5.92 => ( ( divide_divide_nat @ M @ N )
% 5.49/5.92 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % le_div_geq
% 5.49/5.92 thf(fact_2911_split__div_H,axiom,
% 5.49/5.92 ! [P: nat > $o,M: nat,N: nat] :
% 5.49/5.92 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.49/5.92 = ( ( ( N = zero_zero_nat )
% 5.49/5.92 & ( P @ zero_zero_nat ) )
% 5.49/5.92 | ? [Q4: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.49/5.92 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.49/5.92 & ( P @ Q4 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % split_div'
% 5.49/5.92 thf(fact_2912_div__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [A: nat,N: nat,M: nat] :
% 5.49/5.92 ( ( 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 ) )
% 5.49/5.92 = ( 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 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2913_div__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [A: int,N: nat,M: nat] :
% 5.49/5.92 ( ( 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 ) )
% 5.49/5.92 = ( 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 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2914_div__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [A: code_integer,N: nat,M: nat] :
% 5.49/5.92 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.49/5.92 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2915_vebt__pred_Osimps_I6_J,axiom,
% 5.49/5.92 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.49/5.92 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.49/5.92 = none_nat ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_pred.simps(6)
% 5.49/5.92 thf(fact_2916_power2__less__imp__less,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.92 => ( ord_less_real @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_imp_less
% 5.49/5.92 thf(fact_2917_power2__less__imp__less,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.92 => ( ord_less_rat @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_imp_less
% 5.49/5.92 thf(fact_2918_power2__less__imp__less,axiom,
% 5.49/5.92 ! [X: nat,Y2: nat] :
% 5.49/5.92 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y2 )
% 5.49/5.92 => ( ord_less_nat @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_imp_less
% 5.49/5.92 thf(fact_2919_power2__less__imp__less,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.49/5.92 => ( ord_less_int @ X @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % power2_less_imp_less
% 5.49/5.92 thf(fact_2920_sum__power2__le__zero__iff,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.49/5.92 = ( ( X = zero_zero_real )
% 5.49/5.92 & ( Y2 = zero_zero_real ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_le_zero_iff
% 5.49/5.92 thf(fact_2921_sum__power2__le__zero__iff,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.49/5.92 = ( ( X = zero_zero_rat )
% 5.49/5.92 & ( Y2 = zero_zero_rat ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_le_zero_iff
% 5.49/5.92 thf(fact_2922_sum__power2__le__zero__iff,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.49/5.92 = ( ( X = zero_zero_int )
% 5.49/5.92 & ( Y2 = zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_le_zero_iff
% 5.49/5.92 thf(fact_2923_sum__power2__ge__zero,axiom,
% 5.49/5.92 ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_ge_zero
% 5.49/5.92 thf(fact_2924_sum__power2__ge__zero,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_ge_zero
% 5.49/5.92 thf(fact_2925_sum__power2__ge__zero,axiom,
% 5.49/5.92 ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_ge_zero
% 5.49/5.92 thf(fact_2926_sum__power2__gt__zero__iff,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.92 = ( ( X != zero_zero_real )
% 5.49/5.92 | ( Y2 != zero_zero_real ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_gt_zero_iff
% 5.49/5.92 thf(fact_2927_sum__power2__gt__zero__iff,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.92 = ( ( X != zero_zero_rat )
% 5.49/5.92 | ( Y2 != zero_zero_rat ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_gt_zero_iff
% 5.49/5.92 thf(fact_2928_sum__power2__gt__zero__iff,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.92 = ( ( X != zero_zero_int )
% 5.49/5.92 | ( Y2 != zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % sum_power2_gt_zero_iff
% 5.49/5.92 thf(fact_2929_not__sum__power2__lt__zero,axiom,
% 5.49/5.92 ! [X: real,Y2: real] :
% 5.49/5.92 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.49/5.92
% 5.49/5.92 % not_sum_power2_lt_zero
% 5.49/5.92 thf(fact_2930_not__sum__power2__lt__zero,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat] :
% 5.49/5.92 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.49/5.92
% 5.49/5.92 % not_sum_power2_lt_zero
% 5.49/5.92 thf(fact_2931_not__sum__power2__lt__zero,axiom,
% 5.49/5.92 ! [X: int,Y2: int] :
% 5.49/5.92 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.49/5.92
% 5.49/5.92 % not_sum_power2_lt_zero
% 5.49/5.92 thf(fact_2932_zero__le__even__power_H,axiom,
% 5.49/5.92 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_even_power'
% 5.49/5.92 thf(fact_2933_zero__le__even__power_H,axiom,
% 5.49/5.92 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_even_power'
% 5.49/5.92 thf(fact_2934_zero__le__even__power_H,axiom,
% 5.49/5.92 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zero_le_even_power'
% 5.49/5.92 thf(fact_2935_nat__bit__induct,axiom,
% 5.49/5.92 ! [P: nat > $o,N: nat] :
% 5.49/5.92 ( ( P @ zero_zero_nat )
% 5.49/5.92 => ( ! [N3: nat] :
% 5.49/5.92 ( ( P @ N3 )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.49/5.92 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.49/5.92 => ( ! [N3: nat] :
% 5.49/5.92 ( ( P @ N3 )
% 5.49/5.92 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.49/5.92 => ( P @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % nat_bit_induct
% 5.49/5.92 thf(fact_2936_Suc__n__div__2__gt__zero,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Suc_n_div_2_gt_zero
% 5.49/5.92 thf(fact_2937_div__2__gt__zero,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.49/5.92 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_2_gt_zero
% 5.49/5.92 thf(fact_2938_mult__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [M: nat,N: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.92 => ( ( 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 ) )
% 5.49/5.92 = ( 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 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % mult_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2939_mult__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [M: nat,N: nat,A: int] :
% 5.49/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.92 => ( ( 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 ) )
% 5.49/5.92 = ( 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 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % mult_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2940_mult__exp__mod__exp__eq,axiom,
% 5.49/5.92 ! [M: nat,N: nat,A: code_integer] :
% 5.49/5.92 ( ( ord_less_eq_nat @ M @ N )
% 5.49/5.92 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.49/5.92 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % mult_exp_mod_exp_eq
% 5.49/5.92 thf(fact_2941_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.92 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.49/5.92 => ( ( ? [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [S: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.naive_member.elims(1)
% 5.49/5.92 thf(fact_2942_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.92 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.92 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [S: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.92 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.naive_member.elims(2)
% 5.49/5.92 thf(fact_2943_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.92 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.92 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.49/5.92 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [S: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.92 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.naive_member.elims(3)
% 5.49/5.92 thf(fact_2944_odd__0__le__power__imp__0__le,axiom,
% 5.49/5.92 ! [A: real,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.49/5.92 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_0_le_power_imp_0_le
% 5.49/5.92 thf(fact_2945_odd__0__le__power__imp__0__le,axiom,
% 5.49/5.92 ! [A: rat,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.49/5.92 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_0_le_power_imp_0_le
% 5.49/5.92 thf(fact_2946_odd__0__le__power__imp__0__le,axiom,
% 5.49/5.92 ! [A: int,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.49/5.92 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_0_le_power_imp_0_le
% 5.49/5.92 thf(fact_2947_odd__power__less__zero,axiom,
% 5.49/5.92 ! [A: real,N: nat] :
% 5.49/5.92 ( ( ord_less_real @ A @ zero_zero_real )
% 5.49/5.92 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_power_less_zero
% 5.49/5.92 thf(fact_2948_odd__power__less__zero,axiom,
% 5.49/5.92 ! [A: rat,N: nat] :
% 5.49/5.92 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.49/5.92 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_power_less_zero
% 5.49/5.92 thf(fact_2949_odd__power__less__zero,axiom,
% 5.49/5.92 ! [A: int,N: nat] :
% 5.49/5.92 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.92 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % odd_power_less_zero
% 5.49/5.92 thf(fact_2950_vebt__insert_Osimps_I5_J,axiom,
% 5.49/5.92 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.49/5.92 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.49/5.92 = ( if_VEBT_VEBT
% 5.49/5.92 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.49/5.92 & ~ ( ( X = Mi )
% 5.49/5.92 | ( X = Ma ) ) )
% 5.49/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.49/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_insert.simps(5)
% 5.49/5.92 thf(fact_2951_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.49/5.92 ! [X: nat,N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.92 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.exp_split_high_low(1)
% 5.49/5.92 thf(fact_2952_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.49/5.92 ! [X: nat,N: nat,M: nat] :
% 5.49/5.92 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.92 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.exp_split_high_low(2)
% 5.49/5.92 thf(fact_2953_vebt__member_Oelims_I2_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.92 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Summary2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ~ ( ( Xa2 != Mi2 )
% 5.49/5.92 => ( ( Xa2 != Ma2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_member.elims(2)
% 5.49/5.92 thf(fact_2954_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.92 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ( ! [Mi2: nat,Ma2: nat] :
% 5.49/5.92 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( Xa2 = Mi2 )
% 5.49/5.92 | ( Xa2 = Ma2 ) ) ) ) )
% 5.49/5.92 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Vc2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( Xa2 = Mi2 )
% 5.49/5.92 | ( Xa2 = Ma2 )
% 5.49/5.92 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.49/5.92 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Vd2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.membermima.elims(1)
% 5.49/5.92 thf(fact_2955_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.92 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.92 => ( ! [Uu3: $o,Uv2: $o] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.92 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.49/5.92 => ( ! [Mi2: nat,Ma2: nat] :
% 5.49/5.92 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.92 => ( ( Xa2 = Mi2 )
% 5.49/5.92 | ( Xa2 = Ma2 ) ) )
% 5.49/5.92 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Vc2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.92 => ( ( Xa2 = Mi2 )
% 5.49/5.92 | ( Xa2 = Ma2 )
% 5.49/5.92 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.49/5.92 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Vd2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.92 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % VEBT_internal.membermima.elims(3)
% 5.49/5.92 thf(fact_2956_vebt__member_Oelims_I1_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.92 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.49/5.92 => ( ( ? [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.49/5.92 => Y2 )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Summary2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( ~ ( ( Xa2 != Mi2 )
% 5.49/5.92 => ( ( Xa2 != Ma2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_member.elims(1)
% 5.49/5.92 thf(fact_2957_vebt__member_Oelims_I3_J,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.92 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => A3 )
% 5.49/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.92 => B2 )
% 5.49/5.92 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.92 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.92 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.49/5.92 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.49/5.92 ( ? [Summary2: vEBT_VEBT] :
% 5.49/5.92 ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( Xa2 != Mi2 )
% 5.49/5.92 => ( ( Xa2 != Ma2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.92 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_member.elims(3)
% 5.49/5.92 thf(fact_2958_arith__geo__mean,axiom,
% 5.49/5.92 ! [U: real,X: real,Y2: real] :
% 5.49/5.92 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( times_times_real @ X @ Y2 ) )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.49/5.92 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.49/5.92 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % arith_geo_mean
% 5.49/5.92 thf(fact_2959_arith__geo__mean,axiom,
% 5.49/5.92 ! [U: rat,X: rat,Y2: rat] :
% 5.49/5.92 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.92 = ( times_times_rat @ X @ Y2 ) )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.49/5.92 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.49/5.92 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % arith_geo_mean
% 5.49/5.92 thf(fact_2960_invar__vebt_Ocases,axiom,
% 5.49/5.92 ! [A1: vEBT_VEBT,A22: nat] :
% 5.49/5.92 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.49/5.92 => ( ( ? [A3: $o,B2: $o] :
% 5.49/5.92 ( A1
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ( A22
% 5.49/5.92 != ( suc @ zero_zero_nat ) ) )
% 5.49/5.92 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.49/5.92 ( ( A1
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( A22 = Deg2 )
% 5.49/5.92 => ( ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.49/5.92 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.49/5.92 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( M5 = N3 )
% 5.49/5.92 => ( ( Deg2
% 5.49/5.92 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.49/5.92 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.49/5.92 => ~ ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.49/5.92 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.49/5.92 ( ( A1
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( A22 = Deg2 )
% 5.49/5.92 => ( ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.49/5.92 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.49/5.92 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( M5
% 5.49/5.92 = ( suc @ N3 ) )
% 5.49/5.92 => ( ( Deg2
% 5.49/5.92 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.49/5.92 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.49/5.92 => ~ ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.49/5.92 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.49/5.92 ( ( A1
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( A22 = Deg2 )
% 5.49/5.92 => ( ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.49/5.92 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.49/5.92 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( M5 = N3 )
% 5.49/5.92 => ( ( Deg2
% 5.49/5.92 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.49/5.92 => ( ! [I: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X6 ) )
% 5.49/5.92 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.49/5.92 => ( ( ( Mi2 = Ma2 )
% 5.49/5.92 => ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.49/5.92 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.49/5.92 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.49/5.92 => ~ ( ( Mi2 != Ma2 )
% 5.49/5.92 => ! [I: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.49/5.92 = I )
% 5.49/5.92 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.49/5.92 & ! [X5: nat] :
% 5.49/5.92 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.49/5.92 = I )
% 5.49/5.92 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.49/5.92 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.92 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.49/5.92 ( ( A1
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( A22 = Deg2 )
% 5.49/5.92 => ( ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.49/5.92 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.49/5.92 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( M5
% 5.49/5.92 = ( suc @ N3 ) )
% 5.49/5.92 => ( ( Deg2
% 5.49/5.92 = ( plus_plus_nat @ N3 @ M5 ) )
% 5.49/5.92 => ( ! [I: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X6 ) )
% 5.49/5.92 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.49/5.92 => ( ( ( Mi2 = Ma2 )
% 5.49/5.92 => ! [X5: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.49/5.92 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.49/5.92 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.49/5.92 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.49/5.92 => ~ ( ( Mi2 != Ma2 )
% 5.49/5.92 => ! [I: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.49/5.92 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.49/5.92 = I )
% 5.49/5.92 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.49/5.92 & ! [X5: nat] :
% 5.49/5.92 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.49/5.92 = I )
% 5.49/5.92 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.49/5.92 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % invar_vebt.cases
% 5.49/5.92 thf(fact_2961_invar__vebt_Osimps,axiom,
% 5.49/5.92 ( vEBT_invar_vebt
% 5.49/5.92 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.49/5.92 ( ( ? [A4: $o,B3: $o] :
% 5.49/5.92 ( A12
% 5.49/5.92 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.49/5.92 & ( A23
% 5.49/5.92 = ( suc @ zero_zero_nat ) ) )
% 5.49/5.92 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.49/5.92 ( ( A12
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.49/5.92 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.49/5.92 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.92 & ( A23
% 5.49/5.92 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.49/5.92 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.49/5.92 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.49/5.92 ( ( A12
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.49/5.92 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.49/5.92 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.49/5.92 & ( A23
% 5.49/5.92 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.49/5.92 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.49/5.92 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.49/5.92 ( ( A12
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.49/5.92 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.49/5.92 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.92 & ( A23
% 5.49/5.92 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.49/5.92 & ! [I3: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.92 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X6 ) )
% 5.49/5.92 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.49/5.92 & ( ( Mi3 = Ma3 )
% 5.49/5.92 => ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.49/5.92 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.49/5.92 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.49/5.92 & ( ( Mi3 != Ma3 )
% 5.49/5.92 => ! [I3: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.92 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.49/5.92 = I3 )
% 5.49/5.92 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.49/5.92 & ! [X2: nat] :
% 5.49/5.92 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.49/5.92 = I3 )
% 5.49/5.92 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.49/5.92 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.49/5.92 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.49/5.92 ( ( A12
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 5.49/5.92 & ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 5.49/5.92 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.49/5.92 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.49/5.92 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.49/5.92 & ( A23
% 5.49/5.92 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.49/5.92 & ! [I3: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.49/5.92 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X6 ) )
% 5.49/5.92 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.49/5.92 & ( ( Mi3 = Ma3 )
% 5.49/5.92 => ! [X2: vEBT_VEBT] :
% 5.49/5.92 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.49/5.92 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.49/5.92 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.49/5.92 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.49/5.92 & ( ( Mi3 != Ma3 )
% 5.49/5.92 => ! [I3: nat] :
% 5.49/5.92 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.49/5.92 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.49/5.92 = I3 )
% 5.49/5.92 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.49/5.92 & ! [X2: nat] :
% 5.49/5.92 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 5.49/5.92 = I3 )
% 5.49/5.92 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 5.49/5.92 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.49/5.92 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % invar_vebt.simps
% 5.49/5.92 thf(fact_2962_verit__le__mono__div,axiom,
% 5.49/5.92 ! [A2: nat,B4: nat,N: nat] :
% 5.49/5.92 ( ( ord_less_nat @ A2 @ B4 )
% 5.49/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.92 => ( ord_less_eq_nat
% 5.49/5.92 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.49/5.92 @ ( if_nat
% 5.49/5.92 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.49/5.92 = zero_zero_nat )
% 5.49/5.92 @ one_one_nat
% 5.49/5.92 @ zero_zero_nat ) )
% 5.49/5.92 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_le_mono_div
% 5.49/5.92 thf(fact_2963_inrange,axiom,
% 5.49/5.92 ! [T: vEBT_VEBT,N: nat] :
% 5.49/5.92 ( ( vEBT_invar_vebt @ T @ N )
% 5.49/5.92 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % inrange
% 5.49/5.92 thf(fact_2964_finite__Collect__le__nat,axiom,
% 5.49/5.92 ! [K: nat] :
% 5.49/5.92 ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_le_nat
% 5.49/5.92 thf(fact_2965_finite__Collect__less__nat,axiom,
% 5.49/5.92 ! [K: nat] :
% 5.49/5.92 ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_less_nat
% 5.49/5.92 thf(fact_2966_finite__Collect__subsets,axiom,
% 5.49/5.92 ! [A2: set_nat] :
% 5.49/5.92 ( ( finite_finite_nat @ A2 )
% 5.49/5.92 => ( finite1152437895449049373et_nat
% 5.49/5.92 @ ( collect_set_nat
% 5.49/5.92 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_subsets
% 5.49/5.92 thf(fact_2967_finite__Collect__subsets,axiom,
% 5.49/5.92 ! [A2: set_complex] :
% 5.49/5.92 ( ( finite3207457112153483333omplex @ A2 )
% 5.49/5.92 => ( finite6551019134538273531omplex
% 5.49/5.92 @ ( collect_set_complex
% 5.49/5.92 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_subsets
% 5.49/5.92 thf(fact_2968_finite__Collect__subsets,axiom,
% 5.49/5.92 ! [A2: set_int] :
% 5.49/5.92 ( ( finite_finite_int @ A2 )
% 5.49/5.92 => ( finite6197958912794628473et_int
% 5.49/5.92 @ ( collect_set_int
% 5.49/5.92 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_subsets
% 5.49/5.92 thf(fact_2969_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: real > $o,Q: real > real > $o] :
% 5.49/5.92 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.92 => ( ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] :
% 5.49/5.92 ? [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2970_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: real > $o,Q: nat > real > $o] :
% 5.49/5.92 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.92 => ( ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] :
% 5.49/5.92 ? [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2971_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: real > $o,Q: int > real > $o] :
% 5.49/5.92 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.92 => ( ( finite_finite_int
% 5.49/5.92 @ ( collect_int
% 5.49/5.92 @ ^ [X2: int] :
% 5.49/5.92 ? [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_int
% 5.49/5.92 @ ( collect_int
% 5.49/5.92 @ ^ [X2: int] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2972_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: real > $o,Q: complex > real > $o] :
% 5.49/5.92 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.92 => ( ( finite3207457112153483333omplex
% 5.49/5.92 @ ( collect_complex
% 5.49/5.92 @ ^ [X2: complex] :
% 5.49/5.92 ? [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: real] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite3207457112153483333omplex
% 5.49/5.92 @ ( collect_complex
% 5.49/5.92 @ ^ [X2: complex] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2973_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: nat > $o,Q: real > nat > $o] :
% 5.49/5.92 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.92 => ( ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] :
% 5.49/5.92 ? [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2974_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: nat > $o,Q: nat > nat > $o] :
% 5.49/5.92 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.92 => ( ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] :
% 5.49/5.92 ? [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2975_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: nat > $o,Q: int > nat > $o] :
% 5.49/5.92 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.92 => ( ( finite_finite_int
% 5.49/5.92 @ ( collect_int
% 5.49/5.92 @ ^ [X2: int] :
% 5.49/5.92 ? [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_int
% 5.49/5.92 @ ( collect_int
% 5.49/5.92 @ ^ [X2: int] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2976_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: nat > $o,Q: complex > nat > $o] :
% 5.49/5.92 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.92 => ( ( finite3207457112153483333omplex
% 5.49/5.92 @ ( collect_complex
% 5.49/5.92 @ ^ [X2: complex] :
% 5.49/5.92 ? [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: nat] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite3207457112153483333omplex
% 5.49/5.92 @ ( collect_complex
% 5.49/5.92 @ ^ [X2: complex] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2977_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: int > $o,Q: real > int > $o] :
% 5.49/5.92 ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.49/5.92 => ( ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] :
% 5.49/5.92 ? [Y: int] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: int] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [X2: real] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2978_finite__Collect__bounded__ex,axiom,
% 5.49/5.92 ! [P: int > $o,Q: nat > int > $o] :
% 5.49/5.92 ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.49/5.92 => ( ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] :
% 5.49/5.92 ? [Y: int] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 & ( Q @ X2 @ Y ) ) ) )
% 5.49/5.92 = ( ! [Y: int] :
% 5.49/5.92 ( ( P @ Y )
% 5.49/5.92 => ( finite_finite_nat
% 5.49/5.92 @ ( collect_nat
% 5.49/5.92 @ ^ [X2: nat] : ( Q @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_Collect_bounded_ex
% 5.49/5.92 thf(fact_2979_set__bit__0,axiom,
% 5.49/5.92 ! [A: int] :
% 5.49/5.92 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.49/5.92 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % set_bit_0
% 5.49/5.92 thf(fact_2980_set__bit__0,axiom,
% 5.49/5.92 ! [A: nat] :
% 5.49/5.92 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.49/5.92 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % set_bit_0
% 5.49/5.92 thf(fact_2981_finite__roots__unity,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.49/5.92 => ( finite_finite_real
% 5.49/5.92 @ ( collect_real
% 5.49/5.92 @ ^ [Z2: real] :
% 5.49/5.92 ( ( power_power_real @ Z2 @ N )
% 5.49/5.92 = one_one_real ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_roots_unity
% 5.49/5.92 thf(fact_2982_finite__roots__unity,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.49/5.92 => ( finite3207457112153483333omplex
% 5.49/5.92 @ ( collect_complex
% 5.49/5.92 @ ^ [Z2: complex] :
% 5.49/5.92 ( ( power_power_complex @ Z2 @ N )
% 5.49/5.92 = one_one_complex ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_roots_unity
% 5.49/5.92 thf(fact_2983_vebt__pred_Opelims,axiom,
% 5.49/5.92 ! [X: vEBT_VEBT,Xa2: nat,Y2: option_nat] :
% 5.49/5.92 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.49/5.92 = Y2 )
% 5.49/5.92 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.92 => ( ! [Uu3: $o,Uv2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.92 => ( ( Xa2 = zero_zero_nat )
% 5.49/5.92 => ( ( Y2 = none_nat )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.49/5.92 => ( ! [A3: $o,Uw2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.49/5.92 => ( ( Xa2
% 5.49/5.92 = ( suc @ zero_zero_nat ) )
% 5.49/5.92 => ( ( ( A3
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.92 & ( ~ A3
% 5.49/5.92 => ( Y2 = none_nat ) ) )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.49/5.92 => ( ! [A3: $o,B2: $o] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.92 => ! [Va3: nat] :
% 5.49/5.92 ( ( Xa2
% 5.49/5.92 = ( suc @ ( suc @ Va3 ) ) )
% 5.49/5.92 => ( ( ( B2
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ one_one_nat ) ) )
% 5.49/5.92 & ( ~ B2
% 5.49/5.92 => ( ( A3
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ zero_zero_nat ) ) )
% 5.49/5.92 & ( ~ A3
% 5.49/5.92 => ( Y2 = none_nat ) ) ) ) )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.49/5.92 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.49/5.92 => ( ( Y2 = none_nat )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.49/5.92 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.49/5.92 => ( ( Y2 = none_nat )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.49/5.92 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.49/5.92 => ( ( Y2 = none_nat )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.49/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.92 ( ( X
% 5.49/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.92 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( some_nat @ Ma2 ) ) )
% 5.49/5.92 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.92 => ( Y2
% 5.49/5.92 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.92 @ ( if_option_nat
% 5.49/5.92 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 != none_nat )
% 5.49/5.92 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.49/5.92 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.92 @ ( if_option_nat
% 5.49/5.92 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.49/5.92 = none_nat )
% 5.49/5.92 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.49/5.92 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.92 @ none_nat ) ) ) )
% 5.49/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % vebt_pred.pelims
% 5.49/5.92 thf(fact_2984_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: extended_enat,Y2: extended_enat,Z: extended_enat] :
% 5.49/5.92 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 5.49/5.92 & ( ord_le72135733267957522d_enat @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2985_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: real,Y2: real,Z: real] :
% 5.49/5.92 ( ( ord_less_real @ ( ord_max_real @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_less_real @ X @ Z )
% 5.49/5.92 & ( ord_less_real @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2986_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: rat,Y2: rat,Z: rat] :
% 5.49/5.92 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_less_rat @ X @ Z )
% 5.49/5.92 & ( ord_less_rat @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2987_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: num,Y2: num,Z: num] :
% 5.49/5.92 ( ( ord_less_num @ ( ord_max_num @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_less_num @ X @ Z )
% 5.49/5.92 & ( ord_less_num @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2988_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: nat,Y2: nat,Z: nat] :
% 5.49/5.92 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_less_nat @ X @ Z )
% 5.49/5.92 & ( ord_less_nat @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2989_max__less__iff__conj,axiom,
% 5.49/5.92 ! [X: int,Y2: int,Z: int] :
% 5.49/5.92 ( ( ord_less_int @ ( ord_max_int @ X @ Y2 ) @ Z )
% 5.49/5.92 = ( ( ord_less_int @ X @ Z )
% 5.49/5.92 & ( ord_less_int @ Y2 @ Z ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max_less_iff_conj
% 5.49/5.92 thf(fact_2990_verit__eq__simplify_I8_J,axiom,
% 5.49/5.92 ! [X22: num,Y22: num] :
% 5.49/5.92 ( ( ( bit0 @ X22 )
% 5.49/5.92 = ( bit0 @ Y22 ) )
% 5.49/5.92 = ( X22 = Y22 ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_eq_simplify(8)
% 5.49/5.92 thf(fact_2991_div__neg__neg__trivial,axiom,
% 5.49/5.92 ! [K: int,L2: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.49/5.92 => ( ( ord_less_int @ L2 @ K )
% 5.49/5.92 => ( ( divide_divide_int @ K @ L2 )
% 5.49/5.92 = zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_neg_neg_trivial
% 5.49/5.92 thf(fact_2992_div__pos__pos__trivial,axiom,
% 5.49/5.92 ! [K: int,L2: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.92 => ( ( ord_less_int @ K @ L2 )
% 5.49/5.92 => ( ( divide_divide_int @ K @ L2 )
% 5.49/5.92 = zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_pos_pos_trivial
% 5.49/5.92 thf(fact_2993_i0__less,axiom,
% 5.49/5.92 ! [N: extended_enat] :
% 5.49/5.92 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.49/5.92 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.49/5.92
% 5.49/5.92 % i0_less
% 5.49/5.92 thf(fact_2994_idiff__0,axiom,
% 5.49/5.92 ! [N: extended_enat] :
% 5.49/5.92 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.49/5.92 = zero_z5237406670263579293d_enat ) ).
% 5.49/5.92
% 5.49/5.92 % idiff_0
% 5.49/5.92 thf(fact_2995_idiff__0__right,axiom,
% 5.49/5.92 ! [N: extended_enat] :
% 5.49/5.92 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.49/5.92 = N ) ).
% 5.49/5.92
% 5.49/5.92 % idiff_0_right
% 5.49/5.92 thf(fact_2996_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: set_int,L2: set_int,U: set_int] :
% 5.49/5.92 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_set_int @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_2997_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: rat,L2: rat,U: rat] :
% 5.49/5.92 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_rat @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_2998_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: num,L2: num,U: num] :
% 5.49/5.92 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_num @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_2999_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: nat,L2: nat,U: nat] :
% 5.49/5.92 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_nat @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_3000_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: int,L2: int,U: int] :
% 5.49/5.92 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_int @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_3001_atLeastAtMost__iff,axiom,
% 5.49/5.92 ! [I2: real,L2: real,U: real] :
% 5.49/5.92 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.49/5.92 = ( ( ord_less_eq_real @ L2 @ I2 )
% 5.49/5.92 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastAtMost_iff
% 5.49/5.92 thf(fact_3002_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 5.49/5.92 ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 5.49/5.92 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3003_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.49/5.92 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.49/5.92 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3004_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.49/5.92 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.49/5.92 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3005_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.49/5.92 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.49/5.92 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3006_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.49/5.92 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.49/5.92 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3007_Icc__eq__Icc,axiom,
% 5.49/5.92 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.49/5.92 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.49/5.92 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.49/5.92 = ( ( ( L2 = L3 )
% 5.49/5.92 & ( H2 = H3 ) )
% 5.49/5.92 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.49/5.92 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % Icc_eq_Icc
% 5.49/5.92 thf(fact_3008_max_Obounded__iff,axiom,
% 5.49/5.92 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.49/5.92 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.49/5.92 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.49/5.92 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.bounded_iff
% 5.49/5.92 thf(fact_3009_max_Obounded__iff,axiom,
% 5.49/5.92 ! [B: rat,C: rat,A: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.49/5.92 = ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.92 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.bounded_iff
% 5.49/5.92 thf(fact_3010_max_Obounded__iff,axiom,
% 5.49/5.92 ! [B: num,C: num,A: num] :
% 5.49/5.92 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.49/5.92 = ( ( ord_less_eq_num @ B @ A )
% 5.49/5.92 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.bounded_iff
% 5.49/5.92 thf(fact_3011_max_Obounded__iff,axiom,
% 5.49/5.92 ! [B: nat,C: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.49/5.92 = ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.92 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.bounded_iff
% 5.49/5.92 thf(fact_3012_max_Obounded__iff,axiom,
% 5.49/5.92 ! [B: int,C: int,A: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.49/5.92 = ( ( ord_less_eq_int @ B @ A )
% 5.49/5.92 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.bounded_iff
% 5.49/5.92 thf(fact_3013_max_Oabsorb2,axiom,
% 5.49/5.92 ! [A: extended_enat,B: extended_enat] :
% 5.49/5.92 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.49/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb2
% 5.49/5.92 thf(fact_3014_max_Oabsorb2,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ A @ B )
% 5.49/5.92 => ( ( ord_max_rat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb2
% 5.49/5.92 thf(fact_3015_max_Oabsorb2,axiom,
% 5.49/5.92 ! [A: num,B: num] :
% 5.49/5.92 ( ( ord_less_eq_num @ A @ B )
% 5.49/5.92 => ( ( ord_max_num @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb2
% 5.49/5.92 thf(fact_3016_max_Oabsorb2,axiom,
% 5.49/5.92 ! [A: nat,B: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.92 => ( ( ord_max_nat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb2
% 5.49/5.92 thf(fact_3017_max_Oabsorb2,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ A @ B )
% 5.49/5.92 => ( ( ord_max_int @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb2
% 5.49/5.92 thf(fact_3018_max_Oabsorb1,axiom,
% 5.49/5.92 ! [B: extended_enat,A: extended_enat] :
% 5.49/5.92 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.49/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb1
% 5.49/5.92 thf(fact_3019_max_Oabsorb1,axiom,
% 5.49/5.92 ! [B: rat,A: rat] :
% 5.49/5.92 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.92 => ( ( ord_max_rat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb1
% 5.49/5.92 thf(fact_3020_max_Oabsorb1,axiom,
% 5.49/5.92 ! [B: num,A: num] :
% 5.49/5.92 ( ( ord_less_eq_num @ B @ A )
% 5.49/5.92 => ( ( ord_max_num @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb1
% 5.49/5.92 thf(fact_3021_max_Oabsorb1,axiom,
% 5.49/5.92 ! [B: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.92 => ( ( ord_max_nat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb1
% 5.49/5.92 thf(fact_3022_max_Oabsorb1,axiom,
% 5.49/5.92 ! [B: int,A: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.92 => ( ( ord_max_int @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb1
% 5.49/5.92 thf(fact_3023_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: extended_enat,A: extended_enat] :
% 5.49/5.92 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.49/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3024_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: real,A: real] :
% 5.49/5.92 ( ( ord_less_real @ B @ A )
% 5.49/5.92 => ( ( ord_max_real @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3025_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: rat,A: rat] :
% 5.49/5.92 ( ( ord_less_rat @ B @ A )
% 5.49/5.92 => ( ( ord_max_rat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3026_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: num,A: num] :
% 5.49/5.92 ( ( ord_less_num @ B @ A )
% 5.49/5.92 => ( ( ord_max_num @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3027_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_nat @ B @ A )
% 5.49/5.92 => ( ( ord_max_nat @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3028_max_Oabsorb3,axiom,
% 5.49/5.92 ! [B: int,A: int] :
% 5.49/5.92 ( ( ord_less_int @ B @ A )
% 5.49/5.92 => ( ( ord_max_int @ A @ B )
% 5.49/5.92 = A ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb3
% 5.49/5.92 thf(fact_3029_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: extended_enat,B: extended_enat] :
% 5.49/5.92 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.49/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3030_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: real,B: real] :
% 5.49/5.92 ( ( ord_less_real @ A @ B )
% 5.49/5.92 => ( ( ord_max_real @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3031_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( ord_less_rat @ A @ B )
% 5.49/5.92 => ( ( ord_max_rat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3032_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: num,B: num] :
% 5.49/5.92 ( ( ord_less_num @ A @ B )
% 5.49/5.92 => ( ( ord_max_num @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3033_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: nat,B: nat] :
% 5.49/5.92 ( ( ord_less_nat @ A @ B )
% 5.49/5.92 => ( ( ord_max_nat @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3034_max_Oabsorb4,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_int @ A @ B )
% 5.49/5.92 => ( ( ord_max_int @ A @ B )
% 5.49/5.92 = B ) ) ).
% 5.49/5.92
% 5.49/5.92 % max.absorb4
% 5.49/5.92 thf(fact_3035_not__real__square__gt__zero,axiom,
% 5.49/5.92 ! [X: real] :
% 5.49/5.92 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.49/5.92 = ( X = zero_zero_real ) ) ).
% 5.49/5.92
% 5.49/5.92 % not_real_square_gt_zero
% 5.49/5.92 thf(fact_3036_zmod__numeral__Bit0,axiom,
% 5.49/5.92 ! [V: num,W: num] :
% 5.49/5.92 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.49/5.92 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zmod_numeral_Bit0
% 5.49/5.92 thf(fact_3037_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: set_int,B: set_int] :
% 5.49/5.92 ( ( bot_bot_set_set_int
% 5.49/5.92 = ( set_or370866239135849197et_int @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3038_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( bot_bot_set_rat
% 5.49/5.92 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3039_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: num,B: num] :
% 5.49/5.92 ( ( bot_bot_set_num
% 5.49/5.92 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3040_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: nat,B: nat] :
% 5.49/5.92 ( ( bot_bot_set_nat
% 5.49/5.92 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3041_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( bot_bot_set_int
% 5.49/5.92 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3042_atLeastatMost__empty__iff2,axiom,
% 5.49/5.92 ! [A: real,B: real] :
% 5.49/5.92 ( ( bot_bot_set_real
% 5.49/5.92 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff2
% 5.49/5.92 thf(fact_3043_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: set_int,B: set_int] :
% 5.49/5.92 ( ( ( set_or370866239135849197et_int @ A @ B )
% 5.49/5.92 = bot_bot_set_set_int )
% 5.49/5.92 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3044_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.49/5.92 = bot_bot_set_rat )
% 5.49/5.92 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3045_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: num,B: num] :
% 5.49/5.92 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.49/5.92 = bot_bot_set_num )
% 5.49/5.92 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3046_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: nat,B: nat] :
% 5.49/5.92 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.49/5.92 = bot_bot_set_nat )
% 5.49/5.92 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3047_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.49/5.92 = bot_bot_set_int )
% 5.49/5.92 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3048_atLeastatMost__empty__iff,axiom,
% 5.49/5.92 ! [A: real,B: real] :
% 5.49/5.92 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.49/5.92 = bot_bot_set_real )
% 5.49/5.92 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty_iff
% 5.49/5.92 thf(fact_3049_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.49/5.92 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_set_int @ C @ A )
% 5.49/5.92 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3050_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.92 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_rat @ C @ A )
% 5.49/5.92 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3051_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: num,B: num,C: num,D: num] :
% 5.49/5.92 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_num @ C @ A )
% 5.49/5.92 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3052_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.92 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.92 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3053_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.92 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_int @ C @ A )
% 5.49/5.92 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3054_atLeastatMost__subset__iff,axiom,
% 5.49/5.92 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.92 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.49/5.92 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_real @ C @ A )
% 5.49/5.92 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_subset_iff
% 5.49/5.92 thf(fact_3055_atLeastatMost__empty,axiom,
% 5.49/5.92 ! [B: rat,A: rat] :
% 5.49/5.92 ( ( ord_less_rat @ B @ A )
% 5.49/5.92 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.49/5.92 = bot_bot_set_rat ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty
% 5.49/5.92 thf(fact_3056_atLeastatMost__empty,axiom,
% 5.49/5.92 ! [B: num,A: num] :
% 5.49/5.92 ( ( ord_less_num @ B @ A )
% 5.49/5.92 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.49/5.92 = bot_bot_set_num ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty
% 5.49/5.92 thf(fact_3057_atLeastatMost__empty,axiom,
% 5.49/5.92 ! [B: nat,A: nat] :
% 5.49/5.92 ( ( ord_less_nat @ B @ A )
% 5.49/5.92 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.49/5.92 = bot_bot_set_nat ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty
% 5.49/5.92 thf(fact_3058_atLeastatMost__empty,axiom,
% 5.49/5.92 ! [B: int,A: int] :
% 5.49/5.92 ( ( ord_less_int @ B @ A )
% 5.49/5.92 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.49/5.92 = bot_bot_set_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty
% 5.49/5.92 thf(fact_3059_atLeastatMost__empty,axiom,
% 5.49/5.92 ! [B: real,A: real] :
% 5.49/5.92 ( ( ord_less_real @ B @ A )
% 5.49/5.92 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.49/5.92 = bot_bot_set_real ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_empty
% 5.49/5.92 thf(fact_3060_infinite__Icc__iff,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.49/5.92 = ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.92
% 5.49/5.92 % infinite_Icc_iff
% 5.49/5.92 thf(fact_3061_infinite__Icc__iff,axiom,
% 5.49/5.92 ! [A: real,B: real] :
% 5.49/5.92 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.49/5.92 = ( ord_less_real @ A @ B ) ) ).
% 5.49/5.92
% 5.49/5.92 % infinite_Icc_iff
% 5.49/5.92 thf(fact_3062_half__nonnegative__int__iff,axiom,
% 5.49/5.92 ! [K: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.49/5.92 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_nonnegative_int_iff
% 5.49/5.92 thf(fact_3063_half__negative__int__iff,axiom,
% 5.49/5.92 ! [K: int] :
% 5.49/5.92 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.49/5.92 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.49/5.92
% 5.49/5.92 % half_negative_int_iff
% 5.49/5.92 thf(fact_3064_verit__le__mono__div__int,axiom,
% 5.49/5.92 ! [A2: int,B4: int,N: int] :
% 5.49/5.92 ( ( ord_less_int @ A2 @ B4 )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.49/5.92 => ( ord_less_eq_int
% 5.49/5.92 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.49/5.92 @ ( if_int
% 5.49/5.92 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.49/5.92 = zero_zero_int )
% 5.49/5.92 @ one_one_int
% 5.49/5.92 @ zero_zero_int ) )
% 5.49/5.92 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_le_mono_div_int
% 5.49/5.92 thf(fact_3065_split__neg__lemma,axiom,
% 5.49/5.92 ! [K: int,P: int > int > $o,N: int] :
% 5.49/5.92 ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.92 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.49/5.92 = ( ! [I3: int,J3: int] :
% 5.49/5.92 ( ( ( ord_less_int @ K @ J3 )
% 5.49/5.92 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.49/5.92 & ( N
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.92 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % split_neg_lemma
% 5.49/5.92 thf(fact_3066_split__pos__lemma,axiom,
% 5.49/5.92 ! [K: int,P: int > int > $o,N: int] :
% 5.49/5.92 ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.92 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.49/5.92 = ( ! [I3: int,J3: int] :
% 5.49/5.92 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.49/5.92 & ( ord_less_int @ J3 @ K )
% 5.49/5.92 & ( N
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.92 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % split_pos_lemma
% 5.49/5.92 thf(fact_3067_zmod__zmult2__eq,axiom,
% 5.49/5.92 ! [C: int,A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.92 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zmod_zmult2_eq
% 5.49/5.92 thf(fact_3068_div__mod__decomp__int,axiom,
% 5.49/5.92 ! [A2: int,N: int] :
% 5.49/5.92 ( A2
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_mod_decomp_int
% 5.49/5.92 thf(fact_3069_zdiv__zmult2__eq,axiom,
% 5.49/5.92 ! [C: int,A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.49/5.92 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.49/5.92 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_zmult2_eq
% 5.49/5.92 thf(fact_3070_split__zdiv,axiom,
% 5.49/5.92 ! [P: int > $o,N: int,K: int] :
% 5.49/5.92 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.49/5.92 = ( ( ( K = zero_zero_int )
% 5.49/5.92 => ( P @ zero_zero_int ) )
% 5.49/5.92 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.92 => ! [I3: int,J3: int] :
% 5.49/5.92 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.49/5.92 & ( ord_less_int @ J3 @ K )
% 5.49/5.92 & ( N
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.92 => ( P @ I3 ) ) )
% 5.49/5.92 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.92 => ! [I3: int,J3: int] :
% 5.49/5.92 ( ( ( ord_less_int @ K @ J3 )
% 5.49/5.92 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.49/5.92 & ( N
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.92 => ( P @ I3 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % split_zdiv
% 5.49/5.92 thf(fact_3071_int__div__neg__eq,axiom,
% 5.49/5.92 ! [A: int,B: int,Q2: int,R2: int] :
% 5.49/5.92 ( ( A
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.92 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.49/5.92 => ( ( ord_less_int @ B @ R2 )
% 5.49/5.92 => ( ( divide_divide_int @ A @ B )
% 5.49/5.92 = Q2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % int_div_neg_eq
% 5.49/5.92 thf(fact_3072_int__div__pos__eq,axiom,
% 5.49/5.92 ! [A: int,B: int,Q2: int,R2: int] :
% 5.49/5.92 ( ( A
% 5.49/5.92 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.49/5.92 => ( ( ord_less_int @ R2 @ B )
% 5.49/5.92 => ( ( divide_divide_int @ A @ B )
% 5.49/5.92 = Q2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % int_div_pos_eq
% 5.49/5.92 thf(fact_3073_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.49/5.92 = ( ( ord_less_eq_int @ B @ A )
% 5.49/5.92 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % nonneg1_imp_zdiv_pos_iff
% 5.49/5.92 thf(fact_3074_pos__imp__zdiv__nonneg__iff,axiom,
% 5.49/5.92 ! [B: int,A: int] :
% 5.49/5.92 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.49/5.92 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % pos_imp_zdiv_nonneg_iff
% 5.49/5.92 thf(fact_3075_neg__imp__zdiv__nonneg__iff,axiom,
% 5.49/5.92 ! [B: int,A: int] :
% 5.49/5.92 ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.92 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.49/5.92 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % neg_imp_zdiv_nonneg_iff
% 5.49/5.92 thf(fact_3076_pos__imp__zdiv__pos__iff,axiom,
% 5.49/5.92 ! [K: int,I2: int] :
% 5.49/5.92 ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 5.49/5.92 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % pos_imp_zdiv_pos_iff
% 5.49/5.92 thf(fact_3077_div__nonpos__pos__le0,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_nonpos_pos_le0
% 5.49/5.92 thf(fact_3078_div__nonneg__neg__le0,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.92 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_nonneg_neg_le0
% 5.49/5.92 thf(fact_3079_div__positive__int,axiom,
% 5.49/5.92 ! [L2: int,K: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ L2 @ K )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.49/5.92 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_positive_int
% 5.49/5.92 thf(fact_3080_div__int__pos__iff,axiom,
% 5.49/5.92 ! [K: int,L2: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.49/5.92 = ( ( K = zero_zero_int )
% 5.49/5.92 | ( L2 = zero_zero_int )
% 5.49/5.92 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.92 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.49/5.92 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.92 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_int_pos_iff
% 5.49/5.92 thf(fact_3081_zdiv__mono2__neg,axiom,
% 5.49/5.92 ! [A: int,B5: int,B: int] :
% 5.49/5.92 ( ( ord_less_int @ A @ zero_zero_int )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.49/5.92 => ( ( ord_less_eq_int @ B5 @ B )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_mono2_neg
% 5.49/5.92 thf(fact_3082_zdiv__mono1__neg,axiom,
% 5.49/5.92 ! [A: int,A5: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ A @ A5 )
% 5.49/5.92 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_mono1_neg
% 5.49/5.92 thf(fact_3083_zdiv__eq__0__iff,axiom,
% 5.49/5.92 ! [I2: int,K: int] :
% 5.49/5.92 ( ( ( divide_divide_int @ I2 @ K )
% 5.49/5.92 = zero_zero_int )
% 5.49/5.92 = ( ( K = zero_zero_int )
% 5.49/5.92 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.49/5.92 & ( ord_less_int @ I2 @ K ) )
% 5.49/5.92 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.49/5.92 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_eq_0_iff
% 5.49/5.92 thf(fact_3084_zdiv__mono2,axiom,
% 5.49/5.92 ! [A: int,B5: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.49/5.92 => ( ( ord_less_eq_int @ B5 @ B )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_mono2
% 5.49/5.92 thf(fact_3085_zdiv__mono1,axiom,
% 5.49/5.92 ! [A: int,A5: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ A @ A5 )
% 5.49/5.92 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.92 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % zdiv_mono1
% 5.49/5.92 thf(fact_3086_div__pos__geq,axiom,
% 5.49/5.92 ! [L2: int,K: int] :
% 5.49/5.92 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.49/5.92 => ( ( ord_less_eq_int @ L2 @ K )
% 5.49/5.92 => ( ( divide_divide_int @ K @ L2 )
% 5.49/5.92 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % div_pos_geq
% 5.49/5.92 thf(fact_3087_pos__zmod__mult__2,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.92 => ( ( 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 ) )
% 5.49/5.92 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % pos_zmod_mult_2
% 5.49/5.92 thf(fact_3088_neg__zmod__mult__2,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.92 => ( ( 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 ) )
% 5.49/5.92 = ( 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 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % neg_zmod_mult_2
% 5.49/5.92 thf(fact_3089_enat__0__less__mult__iff,axiom,
% 5.49/5.92 ! [M: extended_enat,N: extended_enat] :
% 5.49/5.92 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.49/5.92 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.49/5.92 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % enat_0_less_mult_iff
% 5.49/5.92 thf(fact_3090_not__iless0,axiom,
% 5.49/5.92 ! [N: extended_enat] :
% 5.49/5.92 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.49/5.92
% 5.49/5.92 % not_iless0
% 5.49/5.92 thf(fact_3091_iadd__is__0,axiom,
% 5.49/5.92 ! [M: extended_enat,N: extended_enat] :
% 5.49/5.92 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.49/5.92 = zero_z5237406670263579293d_enat )
% 5.49/5.92 = ( ( M = zero_z5237406670263579293d_enat )
% 5.49/5.92 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % iadd_is_0
% 5.49/5.92 thf(fact_3092_ile0__eq,axiom,
% 5.49/5.92 ! [N: extended_enat] :
% 5.49/5.92 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.49/5.92 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.49/5.92
% 5.49/5.92 % ile0_eq
% 5.49/5.92 thf(fact_3093_i0__lb,axiom,
% 5.49/5.92 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.49/5.92
% 5.49/5.92 % i0_lb
% 5.49/5.92 thf(fact_3094_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.49/5.92 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_set_int @ C @ A )
% 5.49/5.92 & ( ord_less_eq_set_int @ B @ D )
% 5.49/5.92 & ( ( ord_less_set_int @ C @ A )
% 5.49/5.92 | ( ord_less_set_int @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3095_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.49/5.92 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_rat @ C @ A )
% 5.49/5.92 & ( ord_less_eq_rat @ B @ D )
% 5.49/5.92 & ( ( ord_less_rat @ C @ A )
% 5.49/5.92 | ( ord_less_rat @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3096_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: num,B: num,C: num,D: num] :
% 5.49/5.92 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_num @ C @ A )
% 5.49/5.92 & ( ord_less_eq_num @ B @ D )
% 5.49/5.92 & ( ( ord_less_num @ C @ A )
% 5.49/5.92 | ( ord_less_num @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3097_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.49/5.92 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.92 & ( ord_less_eq_nat @ B @ D )
% 5.49/5.92 & ( ( ord_less_nat @ C @ A )
% 5.49/5.92 | ( ord_less_nat @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3098_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: int,B: int,C: int,D: int] :
% 5.49/5.92 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_int @ C @ A )
% 5.49/5.92 & ( ord_less_eq_int @ B @ D )
% 5.49/5.92 & ( ( ord_less_int @ C @ A )
% 5.49/5.92 | ( ord_less_int @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3099_atLeastatMost__psubset__iff,axiom,
% 5.49/5.92 ! [A: real,B: real,C: real,D: real] :
% 5.49/5.92 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.49/5.92 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.49/5.92 | ( ( ord_less_eq_real @ C @ A )
% 5.49/5.92 & ( ord_less_eq_real @ B @ D )
% 5.49/5.92 & ( ( ord_less_real @ C @ A )
% 5.49/5.92 | ( ord_less_real @ B @ D ) ) ) )
% 5.49/5.92 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % atLeastatMost_psubset_iff
% 5.49/5.92 thf(fact_3100_infinite__Icc,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( ord_less_rat @ A @ B )
% 5.49/5.92 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % infinite_Icc
% 5.49/5.92 thf(fact_3101_infinite__Icc,axiom,
% 5.49/5.92 ! [A: real,B: real] :
% 5.49/5.92 ( ( ord_less_real @ A @ B )
% 5.49/5.92 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % infinite_Icc
% 5.49/5.92 thf(fact_3102_all__nat__less,axiom,
% 5.49/5.92 ! [N: nat,P: nat > $o] :
% 5.49/5.92 ( ( ! [M6: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ M6 @ N )
% 5.49/5.92 => ( P @ M6 ) ) )
% 5.49/5.92 = ( ! [X2: nat] :
% 5.49/5.92 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.49/5.92 => ( P @ X2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % all_nat_less
% 5.49/5.92 thf(fact_3103_ex__nat__less,axiom,
% 5.49/5.92 ! [N: nat,P: nat > $o] :
% 5.49/5.92 ( ( ? [M6: nat] :
% 5.49/5.92 ( ( ord_less_eq_nat @ M6 @ N )
% 5.49/5.92 & ( P @ M6 ) ) )
% 5.49/5.92 = ( ? [X2: nat] :
% 5.49/5.92 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.49/5.92 & ( P @ X2 ) ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % ex_nat_less
% 5.49/5.92 thf(fact_3104_finite__maxlen,axiom,
% 5.49/5.92 ! [M7: set_list_VEBT_VEBT] :
% 5.49/5.92 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.49/5.92 => ? [N3: nat] :
% 5.49/5.92 ! [X5: list_VEBT_VEBT] :
% 5.49/5.92 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 5.49/5.92 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_maxlen
% 5.49/5.92 thf(fact_3105_finite__maxlen,axiom,
% 5.49/5.92 ! [M7: set_list_o] :
% 5.49/5.92 ( ( finite_finite_list_o @ M7 )
% 5.49/5.92 => ? [N3: nat] :
% 5.49/5.92 ! [X5: list_o] :
% 5.49/5.92 ( ( member_list_o @ X5 @ M7 )
% 5.49/5.92 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_maxlen
% 5.49/5.92 thf(fact_3106_finite__maxlen,axiom,
% 5.49/5.92 ! [M7: set_list_nat] :
% 5.49/5.92 ( ( finite8100373058378681591st_nat @ M7 )
% 5.49/5.92 => ? [N3: nat] :
% 5.49/5.92 ! [X5: list_nat] :
% 5.49/5.92 ( ( member_list_nat @ X5 @ M7 )
% 5.49/5.92 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_maxlen
% 5.49/5.92 thf(fact_3107_finite__maxlen,axiom,
% 5.49/5.92 ! [M7: set_list_int] :
% 5.49/5.92 ( ( finite3922522038869484883st_int @ M7 )
% 5.49/5.92 => ? [N3: nat] :
% 5.49/5.92 ! [X5: list_int] :
% 5.49/5.92 ( ( member_list_int @ X5 @ M7 )
% 5.49/5.92 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % finite_maxlen
% 5.49/5.92 thf(fact_3108_subset__eq__atLeast0__atMost__finite,axiom,
% 5.49/5.92 ! [N5: set_nat,N: nat] :
% 5.49/5.92 ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.49/5.92 => ( finite_finite_nat @ N5 ) ) ).
% 5.49/5.92
% 5.49/5.92 % subset_eq_atLeast0_atMost_finite
% 5.49/5.92 thf(fact_3109_verit__la__disequality,axiom,
% 5.49/5.92 ! [A: rat,B: rat] :
% 5.49/5.92 ( ( A = B )
% 5.49/5.92 | ~ ( ord_less_eq_rat @ A @ B )
% 5.49/5.92 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_la_disequality
% 5.49/5.92 thf(fact_3110_verit__la__disequality,axiom,
% 5.49/5.92 ! [A: num,B: num] :
% 5.49/5.92 ( ( A = B )
% 5.49/5.92 | ~ ( ord_less_eq_num @ A @ B )
% 5.49/5.92 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_la_disequality
% 5.49/5.92 thf(fact_3111_verit__la__disequality,axiom,
% 5.49/5.92 ! [A: nat,B: nat] :
% 5.49/5.92 ( ( A = B )
% 5.49/5.92 | ~ ( ord_less_eq_nat @ A @ B )
% 5.49/5.92 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_la_disequality
% 5.49/5.92 thf(fact_3112_verit__la__disequality,axiom,
% 5.49/5.92 ! [A: int,B: int] :
% 5.49/5.92 ( ( A = B )
% 5.49/5.92 | ~ ( ord_less_eq_int @ A @ B )
% 5.49/5.92 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.49/5.92
% 5.49/5.92 % verit_la_disequality
% 5.49/5.92 thf(fact_3113_verit__comp__simplify1_I2_J,axiom,
% 5.49/5.92 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(2)
% 5.49/5.92 thf(fact_3114_verit__comp__simplify1_I2_J,axiom,
% 5.49/5.92 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(2)
% 5.49/5.92 thf(fact_3115_verit__comp__simplify1_I2_J,axiom,
% 5.49/5.92 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(2)
% 5.49/5.92 thf(fact_3116_verit__comp__simplify1_I2_J,axiom,
% 5.49/5.92 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(2)
% 5.49/5.92 thf(fact_3117_verit__comp__simplify1_I2_J,axiom,
% 5.49/5.92 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(2)
% 5.49/5.92 thf(fact_3118_verit__comp__simplify1_I1_J,axiom,
% 5.49/5.92 ! [A: real] :
% 5.49/5.92 ~ ( ord_less_real @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(1)
% 5.49/5.92 thf(fact_3119_verit__comp__simplify1_I1_J,axiom,
% 5.49/5.92 ! [A: rat] :
% 5.49/5.92 ~ ( ord_less_rat @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(1)
% 5.49/5.92 thf(fact_3120_verit__comp__simplify1_I1_J,axiom,
% 5.49/5.92 ! [A: num] :
% 5.49/5.92 ~ ( ord_less_num @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(1)
% 5.49/5.92 thf(fact_3121_verit__comp__simplify1_I1_J,axiom,
% 5.49/5.92 ! [A: nat] :
% 5.49/5.92 ~ ( ord_less_nat @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(1)
% 5.49/5.92 thf(fact_3122_verit__comp__simplify1_I1_J,axiom,
% 5.49/5.92 ! [A: int] :
% 5.49/5.92 ~ ( ord_less_int @ A @ A ) ).
% 5.49/5.92
% 5.49/5.92 % verit_comp_simplify1(1)
% 5.49/5.92 thf(fact_3123_not__exp__less__eq__0__int,axiom,
% 5.49/5.92 ! [N: nat] :
% 5.49/5.92 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.49/5.92
% 5.49/5.92 % not_exp_less_eq_0_int
% 5.49/5.92 thf(fact_3124_realpow__pos__nth2,axiom,
% 5.49/5.92 ! [A: real,N: nat] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.92 => ? [R3: real] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.49/5.92 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.49/5.92 = A ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % realpow_pos_nth2
% 5.49/5.92 thf(fact_3125_real__arch__pow__inv,axiom,
% 5.49/5.92 ! [Y2: real,X: real] :
% 5.49/5.92 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.49/5.92 => ( ( ord_less_real @ X @ one_one_real )
% 5.49/5.92 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y2 ) ) ) ).
% 5.49/5.92
% 5.49/5.92 % real_arch_pow_inv
% 5.49/5.92 thf(fact_3126_realpow__pos__nth,axiom,
% 5.49/5.92 ! [N: nat,A: real] :
% 5.49/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.93 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.93 => ? [R3: real] :
% 5.49/5.93 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.49/5.93 & ( ( power_power_real @ R3 @ N )
% 5.49/5.93 = A ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % realpow_pos_nth
% 5.49/5.93 thf(fact_3127_realpow__pos__nth__unique,axiom,
% 5.49/5.93 ! [N: nat,A: real] :
% 5.49/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.93 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.49/5.93 => ? [X3: real] :
% 5.49/5.93 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.49/5.93 & ( ( power_power_real @ X3 @ N )
% 5.49/5.93 = A )
% 5.49/5.93 & ! [Y4: real] :
% 5.49/5.93 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.49/5.93 & ( ( power_power_real @ Y4 @ N )
% 5.49/5.93 = A ) )
% 5.49/5.93 => ( Y4 = X3 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % realpow_pos_nth_unique
% 5.49/5.93 thf(fact_3128_pos__zdiv__mult__2,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.49/5.93 => ( ( 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 ) )
% 5.49/5.93 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % pos_zdiv_mult_2
% 5.49/5.93 thf(fact_3129_neg__zdiv__mult__2,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.49/5.93 => ( ( 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 ) )
% 5.49/5.93 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % neg_zdiv_mult_2
% 5.49/5.93 thf(fact_3130_int__power__div__base,axiom,
% 5.49/5.93 ! [M: nat,K: int] :
% 5.49/5.93 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.93 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.93 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.49/5.93 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % int_power_div_base
% 5.49/5.93 thf(fact_3131_verit__comp__simplify1_I3_J,axiom,
% 5.49/5.93 ! [B5: real,A5: real] :
% 5.49/5.93 ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
% 5.49/5.93 = ( ord_less_real @ A5 @ B5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_comp_simplify1(3)
% 5.49/5.93 thf(fact_3132_verit__comp__simplify1_I3_J,axiom,
% 5.49/5.93 ! [B5: rat,A5: rat] :
% 5.49/5.93 ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 5.49/5.93 = ( ord_less_rat @ A5 @ B5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_comp_simplify1(3)
% 5.49/5.93 thf(fact_3133_verit__comp__simplify1_I3_J,axiom,
% 5.49/5.93 ! [B5: num,A5: num] :
% 5.49/5.93 ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 5.49/5.93 = ( ord_less_num @ A5 @ B5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_comp_simplify1(3)
% 5.49/5.93 thf(fact_3134_verit__comp__simplify1_I3_J,axiom,
% 5.49/5.93 ! [B5: nat,A5: nat] :
% 5.49/5.93 ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 5.49/5.93 = ( ord_less_nat @ A5 @ B5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_comp_simplify1(3)
% 5.49/5.93 thf(fact_3135_verit__comp__simplify1_I3_J,axiom,
% 5.49/5.93 ! [B5: int,A5: int] :
% 5.49/5.93 ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 5.49/5.93 = ( ord_less_int @ A5 @ B5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_comp_simplify1(3)
% 5.49/5.93 thf(fact_3136_verit__sum__simplify,axiom,
% 5.49/5.93 ! [A: complex] :
% 5.49/5.93 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.49/5.93 = A ) ).
% 5.49/5.93
% 5.49/5.93 % verit_sum_simplify
% 5.49/5.93 thf(fact_3137_verit__sum__simplify,axiom,
% 5.49/5.93 ! [A: real] :
% 5.49/5.93 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.49/5.93 = A ) ).
% 5.49/5.93
% 5.49/5.93 % verit_sum_simplify
% 5.49/5.93 thf(fact_3138_verit__sum__simplify,axiom,
% 5.49/5.93 ! [A: rat] :
% 5.49/5.93 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.49/5.93 = A ) ).
% 5.49/5.93
% 5.49/5.93 % verit_sum_simplify
% 5.49/5.93 thf(fact_3139_verit__sum__simplify,axiom,
% 5.49/5.93 ! [A: nat] :
% 5.49/5.93 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.49/5.93 = A ) ).
% 5.49/5.93
% 5.49/5.93 % verit_sum_simplify
% 5.49/5.93 thf(fact_3140_verit__sum__simplify,axiom,
% 5.49/5.93 ! [A: int] :
% 5.49/5.93 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.49/5.93 = A ) ).
% 5.49/5.93
% 5.49/5.93 % verit_sum_simplify
% 5.49/5.93 thf(fact_3141_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_real,A: real] :
% 5.49/5.93 ( ( finite_finite_real @ A2 )
% 5.49/5.93 => ( ( member_real @ A @ A2 )
% 5.49/5.93 => ? [X3: real] :
% 5.49/5.93 ( ( member_real @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_real @ X3 @ A )
% 5.49/5.93 & ! [Xa: real] :
% 5.49/5.93 ( ( member_real @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3142_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_set_int,A: set_int] :
% 5.49/5.93 ( ( finite6197958912794628473et_int @ A2 )
% 5.49/5.93 => ( ( member_set_int @ A @ A2 )
% 5.49/5.93 => ? [X3: set_int] :
% 5.49/5.93 ( ( member_set_int @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_set_int @ X3 @ A )
% 5.49/5.93 & ! [Xa: set_int] :
% 5.49/5.93 ( ( member_set_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3143_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_rat,A: rat] :
% 5.49/5.93 ( ( finite_finite_rat @ A2 )
% 5.49/5.93 => ( ( member_rat @ A @ A2 )
% 5.49/5.93 => ? [X3: rat] :
% 5.49/5.93 ( ( member_rat @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_rat @ X3 @ A )
% 5.49/5.93 & ! [Xa: rat] :
% 5.49/5.93 ( ( member_rat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3144_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_num,A: num] :
% 5.49/5.93 ( ( finite_finite_num @ A2 )
% 5.49/5.93 => ( ( member_num @ A @ A2 )
% 5.49/5.93 => ? [X3: num] :
% 5.49/5.93 ( ( member_num @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_num @ X3 @ A )
% 5.49/5.93 & ! [Xa: num] :
% 5.49/5.93 ( ( member_num @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3145_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_nat,A: nat] :
% 5.49/5.93 ( ( finite_finite_nat @ A2 )
% 5.49/5.93 => ( ( member_nat @ A @ A2 )
% 5.49/5.93 => ? [X3: nat] :
% 5.49/5.93 ( ( member_nat @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_nat @ X3 @ A )
% 5.49/5.93 & ! [Xa: nat] :
% 5.49/5.93 ( ( member_nat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3146_finite__has__minimal2,axiom,
% 5.49/5.93 ! [A2: set_int,A: int] :
% 5.49/5.93 ( ( finite_finite_int @ A2 )
% 5.49/5.93 => ( ( member_int @ A @ A2 )
% 5.49/5.93 => ? [X3: int] :
% 5.49/5.93 ( ( member_int @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_int @ X3 @ A )
% 5.49/5.93 & ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal2
% 5.49/5.93 thf(fact_3147_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_real,A: real] :
% 5.49/5.93 ( ( finite_finite_real @ A2 )
% 5.49/5.93 => ( ( member_real @ A @ A2 )
% 5.49/5.93 => ? [X3: real] :
% 5.49/5.93 ( ( member_real @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_real @ A @ X3 )
% 5.49/5.93 & ! [Xa: real] :
% 5.49/5.93 ( ( member_real @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3148_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_set_int,A: set_int] :
% 5.49/5.93 ( ( finite6197958912794628473et_int @ A2 )
% 5.49/5.93 => ( ( member_set_int @ A @ A2 )
% 5.49/5.93 => ? [X3: set_int] :
% 5.49/5.93 ( ( member_set_int @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_set_int @ A @ X3 )
% 5.49/5.93 & ! [Xa: set_int] :
% 5.49/5.93 ( ( member_set_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3149_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_rat,A: rat] :
% 5.49/5.93 ( ( finite_finite_rat @ A2 )
% 5.49/5.93 => ( ( member_rat @ A @ A2 )
% 5.49/5.93 => ? [X3: rat] :
% 5.49/5.93 ( ( member_rat @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_rat @ A @ X3 )
% 5.49/5.93 & ! [Xa: rat] :
% 5.49/5.93 ( ( member_rat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3150_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_num,A: num] :
% 5.49/5.93 ( ( finite_finite_num @ A2 )
% 5.49/5.93 => ( ( member_num @ A @ A2 )
% 5.49/5.93 => ? [X3: num] :
% 5.49/5.93 ( ( member_num @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_num @ A @ X3 )
% 5.49/5.93 & ! [Xa: num] :
% 5.49/5.93 ( ( member_num @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3151_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_nat,A: nat] :
% 5.49/5.93 ( ( finite_finite_nat @ A2 )
% 5.49/5.93 => ( ( member_nat @ A @ A2 )
% 5.49/5.93 => ? [X3: nat] :
% 5.49/5.93 ( ( member_nat @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_nat @ A @ X3 )
% 5.49/5.93 & ! [Xa: nat] :
% 5.49/5.93 ( ( member_nat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3152_finite__has__maximal2,axiom,
% 5.49/5.93 ! [A2: set_int,A: int] :
% 5.49/5.93 ( ( finite_finite_int @ A2 )
% 5.49/5.93 => ( ( member_int @ A @ A2 )
% 5.49/5.93 => ? [X3: int] :
% 5.49/5.93 ( ( member_int @ X3 @ A2 )
% 5.49/5.93 & ( ord_less_eq_int @ A @ X3 )
% 5.49/5.93 & ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal2
% 5.49/5.93 thf(fact_3153_verit__eq__simplify_I10_J,axiom,
% 5.49/5.93 ! [X22: num] :
% 5.49/5.93 ( one
% 5.49/5.93 != ( bit0 @ X22 ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_eq_simplify(10)
% 5.49/5.93 thf(fact_3154_rev__finite__subset,axiom,
% 5.49/5.93 ! [B4: set_nat,A2: set_nat] :
% 5.49/5.93 ( ( finite_finite_nat @ B4 )
% 5.49/5.93 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.49/5.93 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % rev_finite_subset
% 5.49/5.93 thf(fact_3155_rev__finite__subset,axiom,
% 5.49/5.93 ! [B4: set_complex,A2: set_complex] :
% 5.49/5.93 ( ( finite3207457112153483333omplex @ B4 )
% 5.49/5.93 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.49/5.93 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % rev_finite_subset
% 5.49/5.93 thf(fact_3156_rev__finite__subset,axiom,
% 5.49/5.93 ! [B4: set_int,A2: set_int] :
% 5.49/5.93 ( ( finite_finite_int @ B4 )
% 5.49/5.93 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.49/5.93 => ( finite_finite_int @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % rev_finite_subset
% 5.49/5.93 thf(fact_3157_infinite__super,axiom,
% 5.49/5.93 ! [S3: set_nat,T3: set_nat] :
% 5.49/5.93 ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.49/5.93 => ( ~ ( finite_finite_nat @ S3 )
% 5.49/5.93 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % infinite_super
% 5.49/5.93 thf(fact_3158_infinite__super,axiom,
% 5.49/5.93 ! [S3: set_complex,T3: set_complex] :
% 5.49/5.93 ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.49/5.93 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 5.49/5.93 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % infinite_super
% 5.49/5.93 thf(fact_3159_infinite__super,axiom,
% 5.49/5.93 ! [S3: set_int,T3: set_int] :
% 5.49/5.93 ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.49/5.93 => ( ~ ( finite_finite_int @ S3 )
% 5.49/5.93 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % infinite_super
% 5.49/5.93 thf(fact_3160_finite__subset,axiom,
% 5.49/5.93 ! [A2: set_nat,B4: set_nat] :
% 5.49/5.93 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.49/5.93 => ( ( finite_finite_nat @ B4 )
% 5.49/5.93 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_subset
% 5.49/5.93 thf(fact_3161_finite__subset,axiom,
% 5.49/5.93 ! [A2: set_complex,B4: set_complex] :
% 5.49/5.93 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.49/5.93 => ( ( finite3207457112153483333omplex @ B4 )
% 5.49/5.93 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_subset
% 5.49/5.93 thf(fact_3162_finite__subset,axiom,
% 5.49/5.93 ! [A2: set_int,B4: set_int] :
% 5.49/5.93 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.49/5.93 => ( ( finite_finite_int @ B4 )
% 5.49/5.93 => ( finite_finite_int @ A2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_subset
% 5.49/5.93 thf(fact_3163_max_OcoboundedI2,axiom,
% 5.49/5.93 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.49/5.93 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI2
% 5.49/5.93 thf(fact_3164_max_OcoboundedI2,axiom,
% 5.49/5.93 ! [C: rat,B: rat,A: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ C @ B )
% 5.49/5.93 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI2
% 5.49/5.93 thf(fact_3165_max_OcoboundedI2,axiom,
% 5.49/5.93 ! [C: num,B: num,A: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ C @ B )
% 5.49/5.93 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI2
% 5.49/5.93 thf(fact_3166_max_OcoboundedI2,axiom,
% 5.49/5.93 ! [C: nat,B: nat,A: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ C @ B )
% 5.49/5.93 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI2
% 5.49/5.93 thf(fact_3167_max_OcoboundedI2,axiom,
% 5.49/5.93 ! [C: int,B: int,A: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ C @ B )
% 5.49/5.93 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI2
% 5.49/5.93 thf(fact_3168_max_OcoboundedI1,axiom,
% 5.49/5.93 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.49/5.93 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI1
% 5.49/5.93 thf(fact_3169_max_OcoboundedI1,axiom,
% 5.49/5.93 ! [C: rat,A: rat,B: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ C @ A )
% 5.49/5.93 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI1
% 5.49/5.93 thf(fact_3170_max_OcoboundedI1,axiom,
% 5.49/5.93 ! [C: num,A: num,B: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ C @ A )
% 5.49/5.93 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI1
% 5.49/5.93 thf(fact_3171_max_OcoboundedI1,axiom,
% 5.49/5.93 ! [C: nat,A: nat,B: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.93 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI1
% 5.49/5.93 thf(fact_3172_max_OcoboundedI1,axiom,
% 5.49/5.93 ! [C: int,A: int,B: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ C @ A )
% 5.49/5.93 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.coboundedI1
% 5.49/5.93 thf(fact_3173_max_Oabsorb__iff2,axiom,
% 5.49/5.93 ( ord_le2932123472753598470d_enat
% 5.49/5.93 = ( ^ [A4: extended_enat,B3: extended_enat] :
% 5.49/5.93 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.49/5.93 = B3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff2
% 5.49/5.93 thf(fact_3174_max_Oabsorb__iff2,axiom,
% 5.49/5.93 ( ord_less_eq_rat
% 5.49/5.93 = ( ^ [A4: rat,B3: rat] :
% 5.49/5.93 ( ( ord_max_rat @ A4 @ B3 )
% 5.49/5.93 = B3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff2
% 5.49/5.93 thf(fact_3175_max_Oabsorb__iff2,axiom,
% 5.49/5.93 ( ord_less_eq_num
% 5.49/5.93 = ( ^ [A4: num,B3: num] :
% 5.49/5.93 ( ( ord_max_num @ A4 @ B3 )
% 5.49/5.93 = B3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff2
% 5.49/5.93 thf(fact_3176_max_Oabsorb__iff2,axiom,
% 5.49/5.93 ( ord_less_eq_nat
% 5.49/5.93 = ( ^ [A4: nat,B3: nat] :
% 5.49/5.93 ( ( ord_max_nat @ A4 @ B3 )
% 5.49/5.93 = B3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff2
% 5.49/5.93 thf(fact_3177_max_Oabsorb__iff2,axiom,
% 5.49/5.93 ( ord_less_eq_int
% 5.49/5.93 = ( ^ [A4: int,B3: int] :
% 5.49/5.93 ( ( ord_max_int @ A4 @ B3 )
% 5.49/5.93 = B3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff2
% 5.49/5.93 thf(fact_3178_max_Oabsorb__iff1,axiom,
% 5.49/5.93 ( ord_le2932123472753598470d_enat
% 5.49/5.93 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.49/5.93 ( ( ord_ma741700101516333627d_enat @ A4 @ B3 )
% 5.49/5.93 = A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff1
% 5.49/5.93 thf(fact_3179_max_Oabsorb__iff1,axiom,
% 5.49/5.93 ( ord_less_eq_rat
% 5.49/5.93 = ( ^ [B3: rat,A4: rat] :
% 5.49/5.93 ( ( ord_max_rat @ A4 @ B3 )
% 5.49/5.93 = A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff1
% 5.49/5.93 thf(fact_3180_max_Oabsorb__iff1,axiom,
% 5.49/5.93 ( ord_less_eq_num
% 5.49/5.93 = ( ^ [B3: num,A4: num] :
% 5.49/5.93 ( ( ord_max_num @ A4 @ B3 )
% 5.49/5.93 = A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff1
% 5.49/5.93 thf(fact_3181_max_Oabsorb__iff1,axiom,
% 5.49/5.93 ( ord_less_eq_nat
% 5.49/5.93 = ( ^ [B3: nat,A4: nat] :
% 5.49/5.93 ( ( ord_max_nat @ A4 @ B3 )
% 5.49/5.93 = A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff1
% 5.49/5.93 thf(fact_3182_max_Oabsorb__iff1,axiom,
% 5.49/5.93 ( ord_less_eq_int
% 5.49/5.93 = ( ^ [B3: int,A4: int] :
% 5.49/5.93 ( ( ord_max_int @ A4 @ B3 )
% 5.49/5.93 = A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.absorb_iff1
% 5.49/5.93 thf(fact_3183_le__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 5.49/5.93 | ( ord_le2932123472753598470d_enat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % le_max_iff_disj
% 5.49/5.93 thf(fact_3184_le__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_eq_rat @ Z @ X )
% 5.49/5.93 | ( ord_less_eq_rat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % le_max_iff_disj
% 5.49/5.93 thf(fact_3185_le__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: num,X: num,Y2: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_eq_num @ Z @ X )
% 5.49/5.93 | ( ord_less_eq_num @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % le_max_iff_disj
% 5.49/5.93 thf(fact_3186_le__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: nat,X: nat,Y2: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_eq_nat @ Z @ X )
% 5.49/5.93 | ( ord_less_eq_nat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % le_max_iff_disj
% 5.49/5.93 thf(fact_3187_le__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: int,X: int,Y2: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_eq_int @ Z @ X )
% 5.49/5.93 | ( ord_less_eq_int @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % le_max_iff_disj
% 5.49/5.93 thf(fact_3188_max_Ocobounded2,axiom,
% 5.49/5.93 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded2
% 5.49/5.93 thf(fact_3189_max_Ocobounded2,axiom,
% 5.49/5.93 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded2
% 5.49/5.93 thf(fact_3190_max_Ocobounded2,axiom,
% 5.49/5.93 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded2
% 5.49/5.93 thf(fact_3191_max_Ocobounded2,axiom,
% 5.49/5.93 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded2
% 5.49/5.93 thf(fact_3192_max_Ocobounded2,axiom,
% 5.49/5.93 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded2
% 5.49/5.93 thf(fact_3193_max_Ocobounded1,axiom,
% 5.49/5.93 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded1
% 5.49/5.93 thf(fact_3194_max_Ocobounded1,axiom,
% 5.49/5.93 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded1
% 5.49/5.93 thf(fact_3195_max_Ocobounded1,axiom,
% 5.49/5.93 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded1
% 5.49/5.93 thf(fact_3196_max_Ocobounded1,axiom,
% 5.49/5.93 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded1
% 5.49/5.93 thf(fact_3197_max_Ocobounded1,axiom,
% 5.49/5.93 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.cobounded1
% 5.49/5.93 thf(fact_3198_max_Oorder__iff,axiom,
% 5.49/5.93 ( ord_le2932123472753598470d_enat
% 5.49/5.93 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.49/5.93 ( A4
% 5.49/5.93 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.order_iff
% 5.49/5.93 thf(fact_3199_max_Oorder__iff,axiom,
% 5.49/5.93 ( ord_less_eq_rat
% 5.49/5.93 = ( ^ [B3: rat,A4: rat] :
% 5.49/5.93 ( A4
% 5.49/5.93 = ( ord_max_rat @ A4 @ B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.order_iff
% 5.49/5.93 thf(fact_3200_max_Oorder__iff,axiom,
% 5.49/5.93 ( ord_less_eq_num
% 5.49/5.93 = ( ^ [B3: num,A4: num] :
% 5.49/5.93 ( A4
% 5.49/5.93 = ( ord_max_num @ A4 @ B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.order_iff
% 5.49/5.93 thf(fact_3201_max_Oorder__iff,axiom,
% 5.49/5.93 ( ord_less_eq_nat
% 5.49/5.93 = ( ^ [B3: nat,A4: nat] :
% 5.49/5.93 ( A4
% 5.49/5.93 = ( ord_max_nat @ A4 @ B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.order_iff
% 5.49/5.93 thf(fact_3202_max_Oorder__iff,axiom,
% 5.49/5.93 ( ord_less_eq_int
% 5.49/5.93 = ( ^ [B3: int,A4: int] :
% 5.49/5.93 ( A4
% 5.49/5.93 = ( ord_max_int @ A4 @ B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.order_iff
% 5.49/5.93 thf(fact_3203_max_OboundedI,axiom,
% 5.49/5.93 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.49/5.93 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.49/5.93 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedI
% 5.49/5.93 thf(fact_3204_max_OboundedI,axiom,
% 5.49/5.93 ! [B: rat,A: rat,C: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.93 => ( ( ord_less_eq_rat @ C @ A )
% 5.49/5.93 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedI
% 5.49/5.93 thf(fact_3205_max_OboundedI,axiom,
% 5.49/5.93 ! [B: num,A: num,C: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ B @ A )
% 5.49/5.93 => ( ( ord_less_eq_num @ C @ A )
% 5.49/5.93 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedI
% 5.49/5.93 thf(fact_3206_max_OboundedI,axiom,
% 5.49/5.93 ! [B: nat,A: nat,C: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.93 => ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.93 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedI
% 5.49/5.93 thf(fact_3207_max_OboundedI,axiom,
% 5.49/5.93 ! [B: int,A: int,C: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.93 => ( ( ord_less_eq_int @ C @ A )
% 5.49/5.93 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedI
% 5.49/5.93 thf(fact_3208_max_OboundedE,axiom,
% 5.49/5.93 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.49/5.93 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedE
% 5.49/5.93 thf(fact_3209_max_OboundedE,axiom,
% 5.49/5.93 ! [B: rat,C: rat,A: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.93 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedE
% 5.49/5.93 thf(fact_3210_max_OboundedE,axiom,
% 5.49/5.93 ! [B: num,C: num,A: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.49/5.93 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedE
% 5.49/5.93 thf(fact_3211_max_OboundedE,axiom,
% 5.49/5.93 ! [B: nat,C: nat,A: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.93 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedE
% 5.49/5.93 thf(fact_3212_max_OboundedE,axiom,
% 5.49/5.93 ! [B: int,C: int,A: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.49/5.93 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.boundedE
% 5.49/5.93 thf(fact_3213_max_OorderI,axiom,
% 5.49/5.93 ! [A: extended_enat,B: extended_enat] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.49/5.93 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderI
% 5.49/5.93 thf(fact_3214_max_OorderI,axiom,
% 5.49/5.93 ! [A: rat,B: rat] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( ord_max_rat @ A @ B ) )
% 5.49/5.93 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderI
% 5.49/5.93 thf(fact_3215_max_OorderI,axiom,
% 5.49/5.93 ! [A: num,B: num] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( ord_max_num @ A @ B ) )
% 5.49/5.93 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderI
% 5.49/5.93 thf(fact_3216_max_OorderI,axiom,
% 5.49/5.93 ! [A: nat,B: nat] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( ord_max_nat @ A @ B ) )
% 5.49/5.93 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderI
% 5.49/5.93 thf(fact_3217_max_OorderI,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( ord_max_int @ A @ B ) )
% 5.49/5.93 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderI
% 5.49/5.93 thf(fact_3218_max_OorderE,axiom,
% 5.49/5.93 ! [B: extended_enat,A: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.49/5.93 => ( A
% 5.49/5.93 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderE
% 5.49/5.93 thf(fact_3219_max_OorderE,axiom,
% 5.49/5.93 ! [B: rat,A: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ B @ A )
% 5.49/5.93 => ( A
% 5.49/5.93 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderE
% 5.49/5.93 thf(fact_3220_max_OorderE,axiom,
% 5.49/5.93 ! [B: num,A: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ B @ A )
% 5.49/5.93 => ( A
% 5.49/5.93 = ( ord_max_num @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderE
% 5.49/5.93 thf(fact_3221_max_OorderE,axiom,
% 5.49/5.93 ! [B: nat,A: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ B @ A )
% 5.49/5.93 => ( A
% 5.49/5.93 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderE
% 5.49/5.93 thf(fact_3222_max_OorderE,axiom,
% 5.49/5.93 ! [B: int,A: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ B @ A )
% 5.49/5.93 => ( A
% 5.49/5.93 = ( ord_max_int @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.orderE
% 5.49/5.93 thf(fact_3223_max_Omono,axiom,
% 5.49/5.93 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.49/5.93 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.49/5.93 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.49/5.93 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.mono
% 5.49/5.93 thf(fact_3224_max_Omono,axiom,
% 5.49/5.93 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.49/5.93 ( ( ord_less_eq_rat @ C @ A )
% 5.49/5.93 => ( ( ord_less_eq_rat @ D @ B )
% 5.49/5.93 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.mono
% 5.49/5.93 thf(fact_3225_max_Omono,axiom,
% 5.49/5.93 ! [C: num,A: num,D: num,B: num] :
% 5.49/5.93 ( ( ord_less_eq_num @ C @ A )
% 5.49/5.93 => ( ( ord_less_eq_num @ D @ B )
% 5.49/5.93 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.mono
% 5.49/5.93 thf(fact_3226_max_Omono,axiom,
% 5.49/5.93 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.49/5.93 ( ( ord_less_eq_nat @ C @ A )
% 5.49/5.93 => ( ( ord_less_eq_nat @ D @ B )
% 5.49/5.93 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.mono
% 5.49/5.93 thf(fact_3227_max_Omono,axiom,
% 5.49/5.93 ! [C: int,A: int,D: int,B: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ C @ A )
% 5.49/5.93 => ( ( ord_less_eq_int @ D @ B )
% 5.49/5.93 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.mono
% 5.49/5.93 thf(fact_3228_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: extended_enat,X: extended_enat,Y2: extended_enat] :
% 5.49/5.93 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 5.49/5.93 | ( ord_le72135733267957522d_enat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3229_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: real,X: real,Y2: real] :
% 5.49/5.93 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_real @ Z @ X )
% 5.49/5.93 | ( ord_less_real @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3230_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: rat,X: rat,Y2: rat] :
% 5.49/5.93 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_rat @ Z @ X )
% 5.49/5.93 | ( ord_less_rat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3231_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: num,X: num,Y2: num] :
% 5.49/5.93 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_num @ Z @ X )
% 5.49/5.93 | ( ord_less_num @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3232_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: nat,X: nat,Y2: nat] :
% 5.49/5.93 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_nat @ Z @ X )
% 5.49/5.93 | ( ord_less_nat @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3233_less__max__iff__disj,axiom,
% 5.49/5.93 ! [Z: int,X: int,Y2: int] :
% 5.49/5.93 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y2 ) )
% 5.49/5.93 = ( ( ord_less_int @ Z @ X )
% 5.49/5.93 | ( ord_less_int @ Z @ Y2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % less_max_iff_disj
% 5.49/5.93 thf(fact_3234_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.49/5.93 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.49/5.93 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3235_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: real,C: real,A: real] :
% 5.49/5.93 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_real @ B @ A )
% 5.49/5.93 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3236_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: rat,C: rat,A: rat] :
% 5.49/5.93 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_rat @ B @ A )
% 5.49/5.93 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3237_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: num,C: num,A: num] :
% 5.49/5.93 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_num @ B @ A )
% 5.49/5.93 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3238_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: nat,C: nat,A: nat] :
% 5.49/5.93 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_nat @ B @ A )
% 5.49/5.93 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3239_max_Ostrict__boundedE,axiom,
% 5.49/5.93 ! [B: int,C: int,A: int] :
% 5.49/5.93 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.49/5.93 => ~ ( ( ord_less_int @ B @ A )
% 5.49/5.93 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_boundedE
% 5.49/5.93 thf(fact_3240_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_le72135733267957522d_enat
% 5.49/5.93 = ( ^ [B3: extended_enat,A4: extended_enat] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_ma741700101516333627d_enat @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3241_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_less_real
% 5.49/5.93 = ( ^ [B3: real,A4: real] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_max_real @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3242_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_less_rat
% 5.49/5.93 = ( ^ [B3: rat,A4: rat] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_max_rat @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3243_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_less_num
% 5.49/5.93 = ( ^ [B3: num,A4: num] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_max_num @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3244_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_less_nat
% 5.49/5.93 = ( ^ [B3: nat,A4: nat] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_max_nat @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3245_max_Ostrict__order__iff,axiom,
% 5.49/5.93 ( ord_less_int
% 5.49/5.93 = ( ^ [B3: int,A4: int] :
% 5.49/5.93 ( ( A4
% 5.49/5.93 = ( ord_max_int @ A4 @ B3 ) )
% 5.49/5.93 & ( A4 != B3 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_order_iff
% 5.49/5.93 thf(fact_3246_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.49/5.93 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.49/5.93 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3247_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: real,A: real,B: real] :
% 5.49/5.93 ( ( ord_less_real @ C @ A )
% 5.49/5.93 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3248_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: rat,A: rat,B: rat] :
% 5.49/5.93 ( ( ord_less_rat @ C @ A )
% 5.49/5.93 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3249_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: num,A: num,B: num] :
% 5.49/5.93 ( ( ord_less_num @ C @ A )
% 5.49/5.93 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3250_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: nat,A: nat,B: nat] :
% 5.49/5.93 ( ( ord_less_nat @ C @ A )
% 5.49/5.93 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3251_max_Ostrict__coboundedI1,axiom,
% 5.49/5.93 ! [C: int,A: int,B: int] :
% 5.49/5.93 ( ( ord_less_int @ C @ A )
% 5.49/5.93 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI1
% 5.49/5.93 thf(fact_3252_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.49/5.93 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.49/5.93 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3253_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: real,B: real,A: real] :
% 5.49/5.93 ( ( ord_less_real @ C @ B )
% 5.49/5.93 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3254_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: rat,B: rat,A: rat] :
% 5.49/5.93 ( ( ord_less_rat @ C @ B )
% 5.49/5.93 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3255_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: num,B: num,A: num] :
% 5.49/5.93 ( ( ord_less_num @ C @ B )
% 5.49/5.93 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3256_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: nat,B: nat,A: nat] :
% 5.49/5.93 ( ( ord_less_nat @ C @ B )
% 5.49/5.93 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3257_max_Ostrict__coboundedI2,axiom,
% 5.49/5.93 ! [C: int,B: int,A: int] :
% 5.49/5.93 ( ( ord_less_int @ C @ B )
% 5.49/5.93 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max.strict_coboundedI2
% 5.49/5.93 thf(fact_3258_finite__image__set,axiom,
% 5.49/5.93 ! [P: real > $o,F: real > real] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3259_finite__image__set,axiom,
% 5.49/5.93 ! [P: real > $o,F: real > nat] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3260_finite__image__set,axiom,
% 5.49/5.93 ! [P: real > $o,F: real > int] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [Uu2: int] :
% 5.49/5.93 ? [X2: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3261_finite__image__set,axiom,
% 5.49/5.93 ! [P: real > $o,F: real > complex] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( finite3207457112153483333omplex
% 5.49/5.93 @ ( collect_complex
% 5.49/5.93 @ ^ [Uu2: complex] :
% 5.49/5.93 ? [X2: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3262_finite__image__set,axiom,
% 5.49/5.93 ! [P: nat > $o,F: nat > real] :
% 5.49/5.93 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3263_finite__image__set,axiom,
% 5.49/5.93 ! [P: nat > $o,F: nat > nat] :
% 5.49/5.93 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3264_finite__image__set,axiom,
% 5.49/5.93 ! [P: nat > $o,F: nat > int] :
% 5.49/5.93 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.93 => ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [Uu2: int] :
% 5.49/5.93 ? [X2: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3265_finite__image__set,axiom,
% 5.49/5.93 ! [P: nat > $o,F: nat > complex] :
% 5.49/5.93 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.49/5.93 => ( finite3207457112153483333omplex
% 5.49/5.93 @ ( collect_complex
% 5.49/5.93 @ ^ [Uu2: complex] :
% 5.49/5.93 ? [X2: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3266_finite__image__set,axiom,
% 5.49/5.93 ! [P: int > $o,F: int > real] :
% 5.49/5.93 ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: int] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3267_finite__image__set,axiom,
% 5.49/5.93 ! [P: int > $o,F: int > nat] :
% 5.49/5.93 ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: int] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 ) )
% 5.49/5.93 & ( P @ X2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set
% 5.49/5.93 thf(fact_3268_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: real > $o,F: real > real > real] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: real,Y: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3269_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: real > $o,F: real > real > nat] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: real,Y: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3270_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: real > $o,F: real > real > int] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.49/5.93 => ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [Uu2: int] :
% 5.49/5.93 ? [X2: real,Y: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3271_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: real > $o,F: real > real > complex] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_real @ ( collect_real @ Q ) )
% 5.49/5.93 => ( finite3207457112153483333omplex
% 5.49/5.93 @ ( collect_complex
% 5.49/5.93 @ ^ [Uu2: complex] :
% 5.49/5.93 ? [X2: real,Y: real] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3272_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: nat > $o,F: real > nat > real] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: real,Y: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3273_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: nat > $o,F: real > nat > nat] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: real,Y: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3274_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: nat > $o,F: real > nat > int] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.49/5.93 => ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [Uu2: int] :
% 5.49/5.93 ? [X2: real,Y: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3275_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: nat > $o,F: real > nat > complex] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_nat @ ( collect_nat @ Q ) )
% 5.49/5.93 => ( finite3207457112153483333omplex
% 5.49/5.93 @ ( collect_complex
% 5.49/5.93 @ ^ [Uu2: complex] :
% 5.49/5.93 ? [X2: real,Y: nat] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3276_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: int > $o,F: real > int > real] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_int @ ( collect_int @ Q ) )
% 5.49/5.93 => ( finite_finite_real
% 5.49/5.93 @ ( collect_real
% 5.49/5.93 @ ^ [Uu2: real] :
% 5.49/5.93 ? [X2: real,Y: int] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3277_finite__image__set2,axiom,
% 5.49/5.93 ! [P: real > $o,Q: int > $o,F: real > int > nat] :
% 5.49/5.93 ( ( finite_finite_real @ ( collect_real @ P ) )
% 5.49/5.93 => ( ( finite_finite_int @ ( collect_int @ Q ) )
% 5.49/5.93 => ( finite_finite_nat
% 5.49/5.93 @ ( collect_nat
% 5.49/5.93 @ ^ [Uu2: nat] :
% 5.49/5.93 ? [X2: real,Y: int] :
% 5.49/5.93 ( ( Uu2
% 5.49/5.93 = ( F @ X2 @ Y ) )
% 5.49/5.93 & ( P @ X2 )
% 5.49/5.93 & ( Q @ Y ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_image_set2
% 5.49/5.93 thf(fact_3278_max__def__raw,axiom,
% 5.49/5.93 ( ord_ma741700101516333627d_enat
% 5.49/5.93 = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3279_max__def__raw,axiom,
% 5.49/5.93 ( ord_max_set_int
% 5.49/5.93 = ( ^ [A4: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3280_max__def__raw,axiom,
% 5.49/5.93 ( ord_max_rat
% 5.49/5.93 = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3281_max__def__raw,axiom,
% 5.49/5.93 ( ord_max_num
% 5.49/5.93 = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3282_max__def__raw,axiom,
% 5.49/5.93 ( ord_max_nat
% 5.49/5.93 = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3283_max__def__raw,axiom,
% 5.49/5.93 ( ord_max_int
% 5.49/5.93 = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % max_def_raw
% 5.49/5.93 thf(fact_3284_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_real] :
% 5.49/5.93 ( ( finite_finite_real @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_real )
% 5.49/5.93 => ? [X3: real] :
% 5.49/5.93 ( ( member_real @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: real] :
% 5.49/5.93 ( ( member_real @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3285_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_set_int] :
% 5.49/5.93 ( ( finite6197958912794628473et_int @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_set_int )
% 5.49/5.93 => ? [X3: set_int] :
% 5.49/5.93 ( ( member_set_int @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: set_int] :
% 5.49/5.93 ( ( member_set_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3286_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_rat] :
% 5.49/5.93 ( ( finite_finite_rat @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_rat )
% 5.49/5.93 => ? [X3: rat] :
% 5.49/5.93 ( ( member_rat @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: rat] :
% 5.49/5.93 ( ( member_rat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3287_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_num] :
% 5.49/5.93 ( ( finite_finite_num @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_num )
% 5.49/5.93 => ? [X3: num] :
% 5.49/5.93 ( ( member_num @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: num] :
% 5.49/5.93 ( ( member_num @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3288_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_nat] :
% 5.49/5.93 ( ( finite_finite_nat @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_nat )
% 5.49/5.93 => ? [X3: nat] :
% 5.49/5.93 ( ( member_nat @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: nat] :
% 5.49/5.93 ( ( member_nat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3289_finite__has__minimal,axiom,
% 5.49/5.93 ! [A2: set_int] :
% 5.49/5.93 ( ( finite_finite_int @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_int )
% 5.49/5.93 => ? [X3: int] :
% 5.49/5.93 ( ( member_int @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_minimal
% 5.49/5.93 thf(fact_3290_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_real] :
% 5.49/5.93 ( ( finite_finite_real @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_real )
% 5.49/5.93 => ? [X3: real] :
% 5.49/5.93 ( ( member_real @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: real] :
% 5.49/5.93 ( ( member_real @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3291_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_set_int] :
% 5.49/5.93 ( ( finite6197958912794628473et_int @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_set_int )
% 5.49/5.93 => ? [X3: set_int] :
% 5.49/5.93 ( ( member_set_int @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: set_int] :
% 5.49/5.93 ( ( member_set_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3292_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_rat] :
% 5.49/5.93 ( ( finite_finite_rat @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_rat )
% 5.49/5.93 => ? [X3: rat] :
% 5.49/5.93 ( ( member_rat @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: rat] :
% 5.49/5.93 ( ( member_rat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3293_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_num] :
% 5.49/5.93 ( ( finite_finite_num @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_num )
% 5.49/5.93 => ? [X3: num] :
% 5.49/5.93 ( ( member_num @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: num] :
% 5.49/5.93 ( ( member_num @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3294_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_nat] :
% 5.49/5.93 ( ( finite_finite_nat @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_nat )
% 5.49/5.93 => ? [X3: nat] :
% 5.49/5.93 ( ( member_nat @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: nat] :
% 5.49/5.93 ( ( member_nat @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3295_finite__has__maximal,axiom,
% 5.49/5.93 ! [A2: set_int] :
% 5.49/5.93 ( ( finite_finite_int @ A2 )
% 5.49/5.93 => ( ( A2 != bot_bot_set_int )
% 5.49/5.93 => ? [X3: int] :
% 5.49/5.93 ( ( member_int @ X3 @ A2 )
% 5.49/5.93 & ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ A2 )
% 5.49/5.93 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.49/5.93 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_has_maximal
% 5.49/5.93 thf(fact_3296_div__less__mono,axiom,
% 5.49/5.93 ! [A2: nat,B4: nat,N: nat] :
% 5.49/5.93 ( ( ord_less_nat @ A2 @ B4 )
% 5.49/5.93 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.49/5.93 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.49/5.93 = zero_zero_nat )
% 5.49/5.93 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.49/5.93 = zero_zero_nat )
% 5.49/5.93 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % div_less_mono
% 5.49/5.93 thf(fact_3297_set__bit__Suc,axiom,
% 5.49/5.93 ! [N: nat,A: code_integer] :
% 5.49/5.93 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.49/5.93 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_Suc
% 5.49/5.93 thf(fact_3298_set__bit__Suc,axiom,
% 5.49/5.93 ! [N: nat,A: int] :
% 5.49/5.93 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.49/5.93 = ( 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 ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_Suc
% 5.49/5.93 thf(fact_3299_set__bit__Suc,axiom,
% 5.49/5.93 ! [N: nat,A: nat] :
% 5.49/5.93 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.49/5.93 = ( 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 ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_Suc
% 5.49/5.93 thf(fact_3300_div__mod__decomp,axiom,
% 5.49/5.93 ! [A2: nat,N: nat] :
% 5.49/5.93 ( A2
% 5.49/5.93 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % div_mod_decomp
% 5.49/5.93 thf(fact_3301_vebt__insert_Opelims,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 5.49/5.93 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.49/5.93 = Y2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => ( Y2
% 5.49/5.93 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => ( Y2
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.49/5.93 & ( ( Xa2 != one_one_nat )
% 5.49/5.93 => ( Y2
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( if_VEBT_VEBT
% 5.49/5.93 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 & ~ ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 ) ) )
% 5.49/5.93 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.49/5.93 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % vebt_insert.pelims
% 5.49/5.93 thf(fact_3302_vebt__member_Opelims_I3_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.49/5.93 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.49/5.93 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.49/5.93 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.49/5.93 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( Xa2 != Mi2 )
% 5.49/5.93 => ( ( Xa2 != Ma2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % vebt_member.pelims(3)
% 5.49/5.93 thf(fact_3303_vebt__member_Opelims_I1_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.93 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.93 = Y2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( Xa2 != Mi2 )
% 5.49/5.93 => ( ( Xa2 != Ma2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % vebt_member.pelims(1)
% 5.49/5.93 thf(fact_3304_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.49/5.93 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.49/5.93 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.49/5.93 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.naive_member.pelims(3)
% 5.49/5.93 thf(fact_3305_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.49/5.93 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.naive_member.pelims(2)
% 5.49/5.93 thf(fact_3306_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.93 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.49/5.93 = Y2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Uu3: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu3 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.naive_member.pelims(1)
% 5.49/5.93 thf(fact_3307_vebt__member_Opelims_I2_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [A3: $o,B2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.49/5.93 => A3 )
% 5.49/5.93 & ( ( Xa2 != zero_zero_nat )
% 5.49/5.93 => ( ( ( Xa2 = one_one_nat )
% 5.49/5.93 => B2 )
% 5.49/5.93 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.49/5.93 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( Xa2 != Mi2 )
% 5.49/5.93 => ( ( Xa2 != Ma2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.49/5.93 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.49/5.93 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % vebt_member.pelims(2)
% 5.49/5.93 thf(fact_3308_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [Uu3: $o,Uv2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) )
% 5.49/5.93 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 ) ) ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 )
% 5.49/5.93 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.49/5.93 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.49/5.93 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.membermima.pelims(3)
% 5.49/5.93 thf(fact_3309_max__enat__simps_I2_J,axiom,
% 5.49/5.93 ! [Q2: extended_enat] :
% 5.49/5.93 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.49/5.93 = Q2 ) ).
% 5.49/5.93
% 5.49/5.93 % max_enat_simps(2)
% 5.49/5.93 thf(fact_3310_max__enat__simps_I3_J,axiom,
% 5.49/5.93 ! [Q2: extended_enat] :
% 5.49/5.93 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.49/5.93 = Q2 ) ).
% 5.49/5.93
% 5.49/5.93 % max_enat_simps(3)
% 5.49/5.93 thf(fact_3311_set__bit__nonnegative__int__iff,axiom,
% 5.49/5.93 ! [N: nat,K: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.49/5.93 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_nonnegative_int_iff
% 5.49/5.93 thf(fact_3312_set__bit__negative__int__iff,axiom,
% 5.49/5.93 ! [N: nat,K: int] :
% 5.49/5.93 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.49/5.93 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_negative_int_iff
% 5.49/5.93 thf(fact_3313_mod__pos__pos__trivial,axiom,
% 5.49/5.93 ! [K: int,L2: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.93 => ( ( ord_less_int @ K @ L2 )
% 5.49/5.93 => ( ( modulo_modulo_int @ K @ L2 )
% 5.49/5.93 = K ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % mod_pos_pos_trivial
% 5.49/5.93 thf(fact_3314_mod__neg__neg__trivial,axiom,
% 5.49/5.93 ! [K: int,L2: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.49/5.93 => ( ( ord_less_int @ L2 @ K )
% 5.49/5.93 => ( ( modulo_modulo_int @ K @ L2 )
% 5.49/5.93 = K ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % mod_neg_neg_trivial
% 5.49/5.93 thf(fact_3315_mod__pos__geq,axiom,
% 5.49/5.93 ! [L2: int,K: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.49/5.93 => ( ( ord_less_eq_int @ L2 @ K )
% 5.49/5.93 => ( ( modulo_modulo_int @ K @ L2 )
% 5.49/5.93 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % mod_pos_geq
% 5.49/5.93 thf(fact_3316_zero__one__enat__neq_I1_J,axiom,
% 5.49/5.93 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.49/5.93
% 5.49/5.93 % zero_one_enat_neq(1)
% 5.49/5.93 thf(fact_3317_zmod__eq__0D,axiom,
% 5.49/5.93 ! [M: int,D: int] :
% 5.49/5.93 ( ( ( modulo_modulo_int @ M @ D )
% 5.49/5.93 = zero_zero_int )
% 5.49/5.93 => ? [Q3: int] :
% 5.49/5.93 ( M
% 5.49/5.93 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % zmod_eq_0D
% 5.49/5.93 thf(fact_3318_zmod__eq__0__iff,axiom,
% 5.49/5.93 ! [M: int,D: int] :
% 5.49/5.93 ( ( ( modulo_modulo_int @ M @ D )
% 5.49/5.93 = zero_zero_int )
% 5.49/5.93 = ( ? [Q4: int] :
% 5.49/5.93 ( M
% 5.49/5.93 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % zmod_eq_0_iff
% 5.49/5.93 thf(fact_3319_zmod__le__nonneg__dividend,axiom,
% 5.49/5.93 ! [M: int,K: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.49/5.93 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.49/5.93
% 5.49/5.93 % zmod_le_nonneg_dividend
% 5.49/5.93 thf(fact_3320_neg__mod__conj,axiom,
% 5.49/5.93 ! [B: int,A: int] :
% 5.49/5.93 ( ( ord_less_int @ B @ zero_zero_int )
% 5.49/5.93 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.49/5.93 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % neg_mod_conj
% 5.49/5.93 thf(fact_3321_pos__mod__conj,axiom,
% 5.49/5.93 ! [B: int,A: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.49/5.93 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % pos_mod_conj
% 5.49/5.93 thf(fact_3322_zmod__trivial__iff,axiom,
% 5.49/5.93 ! [I2: int,K: int] :
% 5.49/5.93 ( ( ( modulo_modulo_int @ I2 @ K )
% 5.49/5.93 = I2 )
% 5.49/5.93 = ( ( K = zero_zero_int )
% 5.49/5.93 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.49/5.93 & ( ord_less_int @ I2 @ K ) )
% 5.49/5.93 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.49/5.93 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % zmod_trivial_iff
% 5.49/5.93 thf(fact_3323_mod__pos__neg__trivial,axiom,
% 5.49/5.93 ! [K: int,L2: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.93 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.49/5.93 => ( ( modulo_modulo_int @ K @ L2 )
% 5.49/5.93 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % mod_pos_neg_trivial
% 5.49/5.93 thf(fact_3324_unique__quotient__lemma__neg,axiom,
% 5.49/5.93 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.49/5.93 => ( ( ord_less_int @ B @ R2 )
% 5.49/5.93 => ( ( ord_less_int @ B @ R4 )
% 5.49/5.93 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % unique_quotient_lemma_neg
% 5.49/5.93 thf(fact_3325_unique__quotient__lemma,axiom,
% 5.49/5.93 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.49/5.93 => ( ( ord_less_int @ R4 @ B )
% 5.49/5.93 => ( ( ord_less_int @ R2 @ B )
% 5.49/5.93 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % unique_quotient_lemma
% 5.49/5.93 thf(fact_3326_zdiv__mono2__neg__lemma,axiom,
% 5.49/5.93 ! [B: int,Q2: int,R2: int,B5: int,Q5: int,R4: int] :
% 5.49/5.93 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.49/5.93 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.49/5.93 => ( ( ord_less_int @ R2 @ B )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.49/5.93 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.49/5.93 => ( ( ord_less_eq_int @ B5 @ B )
% 5.49/5.93 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % zdiv_mono2_neg_lemma
% 5.49/5.93 thf(fact_3327_zdiv__mono2__lemma,axiom,
% 5.49/5.93 ! [B: int,Q2: int,R2: int,B5: int,Q5: int,R4: int] :
% 5.49/5.93 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.49/5.93 => ( ( ord_less_int @ R4 @ B5 )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.49/5.93 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.49/5.93 => ( ( ord_less_eq_int @ B5 @ B )
% 5.49/5.93 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % zdiv_mono2_lemma
% 5.49/5.93 thf(fact_3328_int__mod__pos__eq,axiom,
% 5.49/5.93 ! [A: int,B: int,Q2: int,R2: int] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.49/5.93 => ( ( ord_less_int @ R2 @ B )
% 5.49/5.93 => ( ( modulo_modulo_int @ A @ B )
% 5.49/5.93 = R2 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % int_mod_pos_eq
% 5.49/5.93 thf(fact_3329_int__mod__neg__eq,axiom,
% 5.49/5.93 ! [A: int,B: int,Q2: int,R2: int] :
% 5.49/5.93 ( ( A
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.49/5.93 => ( ( ord_less_int @ B @ R2 )
% 5.49/5.93 => ( ( modulo_modulo_int @ A @ B )
% 5.49/5.93 = R2 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % int_mod_neg_eq
% 5.49/5.93 thf(fact_3330_q__pos__lemma,axiom,
% 5.49/5.93 ! [B5: int,Q5: int,R4: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R4 ) )
% 5.49/5.93 => ( ( ord_less_int @ R4 @ B5 )
% 5.49/5.93 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.49/5.93 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % q_pos_lemma
% 5.49/5.93 thf(fact_3331_split__zmod,axiom,
% 5.49/5.93 ! [P: int > $o,N: int,K: int] :
% 5.49/5.93 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.49/5.93 = ( ( ( K = zero_zero_int )
% 5.49/5.93 => ( P @ N ) )
% 5.49/5.93 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.93 => ! [I3: int,J3: int] :
% 5.49/5.93 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.49/5.93 & ( ord_less_int @ J3 @ K )
% 5.49/5.93 & ( N
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.93 => ( P @ J3 ) ) )
% 5.49/5.93 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.93 => ! [I3: int,J3: int] :
% 5.49/5.93 ( ( ( ord_less_int @ K @ J3 )
% 5.49/5.93 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.49/5.93 & ( N
% 5.49/5.93 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.49/5.93 => ( P @ J3 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % split_zmod
% 5.49/5.93 thf(fact_3332_Euclidean__Division_Opos__mod__sign,axiom,
% 5.49/5.93 ! [L2: int,K: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.49/5.93 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % Euclidean_Division.pos_mod_sign
% 5.49/5.93 thf(fact_3333_neg__mod__sign,axiom,
% 5.49/5.93 ! [L2: int,K: int] :
% 5.49/5.93 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.49/5.93 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.49/5.93
% 5.49/5.93 % neg_mod_sign
% 5.49/5.93 thf(fact_3334_Euclidean__Division_Opos__mod__bound,axiom,
% 5.49/5.93 ! [L2: int,K: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.49/5.93 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.49/5.93
% 5.49/5.93 % Euclidean_Division.pos_mod_bound
% 5.49/5.93 thf(fact_3335_neg__mod__bound,axiom,
% 5.49/5.93 ! [L2: int,K: int] :
% 5.49/5.93 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.49/5.93 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % neg_mod_bound
% 5.49/5.93 thf(fact_3336_verit__la__generic,axiom,
% 5.49/5.93 ! [A: int,X: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ A @ X )
% 5.49/5.93 | ( A = X )
% 5.49/5.93 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.49/5.93
% 5.49/5.93 % verit_la_generic
% 5.49/5.93 thf(fact_3337_set__bit__greater__eq,axiom,
% 5.49/5.93 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.49/5.93
% 5.49/5.93 % set_bit_greater_eq
% 5.49/5.93 thf(fact_3338_imult__is__0,axiom,
% 5.49/5.93 ! [M: extended_enat,N: extended_enat] :
% 5.49/5.93 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.49/5.93 = zero_z5237406670263579293d_enat )
% 5.49/5.93 = ( ( M = zero_z5237406670263579293d_enat )
% 5.49/5.93 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % imult_is_0
% 5.49/5.93 thf(fact_3339_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.49/5.93 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 ) ) ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 )
% 5.49/5.93 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.49/5.93 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.49/5.93 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.membermima.pelims(2)
% 5.49/5.93 thf(fact_3340_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.49/5.93 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.49/5.93 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.49/5.93 = Y2 )
% 5.49/5.93 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.49/5.93 => ( ! [Uu3: $o,Uv2: $o] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.49/5.93 => ( ~ Y2
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( Xa2 = Mi2 )
% 5.49/5.93 | ( Xa2 = Ma2 )
% 5.49/5.93 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.49/5.93 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.49/5.93 ( ( X
% 5.49/5.93 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.49/5.93 => ( ( Y2
% 5.49/5.93 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.49/5.93 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.49/5.93 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.49/5.93 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % VEBT_internal.membermima.pelims(1)
% 5.49/5.93 thf(fact_3341_zle__diff1__eq,axiom,
% 5.49/5.93 ! [W: int,Z: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.49/5.93 = ( ord_less_int @ W @ Z ) ) ).
% 5.49/5.93
% 5.49/5.93 % zle_diff1_eq
% 5.49/5.93 thf(fact_3342_zle__add1__eq__le,axiom,
% 5.49/5.93 ! [W: int,Z: int] :
% 5.49/5.93 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.49/5.93 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.49/5.93
% 5.49/5.93 % zle_add1_eq_le
% 5.49/5.93 thf(fact_3343_cpmi,axiom,
% 5.49/5.93 ! [D4: int,P: int > $o,P6: int > $o,B4: set_int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ( ? [Z4: int] :
% 5.49/5.93 ! [X3: int] :
% 5.49/5.93 ( ( ord_less_int @ X3 @ Z4 )
% 5.49/5.93 => ( ( P @ X3 )
% 5.49/5.93 = ( P6 @ X3 ) ) )
% 5.49/5.93 => ( ! [X3: int] :
% 5.49/5.93 ( ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb: int] :
% 5.49/5.93 ( ( member_int @ Xb @ B4 )
% 5.49/5.93 => ( X3
% 5.49/5.93 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.49/5.93 => ( ( P @ X3 )
% 5.49/5.93 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.49/5.93 => ( ! [X3: int,K2: int] :
% 5.49/5.93 ( ( P6 @ X3 )
% 5.49/5.93 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.49/5.93 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.49/5.93 = ( ? [X2: int] :
% 5.49/5.93 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 & ( P6 @ X2 ) )
% 5.49/5.93 | ? [X2: int] :
% 5.49/5.93 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 & ? [Y: int] :
% 5.49/5.93 ( ( member_int @ Y @ B4 )
% 5.49/5.93 & ( P @ ( plus_plus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % cpmi
% 5.49/5.93 thf(fact_3344_cppi,axiom,
% 5.49/5.93 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ( ? [Z4: int] :
% 5.49/5.93 ! [X3: int] :
% 5.49/5.93 ( ( ord_less_int @ Z4 @ X3 )
% 5.49/5.93 => ( ( P @ X3 )
% 5.49/5.93 = ( P6 @ X3 ) ) )
% 5.49/5.93 => ( ! [X3: int] :
% 5.49/5.93 ( ! [Xa: int] :
% 5.49/5.93 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb: int] :
% 5.49/5.93 ( ( member_int @ Xb @ A2 )
% 5.49/5.93 => ( X3
% 5.49/5.93 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.49/5.93 => ( ( P @ X3 )
% 5.49/5.93 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.49/5.93 => ( ! [X3: int,K2: int] :
% 5.49/5.93 ( ( P6 @ X3 )
% 5.49/5.93 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.49/5.93 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.49/5.93 = ( ? [X2: int] :
% 5.49/5.93 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 & ( P6 @ X2 ) )
% 5.49/5.93 | ? [X2: int] :
% 5.49/5.93 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 & ? [Y: int] :
% 5.49/5.93 ( ( member_int @ Y @ A2 )
% 5.49/5.93 & ( P @ ( minus_minus_int @ Y @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % cppi
% 5.49/5.93 thf(fact_3345_bset_I6_J,axiom,
% 5.49/5.93 ! [D4: int,B4: set_int,T: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ! [X5: int] :
% 5.49/5.93 ( ! [Xa3: int] :
% 5.49/5.93 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb3: int] :
% 5.49/5.93 ( ( member_int @ Xb3 @ B4 )
% 5.49/5.93 => ( X5
% 5.49/5.93 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ X5 @ T )
% 5.49/5.93 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % bset(6)
% 5.49/5.93 thf(fact_3346_bset_I8_J,axiom,
% 5.49/5.93 ! [D4: int,T: int,B4: set_int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.49/5.93 => ! [X5: int] :
% 5.49/5.93 ( ! [Xa3: int] :
% 5.49/5.93 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb3: int] :
% 5.49/5.93 ( ( member_int @ Xb3 @ B4 )
% 5.49/5.93 => ( X5
% 5.49/5.93 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ T @ X5 )
% 5.49/5.93 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % bset(8)
% 5.49/5.93 thf(fact_3347_aset_I6_J,axiom,
% 5.49/5.93 ! [D4: int,T: int,A2: set_int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.49/5.93 => ! [X5: int] :
% 5.49/5.93 ( ! [Xa3: int] :
% 5.49/5.93 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb3: int] :
% 5.49/5.93 ( ( member_int @ Xb3 @ A2 )
% 5.49/5.93 => ( X5
% 5.49/5.93 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ X5 @ T )
% 5.49/5.93 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % aset(6)
% 5.49/5.93 thf(fact_3348_aset_I8_J,axiom,
% 5.49/5.93 ! [D4: int,A2: set_int,T: int] :
% 5.49/5.93 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.49/5.93 => ! [X5: int] :
% 5.49/5.93 ( ! [Xa3: int] :
% 5.49/5.93 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.49/5.93 => ! [Xb3: int] :
% 5.49/5.93 ( ( member_int @ Xb3 @ A2 )
% 5.49/5.93 => ( X5
% 5.49/5.93 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.49/5.93 => ( ( ord_less_eq_int @ T @ X5 )
% 5.49/5.93 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % aset(8)
% 5.49/5.93 thf(fact_3349_finite__interval__int1,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [I3: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ A @ I3 )
% 5.49/5.93 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_interval_int1
% 5.49/5.93 thf(fact_3350_double__eq__0__iff,axiom,
% 5.49/5.93 ! [A: real] :
% 5.49/5.93 ( ( ( plus_plus_real @ A @ A )
% 5.49/5.93 = zero_zero_real )
% 5.49/5.93 = ( A = zero_zero_real ) ) ).
% 5.49/5.93
% 5.49/5.93 % double_eq_0_iff
% 5.49/5.93 thf(fact_3351_double__eq__0__iff,axiom,
% 5.49/5.93 ! [A: rat] :
% 5.49/5.93 ( ( ( plus_plus_rat @ A @ A )
% 5.49/5.93 = zero_zero_rat )
% 5.49/5.93 = ( A = zero_zero_rat ) ) ).
% 5.49/5.93
% 5.49/5.93 % double_eq_0_iff
% 5.49/5.93 thf(fact_3352_double__eq__0__iff,axiom,
% 5.49/5.93 ! [A: int] :
% 5.49/5.93 ( ( ( plus_plus_int @ A @ A )
% 5.49/5.93 = zero_zero_int )
% 5.49/5.93 = ( A = zero_zero_int ) ) ).
% 5.49/5.93
% 5.49/5.93 % double_eq_0_iff
% 5.49/5.93 thf(fact_3353_finite__interval__int3,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [I3: int] :
% 5.49/5.93 ( ( ord_less_int @ A @ I3 )
% 5.49/5.93 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_interval_int3
% 5.49/5.93 thf(fact_3354_finite__interval__int2,axiom,
% 5.49/5.93 ! [A: int,B: int] :
% 5.49/5.93 ( finite_finite_int
% 5.49/5.93 @ ( collect_int
% 5.49/5.93 @ ^ [I3: int] :
% 5.49/5.93 ( ( ord_less_eq_int @ A @ I3 )
% 5.49/5.93 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.49/5.93
% 5.49/5.93 % finite_interval_int2
% 5.49/5.93 thf(fact_3355_minf_I7_J,axiom,
% 5.49/5.93 ! [T: real] :
% 5.49/5.93 ? [Z3: real] :
% 5.49/5.93 ! [X5: real] :
% 5.49/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.49/5.93 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(7)
% 5.49/5.93 thf(fact_3356_minf_I7_J,axiom,
% 5.49/5.93 ! [T: rat] :
% 5.49/5.93 ? [Z3: rat] :
% 5.49/5.93 ! [X5: rat] :
% 5.49/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.49/5.93 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(7)
% 5.49/5.93 thf(fact_3357_minf_I7_J,axiom,
% 5.49/5.93 ! [T: num] :
% 5.49/5.93 ? [Z3: num] :
% 5.49/5.93 ! [X5: num] :
% 5.49/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.49/5.93 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(7)
% 5.49/5.93 thf(fact_3358_minf_I7_J,axiom,
% 5.49/5.93 ! [T: nat] :
% 5.49/5.93 ? [Z3: nat] :
% 5.49/5.93 ! [X5: nat] :
% 5.49/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.49/5.93 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(7)
% 5.49/5.93 thf(fact_3359_minf_I7_J,axiom,
% 5.49/5.93 ! [T: int] :
% 5.49/5.93 ? [Z3: int] :
% 5.49/5.93 ! [X5: int] :
% 5.49/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.49/5.93 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(7)
% 5.49/5.93 thf(fact_3360_minf_I5_J,axiom,
% 5.49/5.93 ! [T: real] :
% 5.49/5.93 ? [Z3: real] :
% 5.49/5.93 ! [X5: real] :
% 5.49/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.49/5.93 => ( ord_less_real @ X5 @ T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(5)
% 5.49/5.93 thf(fact_3361_minf_I5_J,axiom,
% 5.49/5.93 ! [T: rat] :
% 5.49/5.93 ? [Z3: rat] :
% 5.49/5.93 ! [X5: rat] :
% 5.49/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.49/5.93 => ( ord_less_rat @ X5 @ T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(5)
% 5.49/5.93 thf(fact_3362_minf_I5_J,axiom,
% 5.49/5.93 ! [T: num] :
% 5.49/5.93 ? [Z3: num] :
% 5.49/5.93 ! [X5: num] :
% 5.49/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.49/5.93 => ( ord_less_num @ X5 @ T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(5)
% 5.49/5.93 thf(fact_3363_minf_I5_J,axiom,
% 5.49/5.93 ! [T: nat] :
% 5.49/5.93 ? [Z3: nat] :
% 5.49/5.93 ! [X5: nat] :
% 5.49/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.49/5.93 => ( ord_less_nat @ X5 @ T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(5)
% 5.49/5.93 thf(fact_3364_minf_I5_J,axiom,
% 5.49/5.93 ! [T: int] :
% 5.49/5.93 ? [Z3: int] :
% 5.49/5.93 ! [X5: int] :
% 5.49/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.49/5.93 => ( ord_less_int @ X5 @ T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(5)
% 5.49/5.93 thf(fact_3365_minf_I4_J,axiom,
% 5.49/5.93 ! [T: real] :
% 5.49/5.93 ? [Z3: real] :
% 5.49/5.93 ! [X5: real] :
% 5.49/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(4)
% 5.49/5.93 thf(fact_3366_minf_I4_J,axiom,
% 5.49/5.93 ! [T: rat] :
% 5.49/5.93 ? [Z3: rat] :
% 5.49/5.93 ! [X5: rat] :
% 5.49/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(4)
% 5.49/5.93 thf(fact_3367_minf_I4_J,axiom,
% 5.49/5.93 ! [T: num] :
% 5.49/5.93 ? [Z3: num] :
% 5.49/5.93 ! [X5: num] :
% 5.49/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(4)
% 5.49/5.93 thf(fact_3368_minf_I4_J,axiom,
% 5.49/5.93 ! [T: nat] :
% 5.49/5.93 ? [Z3: nat] :
% 5.49/5.93 ! [X5: nat] :
% 5.49/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(4)
% 5.49/5.93 thf(fact_3369_minf_I4_J,axiom,
% 5.49/5.93 ! [T: int] :
% 5.49/5.93 ? [Z3: int] :
% 5.49/5.93 ! [X5: int] :
% 5.49/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(4)
% 5.49/5.93 thf(fact_3370_minf_I3_J,axiom,
% 5.49/5.93 ! [T: real] :
% 5.49/5.93 ? [Z3: real] :
% 5.49/5.93 ! [X5: real] :
% 5.49/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.49/5.93 => ( X5 != T ) ) ).
% 5.49/5.93
% 5.49/5.93 % minf(3)
% 5.49/5.93 thf(fact_3371_minf_I3_J,axiom,
% 5.49/5.93 ! [T: rat] :
% 5.49/5.93 ? [Z3: rat] :
% 5.49/5.93 ! [X5: rat] :
% 5.49/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(3)
% 5.68/5.93 thf(fact_3372_minf_I3_J,axiom,
% 5.68/5.93 ! [T: num] :
% 5.68/5.93 ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(3)
% 5.68/5.93 thf(fact_3373_minf_I3_J,axiom,
% 5.68/5.93 ! [T: nat] :
% 5.68/5.93 ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(3)
% 5.68/5.93 thf(fact_3374_minf_I3_J,axiom,
% 5.68/5.93 ! [T: int] :
% 5.68/5.93 ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(3)
% 5.68/5.93 thf(fact_3375_minf_I2_J,axiom,
% 5.68/5.93 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.68/5.93 ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(2)
% 5.68/5.93 thf(fact_3376_minf_I2_J,axiom,
% 5.68/5.93 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.68/5.93 ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(2)
% 5.68/5.93 thf(fact_3377_minf_I2_J,axiom,
% 5.68/5.93 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.68/5.93 ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(2)
% 5.68/5.93 thf(fact_3378_minf_I2_J,axiom,
% 5.68/5.93 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.68/5.93 ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(2)
% 5.68/5.93 thf(fact_3379_minf_I2_J,axiom,
% 5.68/5.93 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.68/5.93 ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(2)
% 5.68/5.93 thf(fact_3380_minf_I1_J,axiom,
% 5.68/5.93 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.68/5.93 ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(1)
% 5.68/5.93 thf(fact_3381_minf_I1_J,axiom,
% 5.68/5.93 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.68/5.93 ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(1)
% 5.68/5.93 thf(fact_3382_minf_I1_J,axiom,
% 5.68/5.93 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.68/5.93 ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(1)
% 5.68/5.93 thf(fact_3383_minf_I1_J,axiom,
% 5.68/5.93 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.68/5.93 ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(1)
% 5.68/5.93 thf(fact_3384_minf_I1_J,axiom,
% 5.68/5.93 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.68/5.93 ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ X3 @ Z4 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ X3 @ Z4 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % minf(1)
% 5.68/5.93 thf(fact_3385_pinf_I7_J,axiom,
% 5.68/5.93 ! [T: real] :
% 5.68/5.93 ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ( ord_less_real @ T @ X5 ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(7)
% 5.68/5.93 thf(fact_3386_pinf_I7_J,axiom,
% 5.68/5.93 ! [T: rat] :
% 5.68/5.93 ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ( ord_less_rat @ T @ X5 ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(7)
% 5.68/5.93 thf(fact_3387_pinf_I7_J,axiom,
% 5.68/5.93 ! [T: num] :
% 5.68/5.93 ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ( ord_less_num @ T @ X5 ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(7)
% 5.68/5.93 thf(fact_3388_pinf_I7_J,axiom,
% 5.68/5.93 ! [T: nat] :
% 5.68/5.93 ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ( ord_less_nat @ T @ X5 ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(7)
% 5.68/5.93 thf(fact_3389_pinf_I7_J,axiom,
% 5.68/5.93 ! [T: int] :
% 5.68/5.93 ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.93 => ( ord_less_int @ T @ X5 ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(7)
% 5.68/5.93 thf(fact_3390_pinf_I5_J,axiom,
% 5.68/5.93 ! [T: real] :
% 5.68/5.93 ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(5)
% 5.68/5.93 thf(fact_3391_pinf_I5_J,axiom,
% 5.68/5.93 ! [T: rat] :
% 5.68/5.93 ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(5)
% 5.68/5.93 thf(fact_3392_pinf_I5_J,axiom,
% 5.68/5.93 ! [T: num] :
% 5.68/5.93 ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(5)
% 5.68/5.93 thf(fact_3393_pinf_I5_J,axiom,
% 5.68/5.93 ! [T: nat] :
% 5.68/5.93 ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(5)
% 5.68/5.93 thf(fact_3394_pinf_I5_J,axiom,
% 5.68/5.93 ! [T: int] :
% 5.68/5.93 ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.93 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(5)
% 5.68/5.93 thf(fact_3395_pinf_I4_J,axiom,
% 5.68/5.93 ! [T: real] :
% 5.68/5.93 ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(4)
% 5.68/5.93 thf(fact_3396_pinf_I4_J,axiom,
% 5.68/5.93 ! [T: rat] :
% 5.68/5.93 ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(4)
% 5.68/5.93 thf(fact_3397_pinf_I4_J,axiom,
% 5.68/5.93 ! [T: num] :
% 5.68/5.93 ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(4)
% 5.68/5.93 thf(fact_3398_pinf_I4_J,axiom,
% 5.68/5.93 ! [T: nat] :
% 5.68/5.93 ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(4)
% 5.68/5.93 thf(fact_3399_pinf_I4_J,axiom,
% 5.68/5.93 ! [T: int] :
% 5.68/5.93 ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(4)
% 5.68/5.93 thf(fact_3400_pinf_I3_J,axiom,
% 5.68/5.93 ! [T: real] :
% 5.68/5.93 ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(3)
% 5.68/5.93 thf(fact_3401_pinf_I3_J,axiom,
% 5.68/5.93 ! [T: rat] :
% 5.68/5.93 ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(3)
% 5.68/5.93 thf(fact_3402_pinf_I3_J,axiom,
% 5.68/5.93 ! [T: num] :
% 5.68/5.93 ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(3)
% 5.68/5.93 thf(fact_3403_pinf_I3_J,axiom,
% 5.68/5.93 ! [T: nat] :
% 5.68/5.93 ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(3)
% 5.68/5.93 thf(fact_3404_pinf_I3_J,axiom,
% 5.68/5.93 ! [T: int] :
% 5.68/5.93 ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.93 => ( X5 != T ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(3)
% 5.68/5.93 thf(fact_3405_pinf_I2_J,axiom,
% 5.68/5.93 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.68/5.93 ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(2)
% 5.68/5.93 thf(fact_3406_pinf_I2_J,axiom,
% 5.68/5.93 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.68/5.93 ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(2)
% 5.68/5.93 thf(fact_3407_pinf_I2_J,axiom,
% 5.68/5.93 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.68/5.93 ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(2)
% 5.68/5.93 thf(fact_3408_pinf_I2_J,axiom,
% 5.68/5.93 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.68/5.93 ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(2)
% 5.68/5.93 thf(fact_3409_pinf_I2_J,axiom,
% 5.68/5.93 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.68/5.93 ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: int] :
% 5.68/5.93 ! [X3: int] :
% 5.68/5.93 ( ( ord_less_int @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: int] :
% 5.68/5.93 ! [X5: int] :
% 5.68/5.93 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 | ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(2)
% 5.68/5.93 thf(fact_3410_pinf_I1_J,axiom,
% 5.68/5.93 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.68/5.93 ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: real] :
% 5.68/5.93 ! [X3: real] :
% 5.68/5.93 ( ( ord_less_real @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: real] :
% 5.68/5.93 ! [X5: real] :
% 5.68/5.93 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(1)
% 5.68/5.93 thf(fact_3411_pinf_I1_J,axiom,
% 5.68/5.93 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.68/5.93 ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: rat] :
% 5.68/5.93 ! [X3: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: rat] :
% 5.68/5.93 ! [X5: rat] :
% 5.68/5.93 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(1)
% 5.68/5.93 thf(fact_3412_pinf_I1_J,axiom,
% 5.68/5.93 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.68/5.93 ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: num] :
% 5.68/5.93 ! [X3: num] :
% 5.68/5.93 ( ( ord_less_num @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: num] :
% 5.68/5.93 ! [X5: num] :
% 5.68/5.93 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.93 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.93
% 5.68/5.93 % pinf(1)
% 5.68/5.93 thf(fact_3413_pinf_I1_J,axiom,
% 5.68/5.93 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.68/5.93 ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z4 @ X3 )
% 5.68/5.93 => ( ( P @ X3 )
% 5.68/5.93 = ( P6 @ X3 ) ) )
% 5.68/5.93 => ( ? [Z4: nat] :
% 5.68/5.93 ! [X3: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z4 @ X3 )
% 5.68/5.93 => ( ( Q @ X3 )
% 5.68/5.93 = ( Q6 @ X3 ) ) )
% 5.68/5.93 => ? [Z3: nat] :
% 5.68/5.93 ! [X5: nat] :
% 5.68/5.93 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.93 => ( ( ( P @ X5 )
% 5.68/5.93 & ( Q @ X5 ) )
% 5.68/5.93 = ( ( P6 @ X5 )
% 5.68/5.94 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(1)
% 5.68/5.94 thf(fact_3414_pinf_I1_J,axiom,
% 5.68/5.94 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.68/5.94 ( ? [Z4: int] :
% 5.68/5.94 ! [X3: int] :
% 5.68/5.94 ( ( ord_less_int @ Z4 @ X3 )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 = ( P6 @ X3 ) ) )
% 5.68/5.94 => ( ? [Z4: int] :
% 5.68/5.94 ! [X3: int] :
% 5.68/5.94 ( ( ord_less_int @ Z4 @ X3 )
% 5.68/5.94 => ( ( Q @ X3 )
% 5.68/5.94 = ( Q6 @ X3 ) ) )
% 5.68/5.94 => ? [Z3: int] :
% 5.68/5.94 ! [X5: int] :
% 5.68/5.94 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.94 => ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 = ( ( P6 @ X5 )
% 5.68/5.94 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(1)
% 5.68/5.94 thf(fact_3415_minf_I8_J,axiom,
% 5.68/5.94 ! [T: real] :
% 5.68/5.94 ? [Z3: real] :
% 5.68/5.94 ! [X5: real] :
% 5.68/5.94 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.94 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(8)
% 5.68/5.94 thf(fact_3416_minf_I8_J,axiom,
% 5.68/5.94 ! [T: rat] :
% 5.68/5.94 ? [Z3: rat] :
% 5.68/5.94 ! [X5: rat] :
% 5.68/5.94 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.94 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(8)
% 5.68/5.94 thf(fact_3417_minf_I8_J,axiom,
% 5.68/5.94 ! [T: num] :
% 5.68/5.94 ? [Z3: num] :
% 5.68/5.94 ! [X5: num] :
% 5.68/5.94 ( ( ord_less_num @ X5 @ Z3 )
% 5.68/5.94 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(8)
% 5.68/5.94 thf(fact_3418_minf_I8_J,axiom,
% 5.68/5.94 ! [T: nat] :
% 5.68/5.94 ? [Z3: nat] :
% 5.68/5.94 ! [X5: nat] :
% 5.68/5.94 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.94 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(8)
% 5.68/5.94 thf(fact_3419_minf_I8_J,axiom,
% 5.68/5.94 ! [T: int] :
% 5.68/5.94 ? [Z3: int] :
% 5.68/5.94 ! [X5: int] :
% 5.68/5.94 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.94 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(8)
% 5.68/5.94 thf(fact_3420_minf_I6_J,axiom,
% 5.68/5.94 ! [T: real] :
% 5.68/5.94 ? [Z3: real] :
% 5.68/5.94 ! [X5: real] :
% 5.68/5.94 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.94 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(6)
% 5.68/5.94 thf(fact_3421_minf_I6_J,axiom,
% 5.68/5.94 ! [T: rat] :
% 5.68/5.94 ? [Z3: rat] :
% 5.68/5.94 ! [X5: rat] :
% 5.68/5.94 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.94 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(6)
% 5.68/5.94 thf(fact_3422_minf_I6_J,axiom,
% 5.68/5.94 ! [T: num] :
% 5.68/5.94 ? [Z3: num] :
% 5.68/5.94 ! [X5: num] :
% 5.68/5.94 ( ( ord_less_num @ X5 @ Z3 )
% 5.68/5.94 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(6)
% 5.68/5.94 thf(fact_3423_minf_I6_J,axiom,
% 5.68/5.94 ! [T: nat] :
% 5.68/5.94 ? [Z3: nat] :
% 5.68/5.94 ! [X5: nat] :
% 5.68/5.94 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.94 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(6)
% 5.68/5.94 thf(fact_3424_minf_I6_J,axiom,
% 5.68/5.94 ! [T: int] :
% 5.68/5.94 ? [Z3: int] :
% 5.68/5.94 ! [X5: int] :
% 5.68/5.94 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.94 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % minf(6)
% 5.68/5.94 thf(fact_3425_pinf_I8_J,axiom,
% 5.68/5.94 ! [T: real] :
% 5.68/5.94 ? [Z3: real] :
% 5.68/5.94 ! [X5: real] :
% 5.68/5.94 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.94 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(8)
% 5.68/5.94 thf(fact_3426_pinf_I8_J,axiom,
% 5.68/5.94 ! [T: rat] :
% 5.68/5.94 ? [Z3: rat] :
% 5.68/5.94 ! [X5: rat] :
% 5.68/5.94 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.94 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(8)
% 5.68/5.94 thf(fact_3427_pinf_I8_J,axiom,
% 5.68/5.94 ! [T: num] :
% 5.68/5.94 ? [Z3: num] :
% 5.68/5.94 ! [X5: num] :
% 5.68/5.94 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.94 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(8)
% 5.68/5.94 thf(fact_3428_pinf_I8_J,axiom,
% 5.68/5.94 ! [T: nat] :
% 5.68/5.94 ? [Z3: nat] :
% 5.68/5.94 ! [X5: nat] :
% 5.68/5.94 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.94 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(8)
% 5.68/5.94 thf(fact_3429_pinf_I8_J,axiom,
% 5.68/5.94 ! [T: int] :
% 5.68/5.94 ? [Z3: int] :
% 5.68/5.94 ! [X5: int] :
% 5.68/5.94 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.94 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(8)
% 5.68/5.94 thf(fact_3430_pinf_I6_J,axiom,
% 5.68/5.94 ! [T: real] :
% 5.68/5.94 ? [Z3: real] :
% 5.68/5.94 ! [X5: real] :
% 5.68/5.94 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.94 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(6)
% 5.68/5.94 thf(fact_3431_pinf_I6_J,axiom,
% 5.68/5.94 ! [T: rat] :
% 5.68/5.94 ? [Z3: rat] :
% 5.68/5.94 ! [X5: rat] :
% 5.68/5.94 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.94 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(6)
% 5.68/5.94 thf(fact_3432_pinf_I6_J,axiom,
% 5.68/5.94 ! [T: num] :
% 5.68/5.94 ? [Z3: num] :
% 5.68/5.94 ! [X5: num] :
% 5.68/5.94 ( ( ord_less_num @ Z3 @ X5 )
% 5.68/5.94 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(6)
% 5.68/5.94 thf(fact_3433_pinf_I6_J,axiom,
% 5.68/5.94 ! [T: nat] :
% 5.68/5.94 ? [Z3: nat] :
% 5.68/5.94 ! [X5: nat] :
% 5.68/5.94 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.94 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(6)
% 5.68/5.94 thf(fact_3434_pinf_I6_J,axiom,
% 5.68/5.94 ! [T: int] :
% 5.68/5.94 ? [Z3: int] :
% 5.68/5.94 ! [X5: int] :
% 5.68/5.94 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.94 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.68/5.94
% 5.68/5.94 % pinf(6)
% 5.68/5.94 thf(fact_3435_inf__period_I1_J,axiom,
% 5.68/5.94 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.68/5.94 ( ! [X3: real,K2: real] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: real,K2: real] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: real,K4: real] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.68/5.94 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(1)
% 5.68/5.94 thf(fact_3436_inf__period_I1_J,axiom,
% 5.68/5.94 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.68/5.94 ( ! [X3: rat,K2: rat] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: rat,K2: rat] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: rat,K4: rat] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.68/5.94 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(1)
% 5.68/5.94 thf(fact_3437_inf__period_I1_J,axiom,
% 5.68/5.94 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int,K4: int] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.68/5.94 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(1)
% 5.68/5.94 thf(fact_3438_inf__period_I2_J,axiom,
% 5.68/5.94 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.68/5.94 ( ! [X3: real,K2: real] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: real,K2: real] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: real,K4: real] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 | ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.68/5.94 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(2)
% 5.68/5.94 thf(fact_3439_inf__period_I2_J,axiom,
% 5.68/5.94 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.68/5.94 ( ! [X3: rat,K2: rat] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: rat,K2: rat] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: rat,K4: rat] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 | ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.68/5.94 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(2)
% 5.68/5.94 thf(fact_3440_inf__period_I2_J,axiom,
% 5.68/5.94 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( Q @ X3 )
% 5.68/5.94 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int,K4: int] :
% 5.68/5.94 ( ( ( P @ X5 )
% 5.68/5.94 | ( Q @ X5 ) )
% 5.68/5.94 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.68/5.94 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % inf_period(2)
% 5.68/5.94 thf(fact_3441_conj__le__cong,axiom,
% 5.68/5.94 ! [X: int,X7: int,P: $o,P6: $o] :
% 5.68/5.94 ( ( X = X7 )
% 5.68/5.94 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.68/5.94 => ( P = P6 ) )
% 5.68/5.94 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/5.94 & P )
% 5.68/5.94 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.68/5.94 & P6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % conj_le_cong
% 5.68/5.94 thf(fact_3442_imp__le__cong,axiom,
% 5.68/5.94 ! [X: int,X7: int,P: $o,P6: $o] :
% 5.68/5.94 ( ( X = X7 )
% 5.68/5.94 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.68/5.94 => ( P = P6 ) )
% 5.68/5.94 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/5.94 => P )
% 5.68/5.94 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.68/5.94 => P6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % imp_le_cong
% 5.68/5.94 thf(fact_3443_less__eq__int__code_I1_J,axiom,
% 5.68/5.94 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.68/5.94
% 5.68/5.94 % less_eq_int_code(1)
% 5.68/5.94 thf(fact_3444_times__int__code_I2_J,axiom,
% 5.68/5.94 ! [L2: int] :
% 5.68/5.94 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.68/5.94 = zero_zero_int ) ).
% 5.68/5.94
% 5.68/5.94 % times_int_code(2)
% 5.68/5.94 thf(fact_3445_times__int__code_I1_J,axiom,
% 5.68/5.94 ! [K: int] :
% 5.68/5.94 ( ( times_times_int @ K @ zero_zero_int )
% 5.68/5.94 = zero_zero_int ) ).
% 5.68/5.94
% 5.68/5.94 % times_int_code(1)
% 5.68/5.94 thf(fact_3446_plus__int__code_I1_J,axiom,
% 5.68/5.94 ! [K: int] :
% 5.68/5.94 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.68/5.94 = K ) ).
% 5.68/5.94
% 5.68/5.94 % plus_int_code(1)
% 5.68/5.94 thf(fact_3447_plus__int__code_I2_J,axiom,
% 5.68/5.94 ! [L2: int] :
% 5.68/5.94 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.68/5.94 = L2 ) ).
% 5.68/5.94
% 5.68/5.94 % plus_int_code(2)
% 5.68/5.94 thf(fact_3448_int__distrib_I2_J,axiom,
% 5.68/5.94 ! [W: int,Z1: int,Z22: int] :
% 5.68/5.94 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.68/5.94 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_distrib(2)
% 5.68/5.94 thf(fact_3449_int__distrib_I1_J,axiom,
% 5.68/5.94 ! [Z1: int,Z22: int,W: int] :
% 5.68/5.94 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.68/5.94 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_distrib(1)
% 5.68/5.94 thf(fact_3450_int__distrib_I3_J,axiom,
% 5.68/5.94 ! [Z1: int,Z22: int,W: int] :
% 5.68/5.94 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.68/5.94 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_distrib(3)
% 5.68/5.94 thf(fact_3451_int__distrib_I4_J,axiom,
% 5.68/5.94 ! [W: int,Z1: int,Z22: int] :
% 5.68/5.94 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.68/5.94 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_distrib(4)
% 5.68/5.94 thf(fact_3452_zmult__zless__mono2,axiom,
% 5.68/5.94 ! [I2: int,J: int,K: int] :
% 5.68/5.94 ( ( ord_less_int @ I2 @ J )
% 5.68/5.94 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.68/5.94 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % zmult_zless_mono2
% 5.68/5.94 thf(fact_3453_odd__nonzero,axiom,
% 5.68/5.94 ! [Z: int] :
% 5.68/5.94 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.68/5.94 != zero_zero_int ) ).
% 5.68/5.94
% 5.68/5.94 % odd_nonzero
% 5.68/5.94 thf(fact_3454_int__ge__induct,axiom,
% 5.68/5.94 ! [K: int,I2: int,P: int > $o] :
% 5.68/5.94 ( ( ord_less_eq_int @ K @ I2 )
% 5.68/5.94 => ( ( P @ K )
% 5.68/5.94 => ( ! [I4: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ K @ I4 )
% 5.68/5.94 => ( ( P @ I4 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.68/5.94 => ( P @ I2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_ge_induct
% 5.68/5.94 thf(fact_3455_int__gr__induct,axiom,
% 5.68/5.94 ! [K: int,I2: int,P: int > $o] :
% 5.68/5.94 ( ( ord_less_int @ K @ I2 )
% 5.68/5.94 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.68/5.94 => ( ! [I4: int] :
% 5.68/5.94 ( ( ord_less_int @ K @ I4 )
% 5.68/5.94 => ( ( P @ I4 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.68/5.94 => ( P @ I2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_gr_induct
% 5.68/5.94 thf(fact_3456_zless__add1__eq,axiom,
% 5.68/5.94 ! [W: int,Z: int] :
% 5.68/5.94 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.68/5.94 = ( ( ord_less_int @ W @ Z )
% 5.68/5.94 | ( W = Z ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % zless_add1_eq
% 5.68/5.94 thf(fact_3457_int__le__induct,axiom,
% 5.68/5.94 ! [I2: int,K: int,P: int > $o] :
% 5.68/5.94 ( ( ord_less_eq_int @ I2 @ K )
% 5.68/5.94 => ( ( P @ K )
% 5.68/5.94 => ( ! [I4: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ I4 @ K )
% 5.68/5.94 => ( ( P @ I4 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.68/5.94 => ( P @ I2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_le_induct
% 5.68/5.94 thf(fact_3458_aset_I2_J,axiom,
% 5.68/5.94 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ A2 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ A2 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( Q @ X3 )
% 5.68/5.94 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ( P @ X5 )
% 5.68/5.94 | ( Q @ X5 ) )
% 5.68/5.94 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.68/5.94 | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(2)
% 5.68/5.94 thf(fact_3459_aset_I1_J,axiom,
% 5.68/5.94 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ A2 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ A2 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( Q @ X3 )
% 5.68/5.94 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.68/5.94 & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(1)
% 5.68/5.94 thf(fact_3460_bset_I2_J,axiom,
% 5.68/5.94 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ B4 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ B4 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( Q @ X3 )
% 5.68/5.94 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ( P @ X5 )
% 5.68/5.94 | ( Q @ X5 ) )
% 5.68/5.94 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.68/5.94 | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(2)
% 5.68/5.94 thf(fact_3461_bset_I1_J,axiom,
% 5.68/5.94 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ B4 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ! [Xa: int] :
% 5.68/5.94 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb: int] :
% 5.68/5.94 ( ( member_int @ Xb @ B4 )
% 5.68/5.94 => ( X3
% 5.68/5.94 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.68/5.94 => ( ( Q @ X3 )
% 5.68/5.94 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ( P @ X5 )
% 5.68/5.94 & ( Q @ X5 ) )
% 5.68/5.94 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.68/5.94 & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(1)
% 5.68/5.94 thf(fact_3462_int__one__le__iff__zero__less,axiom,
% 5.68/5.94 ! [Z: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.68/5.94 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_one_le_iff_zero_less
% 5.68/5.94 thf(fact_3463_pos__zmult__eq__1__iff,axiom,
% 5.68/5.94 ! [M: int,N: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ M )
% 5.68/5.94 => ( ( ( times_times_int @ M @ N )
% 5.68/5.94 = one_one_int )
% 5.68/5.94 = ( ( M = one_one_int )
% 5.68/5.94 & ( N = one_one_int ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % pos_zmult_eq_1_iff
% 5.68/5.94 thf(fact_3464_odd__less__0__iff,axiom,
% 5.68/5.94 ! [Z: int] :
% 5.68/5.94 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.68/5.94 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % odd_less_0_iff
% 5.68/5.94 thf(fact_3465_add1__zle__eq,axiom,
% 5.68/5.94 ! [W: int,Z: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.68/5.94 = ( ord_less_int @ W @ Z ) ) ).
% 5.68/5.94
% 5.68/5.94 % add1_zle_eq
% 5.68/5.94 thf(fact_3466_zless__imp__add1__zle,axiom,
% 5.68/5.94 ! [W: int,Z: int] :
% 5.68/5.94 ( ( ord_less_int @ W @ Z )
% 5.68/5.94 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.68/5.94
% 5.68/5.94 % zless_imp_add1_zle
% 5.68/5.94 thf(fact_3467_minusinfinity,axiom,
% 5.68/5.94 ! [D: int,P1: int > $o,P: int > $o] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.94 => ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( P1 @ X3 )
% 5.68/5.94 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.68/5.94 => ( ? [Z4: int] :
% 5.68/5.94 ! [X3: int] :
% 5.68/5.94 ( ( ord_less_int @ X3 @ Z4 )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 = ( P1 @ X3 ) ) )
% 5.68/5.94 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.68/5.94 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % minusinfinity
% 5.68/5.94 thf(fact_3468_plusinfinity,axiom,
% 5.68/5.94 ! [D: int,P6: int > $o,P: int > $o] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.94 => ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( P6 @ X3 )
% 5.68/5.94 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.68/5.94 => ( ? [Z4: int] :
% 5.68/5.94 ! [X3: int] :
% 5.68/5.94 ( ( ord_less_int @ Z4 @ X3 )
% 5.68/5.94 => ( ( P @ X3 )
% 5.68/5.94 = ( P6 @ X3 ) ) )
% 5.68/5.94 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.68/5.94 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % plusinfinity
% 5.68/5.94 thf(fact_3469_int__induct,axiom,
% 5.68/5.94 ! [P: int > $o,K: int,I2: int] :
% 5.68/5.94 ( ( P @ K )
% 5.68/5.94 => ( ! [I4: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ K @ I4 )
% 5.68/5.94 => ( ( P @ I4 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.68/5.94 => ( ! [I4: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ I4 @ K )
% 5.68/5.94 => ( ( P @ I4 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.68/5.94 => ( P @ I2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % int_induct
% 5.68/5.94 thf(fact_3470_le__imp__0__less,axiom,
% 5.68/5.94 ! [Z: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/5.94 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % le_imp_0_less
% 5.68/5.94 thf(fact_3471_incr__mult__lemma,axiom,
% 5.68/5.94 ! [D: int,P: int > $o,K: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.68/5.94 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ( P @ X5 )
% 5.68/5.94 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % incr_mult_lemma
% 5.68/5.94 thf(fact_3472_decr__mult__lemma,axiom,
% 5.68/5.94 ! [D: int,P: int > $o,K: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.94 => ( ! [X3: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.68/5.94 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ( P @ X5 )
% 5.68/5.94 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % decr_mult_lemma
% 5.68/5.94 thf(fact_3473_periodic__finite__ex,axiom,
% 5.68/5.94 ! [D: int,P: int > $o] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.94 => ( ! [X3: int,K2: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.68/5.94 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.68/5.94 = ( ? [X2: int] :
% 5.68/5.94 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.68/5.94 & ( P @ X2 ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % periodic_finite_ex
% 5.68/5.94 thf(fact_3474_aset_I7_J,axiom,
% 5.68/5.94 ! [D4: int,A2: set_int,T: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ord_less_int @ T @ X5 )
% 5.68/5.94 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(7)
% 5.68/5.94 thf(fact_3475_aset_I5_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,A2: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ T @ A2 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ord_less_int @ X5 @ T )
% 5.68/5.94 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(5)
% 5.68/5.94 thf(fact_3476_aset_I4_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,A2: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ T @ A2 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( X5 != T )
% 5.68/5.94 => ( ( plus_plus_int @ X5 @ D4 )
% 5.68/5.94 != T ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(4)
% 5.68/5.94 thf(fact_3477_aset_I3_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,A2: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( X5 = T )
% 5.68/5.94 => ( ( plus_plus_int @ X5 @ D4 )
% 5.68/5.94 = T ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % aset(3)
% 5.68/5.94 thf(fact_3478_bset_I7_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ T @ B4 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ord_less_int @ T @ X5 )
% 5.68/5.94 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(7)
% 5.68/5.94 thf(fact_3479_bset_I5_J,axiom,
% 5.68/5.94 ! [D4: int,B4: set_int,T: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( ord_less_int @ X5 @ T )
% 5.68/5.94 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(5)
% 5.68/5.94 thf(fact_3480_bset_I4_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ T @ B4 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( X5 != T )
% 5.68/5.94 => ( ( minus_minus_int @ X5 @ D4 )
% 5.68/5.94 != T ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(4)
% 5.68/5.94 thf(fact_3481_bset_I3_J,axiom,
% 5.68/5.94 ! [D4: int,T: int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.68/5.94 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.68/5.94 => ! [X5: int] :
% 5.68/5.94 ( ! [Xa3: int] :
% 5.68/5.94 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.94 => ! [Xb3: int] :
% 5.68/5.94 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.94 => ( X5
% 5.68/5.94 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.94 => ( ( X5 = T )
% 5.68/5.94 => ( ( minus_minus_int @ X5 @ D4 )
% 5.68/5.94 = T ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % bset(3)
% 5.68/5.94 thf(fact_3482_finite__nth__roots,axiom,
% 5.68/5.94 ! [N: nat,C: complex] :
% 5.68/5.94 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.94 => ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [Z2: complex] :
% 5.68/5.94 ( ( power_power_complex @ Z2 @ N )
% 5.68/5.94 = C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % finite_nth_roots
% 5.68/5.94 thf(fact_3483_psubsetI,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( A2 != B4 )
% 5.68/5.94 => ( ord_less_set_int @ A2 @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % psubsetI
% 5.68/5.94 thf(fact_3484_Diff__eq__empty__iff,axiom,
% 5.68/5.94 ! [A2: set_real,B4: set_real] :
% 5.68/5.94 ( ( ( minus_minus_set_real @ A2 @ B4 )
% 5.68/5.94 = bot_bot_set_real )
% 5.68/5.94 = ( ord_less_eq_set_real @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_eq_empty_iff
% 5.68/5.94 thf(fact_3485_Diff__eq__empty__iff,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat] :
% 5.68/5.94 ( ( ( minus_minus_set_nat @ A2 @ B4 )
% 5.68/5.94 = bot_bot_set_nat )
% 5.68/5.94 = ( ord_less_eq_set_nat @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_eq_empty_iff
% 5.68/5.94 thf(fact_3486_Diff__eq__empty__iff,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( ( minus_minus_set_int @ A2 @ B4 )
% 5.68/5.94 = bot_bot_set_int )
% 5.68/5.94 = ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_eq_empty_iff
% 5.68/5.94 thf(fact_3487_empty__subsetI,axiom,
% 5.68/5.94 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % empty_subsetI
% 5.68/5.94 thf(fact_3488_empty__subsetI,axiom,
% 5.68/5.94 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % empty_subsetI
% 5.68/5.94 thf(fact_3489_empty__subsetI,axiom,
% 5.68/5.94 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % empty_subsetI
% 5.68/5.94 thf(fact_3490_subset__empty,axiom,
% 5.68/5.94 ! [A2: set_nat] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.68/5.94 = ( A2 = bot_bot_set_nat ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_empty
% 5.68/5.94 thf(fact_3491_subset__empty,axiom,
% 5.68/5.94 ! [A2: set_real] :
% 5.68/5.94 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.68/5.94 = ( A2 = bot_bot_set_real ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_empty
% 5.68/5.94 thf(fact_3492_subset__empty,axiom,
% 5.68/5.94 ! [A2: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.68/5.94 = ( A2 = bot_bot_set_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_empty
% 5.68/5.94 thf(fact_3493_unset__bit__0,axiom,
% 5.68/5.94 ! [A: int] :
% 5.68/5.94 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.68/5.94 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_0
% 5.68/5.94 thf(fact_3494_unset__bit__0,axiom,
% 5.68/5.94 ! [A: nat] :
% 5.68/5.94 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.68/5.94 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_0
% 5.68/5.94 thf(fact_3495_flip__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: code_integer] :
% 5.68/5.94 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.68/5.94 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % flip_bit_Suc
% 5.68/5.94 thf(fact_3496_flip__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: int] :
% 5.68/5.94 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.68/5.94 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % flip_bit_Suc
% 5.68/5.94 thf(fact_3497_flip__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: nat] :
% 5.68/5.94 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.68/5.94 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % flip_bit_Suc
% 5.68/5.94 thf(fact_3498_unset__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: code_integer] :
% 5.68/5.94 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.68/5.94 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_Suc
% 5.68/5.94 thf(fact_3499_unset__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: int] :
% 5.68/5.94 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.68/5.94 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_Suc
% 5.68/5.94 thf(fact_3500_unset__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,A: nat] :
% 5.68/5.94 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.68/5.94 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_Suc
% 5.68/5.94 thf(fact_3501_subsetI,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat] :
% 5.68/5.94 ( ! [X3: nat] :
% 5.68/5.94 ( ( member_nat @ X3 @ A2 )
% 5.68/5.94 => ( member_nat @ X3 @ B4 ) )
% 5.68/5.94 => ( ord_less_eq_set_nat @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetI
% 5.68/5.94 thf(fact_3502_subsetI,axiom,
% 5.68/5.94 ! [A2: set_real,B4: set_real] :
% 5.68/5.94 ( ! [X3: real] :
% 5.68/5.94 ( ( member_real @ X3 @ A2 )
% 5.68/5.94 => ( member_real @ X3 @ B4 ) )
% 5.68/5.94 => ( ord_less_eq_set_real @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetI
% 5.68/5.94 thf(fact_3503_subsetI,axiom,
% 5.68/5.94 ! [A2: set_complex,B4: set_complex] :
% 5.68/5.94 ( ! [X3: complex] :
% 5.68/5.94 ( ( member_complex @ X3 @ A2 )
% 5.68/5.94 => ( member_complex @ X3 @ B4 ) )
% 5.68/5.94 => ( ord_le211207098394363844omplex @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetI
% 5.68/5.94 thf(fact_3504_subsetI,axiom,
% 5.68/5.94 ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.68/5.94 ( ! [X3: product_prod_nat_nat] :
% 5.68/5.94 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.68/5.94 => ( member8440522571783428010at_nat @ X3 @ B4 ) )
% 5.68/5.94 => ( ord_le3146513528884898305at_nat @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetI
% 5.68/5.94 thf(fact_3505_subsetI,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ( member_int @ X3 @ A2 )
% 5.68/5.94 => ( member_int @ X3 @ B4 ) )
% 5.68/5.94 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetI
% 5.68/5.94 thf(fact_3506_subset__antisym,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.94 => ( A2 = B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_antisym
% 5.68/5.94 thf(fact_3507_unset__bit__nonnegative__int__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.68/5.94 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_nonnegative_int_iff
% 5.68/5.94 thf(fact_3508_flip__bit__nonnegative__int__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.68/5.94 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/5.94
% 5.68/5.94 % flip_bit_nonnegative_int_iff
% 5.68/5.94 thf(fact_3509_unset__bit__negative__int__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int] :
% 5.68/5.94 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.68/5.94 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_negative_int_iff
% 5.68/5.94 thf(fact_3510_flip__bit__negative__int__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int] :
% 5.68/5.94 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.68/5.94 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % flip_bit_negative_int_iff
% 5.68/5.94 thf(fact_3511_unset__bit__less__eq,axiom,
% 5.68/5.94 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.68/5.94
% 5.68/5.94 % unset_bit_less_eq
% 5.68/5.94 thf(fact_3512_double__diff,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat,C4: set_nat] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_eq_set_nat @ B4 @ C4 )
% 5.68/5.94 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.68/5.94 = A2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % double_diff
% 5.68/5.94 thf(fact_3513_double__diff,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,C4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.68/5.94 => ( ( minus_minus_set_int @ B4 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.68/5.94 = A2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % double_diff
% 5.68/5.94 thf(fact_3514_Diff__subset,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_subset
% 5.68/5.94 thf(fact_3515_Diff__subset,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_subset
% 5.68/5.94 thf(fact_3516_Diff__mono,axiom,
% 5.68/5.94 ! [A2: set_nat,C4: set_nat,D4: set_nat,B4: set_nat] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.68/5.94 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 5.68/5.94 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_mono
% 5.68/5.94 thf(fact_3517_Diff__mono,axiom,
% 5.68/5.94 ! [A2: set_int,C4: set_int,D4: set_int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ D4 @ B4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Diff_mono
% 5.68/5.94 thf(fact_3518_in__mono,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat,X: nat] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.94 => ( ( member_nat @ X @ A2 )
% 5.68/5.94 => ( member_nat @ X @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % in_mono
% 5.68/5.94 thf(fact_3519_in__mono,axiom,
% 5.68/5.94 ! [A2: set_real,B4: set_real,X: real] :
% 5.68/5.94 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.94 => ( ( member_real @ X @ A2 )
% 5.68/5.94 => ( member_real @ X @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % in_mono
% 5.68/5.94 thf(fact_3520_in__mono,axiom,
% 5.68/5.94 ! [A2: set_complex,B4: set_complex,X: complex] :
% 5.68/5.94 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.94 => ( ( member_complex @ X @ A2 )
% 5.68/5.94 => ( member_complex @ X @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % in_mono
% 5.68/5.94 thf(fact_3521_in__mono,axiom,
% 5.68/5.94 ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.68/5.94 ( ( ord_le3146513528884898305at_nat @ A2 @ B4 )
% 5.68/5.94 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.68/5.94 => ( member8440522571783428010at_nat @ X @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % in_mono
% 5.68/5.94 thf(fact_3522_in__mono,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,X: int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( member_int @ X @ A2 )
% 5.68/5.94 => ( member_int @ X @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % in_mono
% 5.68/5.94 thf(fact_3523_subsetD,axiom,
% 5.68/5.94 ! [A2: set_nat,B4: set_nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.94 => ( ( member_nat @ C @ A2 )
% 5.68/5.94 => ( member_nat @ C @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetD
% 5.68/5.94 thf(fact_3524_subsetD,axiom,
% 5.68/5.94 ! [A2: set_real,B4: set_real,C: real] :
% 5.68/5.94 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.94 => ( ( member_real @ C @ A2 )
% 5.68/5.94 => ( member_real @ C @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetD
% 5.68/5.94 thf(fact_3525_subsetD,axiom,
% 5.68/5.94 ! [A2: set_complex,B4: set_complex,C: complex] :
% 5.68/5.94 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.94 => ( ( member_complex @ C @ A2 )
% 5.68/5.94 => ( member_complex @ C @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetD
% 5.68/5.94 thf(fact_3526_subsetD,axiom,
% 5.68/5.94 ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.68/5.94 ( ( ord_le3146513528884898305at_nat @ A2 @ B4 )
% 5.68/5.94 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.68/5.94 => ( member8440522571783428010at_nat @ C @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetD
% 5.68/5.94 thf(fact_3527_subsetD,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( member_int @ C @ A2 )
% 5.68/5.94 => ( member_int @ C @ B4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subsetD
% 5.68/5.94 thf(fact_3528_equalityE,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( A2 = B4 )
% 5.68/5.94 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ~ ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % equalityE
% 5.68/5.94 thf(fact_3529_subset__eq,axiom,
% 5.68/5.94 ( ord_less_eq_set_nat
% 5.68/5.94 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.68/5.94 ! [X2: nat] :
% 5.68/5.94 ( ( member_nat @ X2 @ A6 )
% 5.68/5.94 => ( member_nat @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_eq
% 5.68/5.94 thf(fact_3530_subset__eq,axiom,
% 5.68/5.94 ( ord_less_eq_set_real
% 5.68/5.94 = ( ^ [A6: set_real,B6: set_real] :
% 5.68/5.94 ! [X2: real] :
% 5.68/5.94 ( ( member_real @ X2 @ A6 )
% 5.68/5.94 => ( member_real @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_eq
% 5.68/5.94 thf(fact_3531_subset__eq,axiom,
% 5.68/5.94 ( ord_le211207098394363844omplex
% 5.68/5.94 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.68/5.94 ! [X2: complex] :
% 5.68/5.94 ( ( member_complex @ X2 @ A6 )
% 5.68/5.94 => ( member_complex @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_eq
% 5.68/5.94 thf(fact_3532_subset__eq,axiom,
% 5.68/5.94 ( ord_le3146513528884898305at_nat
% 5.68/5.94 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.68/5.94 ! [X2: product_prod_nat_nat] :
% 5.68/5.94 ( ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.68/5.94 => ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_eq
% 5.68/5.94 thf(fact_3533_subset__eq,axiom,
% 5.68/5.94 ( ord_less_eq_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ! [X2: int] :
% 5.68/5.94 ( ( member_int @ X2 @ A6 )
% 5.68/5.94 => ( member_int @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_eq
% 5.68/5.94 thf(fact_3534_equalityD1,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( A2 = B4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % equalityD1
% 5.68/5.94 thf(fact_3535_equalityD2,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( A2 = B4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % equalityD2
% 5.68/5.94 thf(fact_3536_subset__iff,axiom,
% 5.68/5.94 ( ord_less_eq_set_nat
% 5.68/5.94 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.68/5.94 ! [T2: nat] :
% 5.68/5.94 ( ( member_nat @ T2 @ A6 )
% 5.68/5.94 => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff
% 5.68/5.94 thf(fact_3537_subset__iff,axiom,
% 5.68/5.94 ( ord_less_eq_set_real
% 5.68/5.94 = ( ^ [A6: set_real,B6: set_real] :
% 5.68/5.94 ! [T2: real] :
% 5.68/5.94 ( ( member_real @ T2 @ A6 )
% 5.68/5.94 => ( member_real @ T2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff
% 5.68/5.94 thf(fact_3538_subset__iff,axiom,
% 5.68/5.94 ( ord_le211207098394363844omplex
% 5.68/5.94 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.68/5.94 ! [T2: complex] :
% 5.68/5.94 ( ( member_complex @ T2 @ A6 )
% 5.68/5.94 => ( member_complex @ T2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff
% 5.68/5.94 thf(fact_3539_subset__iff,axiom,
% 5.68/5.94 ( ord_le3146513528884898305at_nat
% 5.68/5.94 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.68/5.94 ! [T2: product_prod_nat_nat] :
% 5.68/5.94 ( ( member8440522571783428010at_nat @ T2 @ A6 )
% 5.68/5.94 => ( member8440522571783428010at_nat @ T2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff
% 5.68/5.94 thf(fact_3540_subset__iff,axiom,
% 5.68/5.94 ( ord_less_eq_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ! [T2: int] :
% 5.68/5.94 ( ( member_int @ T2 @ A6 )
% 5.68/5.94 => ( member_int @ T2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff
% 5.68/5.94 thf(fact_3541_subset__refl,axiom,
% 5.68/5.94 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % subset_refl
% 5.68/5.94 thf(fact_3542_Collect__mono,axiom,
% 5.68/5.94 ! [P: complex > $o,Q: complex > $o] :
% 5.68/5.94 ( ! [X3: complex] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( Q @ X3 ) )
% 5.68/5.94 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono
% 5.68/5.94 thf(fact_3543_Collect__mono,axiom,
% 5.68/5.94 ! [P: real > $o,Q: real > $o] :
% 5.68/5.94 ( ! [X3: real] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( Q @ X3 ) )
% 5.68/5.94 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono
% 5.68/5.94 thf(fact_3544_Collect__mono,axiom,
% 5.68/5.94 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.68/5.94 ( ! [X3: list_nat] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( Q @ X3 ) )
% 5.68/5.94 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono
% 5.68/5.94 thf(fact_3545_Collect__mono,axiom,
% 5.68/5.94 ! [P: nat > $o,Q: nat > $o] :
% 5.68/5.94 ( ! [X3: nat] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( Q @ X3 ) )
% 5.68/5.94 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono
% 5.68/5.94 thf(fact_3546_Collect__mono,axiom,
% 5.68/5.94 ! [P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ! [X3: int] :
% 5.68/5.94 ( ( P @ X3 )
% 5.68/5.94 => ( Q @ X3 ) )
% 5.68/5.94 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono
% 5.68/5.94 thf(fact_3547_subset__trans,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,C4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_trans
% 5.68/5.94 thf(fact_3548_set__eq__subset,axiom,
% 5.68/5.94 ( ( ^ [Y5: set_int,Z5: set_int] : ( Y5 = Z5 ) )
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.68/5.94 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % set_eq_subset
% 5.68/5.94 thf(fact_3549_Collect__mono__iff,axiom,
% 5.68/5.94 ! [P: complex > $o,Q: complex > $o] :
% 5.68/5.94 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.68/5.94 = ( ! [X2: complex] :
% 5.68/5.94 ( ( P @ X2 )
% 5.68/5.94 => ( Q @ X2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono_iff
% 5.68/5.94 thf(fact_3550_Collect__mono__iff,axiom,
% 5.68/5.94 ! [P: real > $o,Q: real > $o] :
% 5.68/5.94 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.68/5.94 = ( ! [X2: real] :
% 5.68/5.94 ( ( P @ X2 )
% 5.68/5.94 => ( Q @ X2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono_iff
% 5.68/5.94 thf(fact_3551_Collect__mono__iff,axiom,
% 5.68/5.94 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.68/5.94 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.68/5.94 = ( ! [X2: list_nat] :
% 5.68/5.94 ( ( P @ X2 )
% 5.68/5.94 => ( Q @ X2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono_iff
% 5.68/5.94 thf(fact_3552_Collect__mono__iff,axiom,
% 5.68/5.94 ! [P: nat > $o,Q: nat > $o] :
% 5.68/5.94 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.68/5.94 = ( ! [X2: nat] :
% 5.68/5.94 ( ( P @ X2 )
% 5.68/5.94 => ( Q @ X2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono_iff
% 5.68/5.94 thf(fact_3553_Collect__mono__iff,axiom,
% 5.68/5.94 ! [P: int > $o,Q: int > $o] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.68/5.94 = ( ! [X2: int] :
% 5.68/5.94 ( ( P @ X2 )
% 5.68/5.94 => ( Q @ X2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_mono_iff
% 5.68/5.94 thf(fact_3554_less__eq__set__def,axiom,
% 5.68/5.94 ( ord_less_eq_set_nat
% 5.68/5.94 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.68/5.94 ( ord_less_eq_nat_o
% 5.68/5.94 @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 5.68/5.94 @ ^ [X2: nat] : ( member_nat @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % less_eq_set_def
% 5.68/5.94 thf(fact_3555_less__eq__set__def,axiom,
% 5.68/5.94 ( ord_less_eq_set_real
% 5.68/5.94 = ( ^ [A6: set_real,B6: set_real] :
% 5.68/5.94 ( ord_less_eq_real_o
% 5.68/5.94 @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 5.68/5.94 @ ^ [X2: real] : ( member_real @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % less_eq_set_def
% 5.68/5.94 thf(fact_3556_less__eq__set__def,axiom,
% 5.68/5.94 ( ord_le211207098394363844omplex
% 5.68/5.94 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.68/5.94 ( ord_le4573692005234683329plex_o
% 5.68/5.94 @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 5.68/5.94 @ ^ [X2: complex] : ( member_complex @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % less_eq_set_def
% 5.68/5.94 thf(fact_3557_less__eq__set__def,axiom,
% 5.68/5.94 ( ord_le3146513528884898305at_nat
% 5.68/5.94 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.68/5.94 ( ord_le704812498762024988_nat_o
% 5.68/5.94 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.68/5.94 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % less_eq_set_def
% 5.68/5.94 thf(fact_3558_less__eq__set__def,axiom,
% 5.68/5.94 ( ord_less_eq_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ( ord_less_eq_int_o
% 5.68/5.94 @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 5.68/5.94 @ ^ [X2: int] : ( member_int @ X2 @ B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % less_eq_set_def
% 5.68/5.94 thf(fact_3559_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.68/5.94 ( ord_le3146513528884898305at_nat
% 5.68/5.94 @ ( collec3392354462482085612at_nat
% 5.68/5.94 @ ^ [X2: product_prod_nat_nat] :
% 5.68/5.94 ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3560_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_complex,P: complex > $o] :
% 5.68/5.94 ( ord_le211207098394363844omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [X2: complex] :
% 5.68/5.94 ( ( member_complex @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3561_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_real,P: real > $o] :
% 5.68/5.94 ( ord_less_eq_set_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [X2: real] :
% 5.68/5.94 ( ( member_real @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3562_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_list_nat,P: list_nat > $o] :
% 5.68/5.94 ( ord_le6045566169113846134st_nat
% 5.68/5.94 @ ( collect_list_nat
% 5.68/5.94 @ ^ [X2: list_nat] :
% 5.68/5.94 ( ( member_list_nat @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3563_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_nat,P: nat > $o] :
% 5.68/5.94 ( ord_less_eq_set_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [X2: nat] :
% 5.68/5.94 ( ( member_nat @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3564_Collect__subset,axiom,
% 5.68/5.94 ! [A2: set_int,P: int > $o] :
% 5.68/5.94 ( ord_less_eq_set_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [X2: int] :
% 5.68/5.94 ( ( member_int @ X2 @ A2 )
% 5.68/5.94 & ( P @ X2 ) ) )
% 5.68/5.94 @ A2 ) ).
% 5.68/5.94
% 5.68/5.94 % Collect_subset
% 5.68/5.94 thf(fact_3565_subset__iff__psubset__eq,axiom,
% 5.68/5.94 ( ord_less_eq_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ( ( ord_less_set_int @ A6 @ B6 )
% 5.68/5.94 | ( A6 = B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_iff_psubset_eq
% 5.68/5.94 thf(fact_3566_subset__psubset__trans,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,C4: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_set_int @ B4 @ C4 )
% 5.68/5.94 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_psubset_trans
% 5.68/5.94 thf(fact_3567_subset__not__subset__eq,axiom,
% 5.68/5.94 ( ord_less_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.68/5.94 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % subset_not_subset_eq
% 5.68/5.94 thf(fact_3568_psubset__subset__trans,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int,C4: set_int] :
% 5.68/5.94 ( ( ord_less_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ B4 @ C4 )
% 5.68/5.94 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % psubset_subset_trans
% 5.68/5.94 thf(fact_3569_psubset__imp__subset,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % psubset_imp_subset
% 5.68/5.94 thf(fact_3570_psubset__eq,axiom,
% 5.68/5.94 ( ord_less_set_int
% 5.68/5.94 = ( ^ [A6: set_int,B6: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.68/5.94 & ( A6 != B6 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % psubset_eq
% 5.68/5.94 thf(fact_3571_psubsetE,axiom,
% 5.68/5.94 ! [A2: set_int,B4: set_int] :
% 5.68/5.94 ( ( ord_less_set_int @ A2 @ B4 )
% 5.68/5.94 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.94 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % psubsetE
% 5.68/5.94 thf(fact_3572_Bolzano,axiom,
% 5.68/5.94 ! [A: real,B: real,P: real > real > $o] :
% 5.68/5.94 ( ( ord_less_eq_real @ A @ B )
% 5.68/5.94 => ( ! [A3: real,B2: real,C2: real] :
% 5.68/5.94 ( ( P @ A3 @ B2 )
% 5.68/5.94 => ( ( P @ B2 @ C2 )
% 5.68/5.94 => ( ( ord_less_eq_real @ A3 @ B2 )
% 5.68/5.94 => ( ( ord_less_eq_real @ B2 @ C2 )
% 5.68/5.94 => ( P @ A3 @ C2 ) ) ) ) )
% 5.68/5.94 => ( ! [X3: real] :
% 5.68/5.94 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/5.94 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/5.94 => ? [D5: real] :
% 5.68/5.94 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.68/5.94 & ! [A3: real,B2: real] :
% 5.68/5.94 ( ( ( ord_less_eq_real @ A3 @ X3 )
% 5.68/5.94 & ( ord_less_eq_real @ X3 @ B2 )
% 5.68/5.94 & ( ord_less_real @ ( minus_minus_real @ B2 @ A3 ) @ D5 ) )
% 5.68/5.94 => ( P @ A3 @ B2 ) ) ) ) )
% 5.68/5.94 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Bolzano
% 5.68/5.94 thf(fact_3573_mult__le__cancel__iff1,axiom,
% 5.68/5.94 ! [Z: real,X: real,Y2: real] :
% 5.68/5.94 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.68/5.94 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff1
% 5.68/5.94 thf(fact_3574_mult__le__cancel__iff1,axiom,
% 5.68/5.94 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.94 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.68/5.94 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff1
% 5.68/5.94 thf(fact_3575_mult__le__cancel__iff1,axiom,
% 5.68/5.94 ! [Z: int,X: int,Y2: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/5.94 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff1
% 5.68/5.94 thf(fact_3576_mult__le__cancel__iff2,axiom,
% 5.68/5.94 ! [Z: real,X: real,Y2: real] :
% 5.68/5.94 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.68/5.94 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y2 ) )
% 5.68/5.94 = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff2
% 5.68/5.94 thf(fact_3577_mult__le__cancel__iff2,axiom,
% 5.68/5.94 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.94 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.68/5.94 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y2 ) )
% 5.68/5.94 = ( ord_less_eq_rat @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff2
% 5.68/5.94 thf(fact_3578_mult__le__cancel__iff2,axiom,
% 5.68/5.94 ! [Z: int,X: int,Y2: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/5.94 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y2 ) )
% 5.68/5.94 = ( ord_less_eq_int @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_le_cancel_iff2
% 5.68/5.94 thf(fact_3579_divides__aux__eq,axiom,
% 5.68/5.94 ! [Q2: nat,R2: nat] :
% 5.68/5.94 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.68/5.94 = ( R2 = zero_zero_nat ) ) ).
% 5.68/5.94
% 5.68/5.94 % divides_aux_eq
% 5.68/5.94 thf(fact_3580_divides__aux__eq,axiom,
% 5.68/5.94 ! [Q2: int,R2: int] :
% 5.68/5.94 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 = ( R2 = zero_zero_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % divides_aux_eq
% 5.68/5.94 thf(fact_3581_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3582_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3583_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3584_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3585_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3586_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3587_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3588_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3589_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3590_product__nth,axiom,
% 5.68/5.94 ! [N: nat,Xs2: list_nat,Ys: list_o] :
% 5.68/5.94 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.68/5.94 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs2 @ Ys ) @ N )
% 5.68/5.94 = ( product_Pair_nat_o @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % product_nth
% 5.68/5.94 thf(fact_3591_neg__eucl__rel__int__mult__2,axiom,
% 5.68/5.94 ! [B: int,A: int,Q2: int,R2: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.68/5.94 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( 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 ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % neg_eucl_rel_int_mult_2
% 5.68/5.94 thf(fact_3592_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > complex,Y2: real > complex] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3593_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > complex,Y2: nat > complex] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3594_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_int,X: int > complex,Y2: int > complex] :
% 5.68/5.94 ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3595_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_complex,X: complex > complex,Y2: complex > complex] :
% 5.68/5.94 ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_complex ) ) ) )
% 5.68/5.94 => ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3596_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > real,Y2: real > real] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3597_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > real,Y2: nat > real] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3598_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_int,X: int > real,Y2: int > real] :
% 5.68/5.94 ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3599_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_complex,X: complex > real,Y2: complex > real] :
% 5.68/5.94 ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_real ) ) ) )
% 5.68/5.94 => ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3600_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > rat,Y2: real > rat] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_rat ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_rat ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_rat ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3601_prod_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > rat,Y2: nat > rat] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != one_one_rat ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != one_one_rat ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != one_one_rat ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.finite_Collect_op
% 5.68/5.94 thf(fact_3602_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3603_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.68/5.94 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3604_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.68/5.94 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3605_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.68/5.94 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3606_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3607_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_o,Ys: list_o] :
% 5.68/5.94 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3608_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_o,Ys: list_nat] :
% 5.68/5.94 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3609_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_o,Ys: list_int] :
% 5.68/5.94 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3610_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.68/5.94 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3611_length__product,axiom,
% 5.68/5.94 ! [Xs2: list_nat,Ys: list_o] :
% 5.68/5.94 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.68/5.94 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % length_product
% 5.68/5.94 thf(fact_3612_unique__remainder,axiom,
% 5.68/5.94 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.68/5.94 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.68/5.94 => ( R2 = R4 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unique_remainder
% 5.68/5.94 thf(fact_3613_unique__quotient,axiom,
% 5.68/5.94 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.68/5.94 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.68/5.94 => ( Q2 = Q5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % unique_quotient
% 5.68/5.94 thf(fact_3614_eucl__rel__int__by0,axiom,
% 5.68/5.94 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.68/5.94
% 5.68/5.94 % eucl_rel_int_by0
% 5.68/5.94 thf(fact_3615_div__int__unique,axiom,
% 5.68/5.94 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.68/5.94 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( ( divide_divide_int @ K @ L2 )
% 5.68/5.94 = Q2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % div_int_unique
% 5.68/5.94 thf(fact_3616_mod__int__unique,axiom,
% 5.68/5.94 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.68/5.94 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( ( modulo_modulo_int @ K @ L2 )
% 5.68/5.94 = R2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % mod_int_unique
% 5.68/5.94 thf(fact_3617_eucl__rel__int__dividesI,axiom,
% 5.68/5.94 ! [L2: int,K: int,Q2: int] :
% 5.68/5.94 ( ( L2 != zero_zero_int )
% 5.68/5.94 => ( ( K
% 5.68/5.94 = ( times_times_int @ Q2 @ L2 ) )
% 5.68/5.94 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % eucl_rel_int_dividesI
% 5.68/5.94 thf(fact_3618_eucl__rel__int,axiom,
% 5.68/5.94 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % eucl_rel_int
% 5.68/5.94 thf(fact_3619_eucl__rel__int__iff,axiom,
% 5.68/5.94 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.68/5.94 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 = ( ( K
% 5.68/5.94 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 5.68/5.94 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.68/5.94 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.68/5.94 & ( ord_less_int @ R2 @ L2 ) ) )
% 5.68/5.94 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.68/5.94 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.68/5.94 => ( ( ord_less_int @ L2 @ R2 )
% 5.68/5.94 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.68/5.94 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.68/5.94 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % eucl_rel_int_iff
% 5.68/5.94 thf(fact_3620_mult__less__iff1,axiom,
% 5.68/5.94 ! [Z: real,X: real,Y2: real] :
% 5.68/5.94 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.68/5.94 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_real @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_less_iff1
% 5.68/5.94 thf(fact_3621_mult__less__iff1,axiom,
% 5.68/5.94 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.94 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.68/5.94 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_rat @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_less_iff1
% 5.68/5.94 thf(fact_3622_mult__less__iff1,axiom,
% 5.68/5.94 ! [Z: int,X: int,Y2: int] :
% 5.68/5.94 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/5.94 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y2 @ Z ) )
% 5.68/5.94 = ( ord_less_int @ X @ Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % mult_less_iff1
% 5.68/5.94 thf(fact_3623_pos__eucl__rel__int__mult__2,axiom,
% 5.68/5.94 ! [B: int,A: int,Q2: int,R2: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.68/5.94 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.94 => ( 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 ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % pos_eucl_rel_int_mult_2
% 5.68/5.94 thf(fact_3624_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > complex,Y2: real > complex] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3625_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > complex,Y2: nat > complex] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3626_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_int,X: int > complex,Y2: int > complex] :
% 5.68/5.94 ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3627_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_complex,X: complex > complex,Y2: complex > complex] :
% 5.68/5.94 ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_complex ) ) ) )
% 5.68/5.94 => ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_complex ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3628_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > real,Y2: real > real] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3629_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > real,Y2: nat > real] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3630_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_int,X: int > real,Y2: int > real] :
% 5.68/5.94 ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( finite_finite_int
% 5.68/5.94 @ ( collect_int
% 5.68/5.94 @ ^ [I3: int] :
% 5.68/5.94 ( ( member_int @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3631_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_complex,X: complex > real,Y2: complex > real] :
% 5.68/5.94 ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_real ) ) ) )
% 5.68/5.94 => ( finite3207457112153483333omplex
% 5.68/5.94 @ ( collect_complex
% 5.68/5.94 @ ^ [I3: complex] :
% 5.68/5.94 ( ( member_complex @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3632_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_real,X: real > rat,Y2: real > rat] :
% 5.68/5.94 ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_rat ) ) ) )
% 5.68/5.94 => ( ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_rat ) ) ) )
% 5.68/5.94 => ( finite_finite_real
% 5.68/5.94 @ ( collect_real
% 5.68/5.94 @ ^ [I3: real] :
% 5.68/5.94 ( ( member_real @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3633_sum_Ofinite__Collect__op,axiom,
% 5.68/5.94 ! [I5: set_nat,X: nat > rat,Y2: nat > rat] :
% 5.68/5.94 ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( X @ I3 )
% 5.68/5.94 != zero_zero_rat ) ) ) )
% 5.68/5.94 => ( ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( Y2 @ I3 )
% 5.68/5.94 != zero_zero_rat ) ) ) )
% 5.68/5.94 => ( finite_finite_nat
% 5.68/5.94 @ ( collect_nat
% 5.68/5.94 @ ^ [I3: nat] :
% 5.68/5.94 ( ( member_nat @ I3 @ I5 )
% 5.68/5.94 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y2 @ I3 ) )
% 5.68/5.94 != zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % sum.finite_Collect_op
% 5.68/5.94 thf(fact_3634_prod_Oinject,axiom,
% 5.68/5.94 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 5.68/5.94 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.68/5.94 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.68/5.94 = ( ( X1 = Y1 )
% 5.68/5.94 & ( X22 = Y22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.inject
% 5.68/5.94 thf(fact_3635_prod_Oinject,axiom,
% 5.68/5.94 ! [X1: code_integer > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc6137756002093451184nteger @ X1 @ X22 )
% 5.68/5.94 = ( produc6137756002093451184nteger @ Y1 @ Y22 ) )
% 5.68/5.94 = ( ( X1 = Y1 )
% 5.68/5.94 & ( X22 = Y22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.inject
% 5.68/5.94 thf(fact_3636_prod_Oinject,axiom,
% 5.68/5.94 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 5.68/5.94 = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 5.68/5.94 = ( ( X1 = Y1 )
% 5.68/5.94 & ( X22 = Y22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.inject
% 5.68/5.94 thf(fact_3637_prod_Oinject,axiom,
% 5.68/5.94 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 5.68/5.94 = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 5.68/5.94 = ( ( X1 = Y1 )
% 5.68/5.94 & ( X22 = Y22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.inject
% 5.68/5.94 thf(fact_3638_prod_Oinject,axiom,
% 5.68/5.94 ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 5.68/5.94 = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 5.68/5.94 = ( ( X1 = Y1 )
% 5.68/5.94 & ( X22 = Y22 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod.inject
% 5.68/5.94 thf(fact_3639_old_Oprod_Oinject,axiom,
% 5.68/5.94 ! [A: int,B: int,A5: int,B5: int] :
% 5.68/5.94 ( ( ( product_Pair_int_int @ A @ B )
% 5.68/5.94 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.68/5.94 = ( ( A = A5 )
% 5.68/5.94 & ( B = B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.inject
% 5.68/5.94 thf(fact_3640_old_Oprod_Oinject,axiom,
% 5.68/5.94 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.68/5.94 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.68/5.94 = ( ( A = A5 )
% 5.68/5.94 & ( B = B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.inject
% 5.68/5.94 thf(fact_3641_old_Oprod_Oinject,axiom,
% 5.68/5.94 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.68/5.94 = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.68/5.94 = ( ( A = A5 )
% 5.68/5.94 & ( B = B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.inject
% 5.68/5.94 thf(fact_3642_old_Oprod_Oinject,axiom,
% 5.68/5.94 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.68/5.94 = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.68/5.94 = ( ( A = A5 )
% 5.68/5.94 & ( B = B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.inject
% 5.68/5.94 thf(fact_3643_old_Oprod_Oinject,axiom,
% 5.68/5.94 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.68/5.94 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.68/5.94 = ( ( A = A5 )
% 5.68/5.94 & ( B = B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.inject
% 5.68/5.94 thf(fact_3644_old_Oprod_Oexhaust,axiom,
% 5.68/5.94 ! [Y2: product_prod_int_int] :
% 5.68/5.94 ~ ! [A3: int,B2: int] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( product_Pair_int_int @ A3 @ B2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.exhaust
% 5.68/5.94 thf(fact_3645_old_Oprod_Oexhaust,axiom,
% 5.68/5.94 ! [Y2: produc8763457246119570046nteger] :
% 5.68/5.94 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc6137756002093451184nteger @ A3 @ B2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.exhaust
% 5.68/5.94 thf(fact_3646_old_Oprod_Oexhaust,axiom,
% 5.68/5.94 ! [Y2: produc1908205239877642774nteger] :
% 5.68/5.94 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc8603105652947943368nteger @ A3 @ B2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.exhaust
% 5.68/5.94 thf(fact_3647_old_Oprod_Oexhaust,axiom,
% 5.68/5.94 ! [Y2: produc2285326912895808259nt_int] :
% 5.68/5.94 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc5700946648718959541nt_int @ A3 @ B2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.exhaust
% 5.68/5.94 thf(fact_3648_old_Oprod_Oexhaust,axiom,
% 5.68/5.94 ! [Y2: produc7773217078559923341nt_int] :
% 5.68/5.94 ~ ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc4305682042979456191nt_int @ A3 @ B2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % old.prod.exhaust
% 5.68/5.94 thf(fact_3649_surj__pair,axiom,
% 5.68/5.94 ! [P4: product_prod_int_int] :
% 5.68/5.94 ? [X3: int,Y3: int] :
% 5.68/5.94 ( P4
% 5.68/5.94 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 5.68/5.94
% 5.68/5.94 % surj_pair
% 5.68/5.94 thf(fact_3650_surj__pair,axiom,
% 5.68/5.94 ! [P4: produc8763457246119570046nteger] :
% 5.68/5.94 ? [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/5.94 ( P4
% 5.68/5.94 = ( produc6137756002093451184nteger @ X3 @ Y3 ) ) ).
% 5.68/5.94
% 5.68/5.94 % surj_pair
% 5.68/5.94 thf(fact_3651_surj__pair,axiom,
% 5.68/5.94 ! [P4: produc1908205239877642774nteger] :
% 5.68/5.94 ? [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/5.94 ( P4
% 5.68/5.94 = ( produc8603105652947943368nteger @ X3 @ Y3 ) ) ).
% 5.68/5.94
% 5.68/5.94 % surj_pair
% 5.68/5.94 thf(fact_3652_surj__pair,axiom,
% 5.68/5.94 ! [P4: produc2285326912895808259nt_int] :
% 5.68/5.94 ? [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/5.94 ( P4
% 5.68/5.94 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ).
% 5.68/5.94
% 5.68/5.94 % surj_pair
% 5.68/5.94 thf(fact_3653_surj__pair,axiom,
% 5.68/5.94 ! [P4: produc7773217078559923341nt_int] :
% 5.68/5.94 ? [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/5.94 ( P4
% 5.68/5.94 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ).
% 5.68/5.94
% 5.68/5.94 % surj_pair
% 5.68/5.94 thf(fact_3654_prod__cases,axiom,
% 5.68/5.94 ! [P: product_prod_int_int > $o,P4: product_prod_int_int] :
% 5.68/5.94 ( ! [A3: int,B2: int] : ( P @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/5.94 => ( P @ P4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases
% 5.68/5.94 thf(fact_3655_prod__cases,axiom,
% 5.68/5.94 ! [P: produc8763457246119570046nteger > $o,P4: produc8763457246119570046nteger] :
% 5.68/5.94 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/5.94 => ( P @ P4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases
% 5.68/5.94 thf(fact_3656_prod__cases,axiom,
% 5.68/5.94 ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 5.68/5.94 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 5.68/5.94 => ( P @ P4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases
% 5.68/5.94 thf(fact_3657_prod__cases,axiom,
% 5.68/5.94 ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 5.68/5.94 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 5.68/5.94 => ( P @ P4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases
% 5.68/5.94 thf(fact_3658_prod__cases,axiom,
% 5.68/5.94 ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 5.68/5.94 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.68/5.94 => ( P @ P4 ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases
% 5.68/5.94 thf(fact_3659_Pair__inject,axiom,
% 5.68/5.94 ! [A: int,B: int,A5: int,B5: int] :
% 5.68/5.94 ( ( ( product_Pair_int_int @ A @ B )
% 5.68/5.94 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.68/5.94 => ~ ( ( A = A5 )
% 5.68/5.94 => ( B != B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Pair_inject
% 5.68/5.94 thf(fact_3660_Pair__inject,axiom,
% 5.68/5.94 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.68/5.94 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.68/5.94 => ~ ( ( A = A5 )
% 5.68/5.94 => ( B != B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Pair_inject
% 5.68/5.94 thf(fact_3661_Pair__inject,axiom,
% 5.68/5.94 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.68/5.94 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.68/5.94 = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.68/5.94 => ~ ( ( A = A5 )
% 5.68/5.94 => ( B != B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Pair_inject
% 5.68/5.94 thf(fact_3662_Pair__inject,axiom,
% 5.68/5.94 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.68/5.94 = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.68/5.94 => ~ ( ( A = A5 )
% 5.68/5.94 => ( B != B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Pair_inject
% 5.68/5.94 thf(fact_3663_Pair__inject,axiom,
% 5.68/5.94 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.68/5.94 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.68/5.94 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.68/5.94 => ~ ( ( A = A5 )
% 5.68/5.94 => ( B != B5 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Pair_inject
% 5.68/5.94 thf(fact_3664_prod__cases3,axiom,
% 5.68/5.94 ! [Y2: produc8763457246119570046nteger] :
% 5.68/5.94 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C2: code_integer] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases3
% 5.68/5.94 thf(fact_3665_prod__cases3,axiom,
% 5.68/5.94 ! [Y2: produc1908205239877642774nteger] :
% 5.68/5.94 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C2: code_integer] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases3
% 5.68/5.94 thf(fact_3666_prod__cases3,axiom,
% 5.68/5.94 ! [Y2: produc2285326912895808259nt_int] :
% 5.68/5.94 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C2: int] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases3
% 5.68/5.94 thf(fact_3667_prod__cases3,axiom,
% 5.68/5.94 ! [Y2: produc7773217078559923341nt_int] :
% 5.68/5.94 ~ ! [A3: int > option6357759511663192854e_term,B2: int,C2: int] :
% 5.68/5.94 ( Y2
% 5.68/5.94 != ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_cases3
% 5.68/5.94 thf(fact_3668_prod__induct3,axiom,
% 5.68/5.94 ! [P: produc8763457246119570046nteger > $o,X: produc8763457246119570046nteger] :
% 5.68/5.94 ( ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C2: code_integer] : ( P @ ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C2 ) ) )
% 5.68/5.94 => ( P @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_induct3
% 5.68/5.94 thf(fact_3669_prod__induct3,axiom,
% 5.68/5.94 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 5.68/5.94 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C2: code_integer] : ( P @ ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C2 ) ) )
% 5.68/5.94 => ( P @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_induct3
% 5.68/5.94 thf(fact_3670_prod__induct3,axiom,
% 5.68/5.94 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 5.68/5.94 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C2 ) ) )
% 5.68/5.94 => ( P @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_induct3
% 5.68/5.94 thf(fact_3671_prod__induct3,axiom,
% 5.68/5.94 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 5.68/5.94 ( ! [A3: int > option6357759511663192854e_term,B2: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C2 ) ) )
% 5.68/5.94 => ( P @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % prod_induct3
% 5.68/5.94 thf(fact_3672_gcd__nat__induct,axiom,
% 5.68/5.94 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.68/5.94 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.68/5.94 => ( ! [M5: nat,N3: nat] :
% 5.68/5.94 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.68/5.94 => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 5.68/5.94 => ( P @ M5 @ N3 ) ) )
% 5.68/5.94 => ( P @ M @ N ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % gcd_nat_induct
% 5.68/5.94 thf(fact_3673_concat__bit__Suc,axiom,
% 5.68/5.94 ! [N: nat,K: int,L2: int] :
% 5.68/5.94 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.68/5.94 = ( 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 ) ) ) @ L2 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % concat_bit_Suc
% 5.68/5.94 thf(fact_3674_dbl__simps_I3_J,axiom,
% 5.68/5.94 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.68/5.94 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(3)
% 5.68/5.94 thf(fact_3675_dbl__simps_I3_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.68/5.94 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(3)
% 5.68/5.94 thf(fact_3676_dbl__simps_I3_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.68/5.94 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(3)
% 5.68/5.94 thf(fact_3677_dbl__simps_I3_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.68/5.94 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(3)
% 5.68/5.94 thf(fact_3678_dual__order_Orefl,axiom,
% 5.68/5.94 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.68/5.94
% 5.68/5.94 % dual_order.refl
% 5.68/5.94 thf(fact_3679_dual__order_Orefl,axiom,
% 5.68/5.94 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.68/5.94
% 5.68/5.94 % dual_order.refl
% 5.68/5.94 thf(fact_3680_dual__order_Orefl,axiom,
% 5.68/5.94 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.68/5.94
% 5.68/5.94 % dual_order.refl
% 5.68/5.94 thf(fact_3681_dual__order_Orefl,axiom,
% 5.68/5.94 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.68/5.94
% 5.68/5.94 % dual_order.refl
% 5.68/5.94 thf(fact_3682_dual__order_Orefl,axiom,
% 5.68/5.94 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.68/5.94
% 5.68/5.94 % dual_order.refl
% 5.68/5.94 thf(fact_3683_order__refl,axiom,
% 5.68/5.94 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 5.68/5.94
% 5.68/5.94 % order_refl
% 5.68/5.94 thf(fact_3684_order__refl,axiom,
% 5.68/5.94 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.68/5.94
% 5.68/5.94 % order_refl
% 5.68/5.94 thf(fact_3685_order__refl,axiom,
% 5.68/5.94 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.68/5.94
% 5.68/5.94 % order_refl
% 5.68/5.94 thf(fact_3686_order__refl,axiom,
% 5.68/5.94 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.68/5.94
% 5.68/5.94 % order_refl
% 5.68/5.94 thf(fact_3687_order__refl,axiom,
% 5.68/5.94 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.68/5.94
% 5.68/5.94 % order_refl
% 5.68/5.94 thf(fact_3688_concat__bit__0,axiom,
% 5.68/5.94 ! [K: int,L2: int] :
% 5.68/5.94 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.68/5.94 = L2 ) ).
% 5.68/5.94
% 5.68/5.94 % concat_bit_0
% 5.68/5.94 thf(fact_3689_dbl__simps_I2_J,axiom,
% 5.68/5.94 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.68/5.94 = zero_zero_complex ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(2)
% 5.68/5.94 thf(fact_3690_dbl__simps_I2_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.68/5.94 = zero_zero_real ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(2)
% 5.68/5.94 thf(fact_3691_dbl__simps_I2_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.68/5.94 = zero_zero_rat ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(2)
% 5.68/5.94 thf(fact_3692_dbl__simps_I2_J,axiom,
% 5.68/5.94 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.68/5.94 = zero_zero_int ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(2)
% 5.68/5.94 thf(fact_3693_concat__bit__nonnegative__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int,L2: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.68/5.94 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % concat_bit_nonnegative_iff
% 5.68/5.94 thf(fact_3694_concat__bit__negative__iff,axiom,
% 5.68/5.94 ! [N: nat,K: int,L2: int] :
% 5.68/5.94 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 5.68/5.94 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.68/5.94
% 5.68/5.94 % concat_bit_negative_iff
% 5.68/5.94 thf(fact_3695_dbl__simps_I5_J,axiom,
% 5.68/5.94 ! [K: num] :
% 5.68/5.94 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.68/5.94 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(5)
% 5.68/5.94 thf(fact_3696_dbl__simps_I5_J,axiom,
% 5.68/5.94 ! [K: num] :
% 5.68/5.94 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.68/5.94 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(5)
% 5.68/5.94 thf(fact_3697_dbl__simps_I5_J,axiom,
% 5.68/5.94 ! [K: num] :
% 5.68/5.94 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.68/5.94 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(5)
% 5.68/5.94 thf(fact_3698_dbl__simps_I5_J,axiom,
% 5.68/5.94 ! [K: num] :
% 5.68/5.94 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.68/5.94 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_simps(5)
% 5.68/5.94 thf(fact_3699_concat__bit__assoc,axiom,
% 5.68/5.94 ! [N: nat,K: int,M: nat,L2: int,R2: int] :
% 5.68/5.94 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 5.68/5.94 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % concat_bit_assoc
% 5.68/5.94 thf(fact_3700_dbl__def,axiom,
% 5.68/5.94 ( neg_numeral_dbl_real
% 5.68/5.94 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_def
% 5.68/5.94 thf(fact_3701_dbl__def,axiom,
% 5.68/5.94 ( neg_numeral_dbl_rat
% 5.68/5.94 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_def
% 5.68/5.94 thf(fact_3702_dbl__def,axiom,
% 5.68/5.94 ( neg_numeral_dbl_int
% 5.68/5.94 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % dbl_def
% 5.68/5.94 thf(fact_3703_order__antisym__conv,axiom,
% 5.68/5.94 ! [Y2: set_int,X: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ Y2 @ X )
% 5.68/5.94 => ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.94 = ( X = Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_antisym_conv
% 5.68/5.94 thf(fact_3704_order__antisym__conv,axiom,
% 5.68/5.94 ! [Y2: rat,X: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.94 => ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.94 = ( X = Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_antisym_conv
% 5.68/5.94 thf(fact_3705_order__antisym__conv,axiom,
% 5.68/5.94 ! [Y2: num,X: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.94 => ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.94 = ( X = Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_antisym_conv
% 5.68/5.94 thf(fact_3706_order__antisym__conv,axiom,
% 5.68/5.94 ! [Y2: nat,X: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.94 => ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.94 = ( X = Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_antisym_conv
% 5.68/5.94 thf(fact_3707_order__antisym__conv,axiom,
% 5.68/5.94 ! [Y2: int,X: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.94 => ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.94 = ( X = Y2 ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_antisym_conv
% 5.68/5.94 thf(fact_3708_linorder__le__cases,axiom,
% 5.68/5.94 ! [X: rat,Y2: rat] :
% 5.68/5.94 ( ~ ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.94 => ( ord_less_eq_rat @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_le_cases
% 5.68/5.94 thf(fact_3709_linorder__le__cases,axiom,
% 5.68/5.94 ! [X: num,Y2: num] :
% 5.68/5.94 ( ~ ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.94 => ( ord_less_eq_num @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_le_cases
% 5.68/5.94 thf(fact_3710_linorder__le__cases,axiom,
% 5.68/5.94 ! [X: nat,Y2: nat] :
% 5.68/5.94 ( ~ ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.94 => ( ord_less_eq_nat @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_le_cases
% 5.68/5.94 thf(fact_3711_linorder__le__cases,axiom,
% 5.68/5.94 ! [X: int,Y2: int] :
% 5.68/5.94 ( ~ ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.94 => ( ord_less_eq_int @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_le_cases
% 5.68/5.94 thf(fact_3712_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3713_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3714_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3715_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3716_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3717_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3718_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3719_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3720_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3721_ord__le__eq__subst,axiom,
% 5.68/5.94 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.94 => ( ( ( F @ B )
% 5.68/5.94 = C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_le_eq_subst
% 5.68/5.94 thf(fact_3722_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3723_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3724_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3725_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3726_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3727_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: num,F: num > num,B: num,C: num] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3728_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3729_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: int,F: num > int,B: num,C: num] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3730_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3731_ord__eq__le__subst,axiom,
% 5.68/5.94 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.68/5.94 ( ( A
% 5.68/5.94 = ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % ord_eq_le_subst
% 5.68/5.94 thf(fact_3732_linorder__linear,axiom,
% 5.68/5.94 ! [X: rat,Y2: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.94 | ( ord_less_eq_rat @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_linear
% 5.68/5.94 thf(fact_3733_linorder__linear,axiom,
% 5.68/5.94 ! [X: num,Y2: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.94 | ( ord_less_eq_num @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_linear
% 5.68/5.94 thf(fact_3734_linorder__linear,axiom,
% 5.68/5.94 ! [X: nat,Y2: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.94 | ( ord_less_eq_nat @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_linear
% 5.68/5.94 thf(fact_3735_linorder__linear,axiom,
% 5.68/5.94 ! [X: int,Y2: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.94 | ( ord_less_eq_int @ Y2 @ X ) ) ).
% 5.68/5.94
% 5.68/5.94 % linorder_linear
% 5.68/5.94 thf(fact_3736_order__eq__refl,axiom,
% 5.68/5.94 ! [X: set_int,Y2: set_int] :
% 5.68/5.94 ( ( X = Y2 )
% 5.68/5.94 => ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_eq_refl
% 5.68/5.94 thf(fact_3737_order__eq__refl,axiom,
% 5.68/5.94 ! [X: rat,Y2: rat] :
% 5.68/5.94 ( ( X = Y2 )
% 5.68/5.94 => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_eq_refl
% 5.68/5.94 thf(fact_3738_order__eq__refl,axiom,
% 5.68/5.94 ! [X: num,Y2: num] :
% 5.68/5.94 ( ( X = Y2 )
% 5.68/5.94 => ( ord_less_eq_num @ X @ Y2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_eq_refl
% 5.68/5.94 thf(fact_3739_order__eq__refl,axiom,
% 5.68/5.94 ! [X: nat,Y2: nat] :
% 5.68/5.94 ( ( X = Y2 )
% 5.68/5.94 => ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_eq_refl
% 5.68/5.94 thf(fact_3740_order__eq__refl,axiom,
% 5.68/5.94 ! [X: int,Y2: int] :
% 5.68/5.94 ( ( X = Y2 )
% 5.68/5.94 => ( ord_less_eq_int @ X @ Y2 ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_eq_refl
% 5.68/5.94 thf(fact_3741_order__subst2,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3742_order__subst2,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3743_order__subst2,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3744_order__subst2,axiom,
% 5.68/5.94 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3745_order__subst2,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3746_order__subst2,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3747_order__subst2,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3748_order__subst2,axiom,
% 5.68/5.94 ! [A: num,B: num,F: num > int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3749_order__subst2,axiom,
% 5.68/5.94 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3750_order__subst2,axiom,
% 5.68/5.94 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.94 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst2
% 5.68/5.94 thf(fact_3751_order__subst1,axiom,
% 5.68/5.94 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3752_order__subst1,axiom,
% 5.68/5.94 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3753_order__subst1,axiom,
% 5.68/5.94 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3754_order__subst1,axiom,
% 5.68/5.94 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_int @ B @ C )
% 5.68/5.94 => ( ! [X3: int,Y3: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3755_order__subst1,axiom,
% 5.68/5.94 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3756_order__subst1,axiom,
% 5.68/5.94 ! [A: num,F: num > num,B: num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3757_order__subst1,axiom,
% 5.68/5.94 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.94 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3758_order__subst1,axiom,
% 5.68/5.94 ! [A: num,F: int > num,B: int,C: int] :
% 5.68/5.94 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_int @ B @ C )
% 5.68/5.94 => ( ! [X3: int,Y3: int] :
% 5.68/5.94 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3759_order__subst1,axiom,
% 5.68/5.94 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.94 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3760_order__subst1,axiom,
% 5.68/5.94 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.68/5.94 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.68/5.94 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.94 => ( ! [X3: num,Y3: num] :
% 5.68/5.94 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.94 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.94 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % order_subst1
% 5.68/5.94 thf(fact_3761_Orderings_Oorder__eq__iff,axiom,
% 5.68/5.94 ( ( ^ [Y5: set_int,Z5: set_int] : ( Y5 = Z5 ) )
% 5.68/5.94 = ( ^ [A4: set_int,B3: set_int] :
% 5.68/5.94 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.68/5.94 & ( ord_less_eq_set_int @ B3 @ A4 ) ) ) ) ).
% 5.68/5.94
% 5.68/5.94 % Orderings.order_eq_iff
% 5.68/5.94 thf(fact_3762_Orderings_Oorder__eq__iff,axiom,
% 5.68/5.94 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.68/5.94 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.94 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.68/5.94 & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % Orderings.order_eq_iff
% 5.68/5.95 thf(fact_3763_Orderings_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: num,Z5: num] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: num,B3: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.68/5.95 & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % Orderings.order_eq_iff
% 5.68/5.95 thf(fact_3764_Orderings_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.68/5.95 & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % Orderings.order_eq_iff
% 5.68/5.95 thf(fact_3765_Orderings_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: int,B3: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.68/5.95 & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % Orderings.order_eq_iff
% 5.68/5.95 thf(fact_3766_antisym,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ B @ A )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym
% 5.68/5.95 thf(fact_3767_antisym,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_rat @ B @ A )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym
% 5.68/5.95 thf(fact_3768_antisym,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_num @ B @ A )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym
% 5.68/5.95 thf(fact_3769_antisym,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_nat @ B @ A )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym
% 5.68/5.95 thf(fact_3770_antisym,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_int @ B @ A )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym
% 5.68/5.95 thf(fact_3771_dual__order_Otrans,axiom,
% 5.68/5.95 ! [B: set_int,A: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ C @ B )
% 5.68/5.95 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.trans
% 5.68/5.95 thf(fact_3772_dual__order_Otrans,axiom,
% 5.68/5.95 ! [B: rat,A: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_rat @ C @ B )
% 5.68/5.95 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.trans
% 5.68/5.95 thf(fact_3773_dual__order_Otrans,axiom,
% 5.68/5.95 ! [B: num,A: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_num @ C @ B )
% 5.68/5.95 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.trans
% 5.68/5.95 thf(fact_3774_dual__order_Otrans,axiom,
% 5.68/5.95 ! [B: nat,A: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_nat @ C @ B )
% 5.68/5.95 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.trans
% 5.68/5.95 thf(fact_3775_dual__order_Otrans,axiom,
% 5.68/5.95 ! [B: int,A: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_int @ C @ B )
% 5.68/5.95 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.trans
% 5.68/5.95 thf(fact_3776_dual__order_Oantisym,axiom,
% 5.68/5.95 ! [B: set_int,A: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.antisym
% 5.68/5.95 thf(fact_3777_dual__order_Oantisym,axiom,
% 5.68/5.95 ! [B: rat,A: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.antisym
% 5.68/5.95 thf(fact_3778_dual__order_Oantisym,axiom,
% 5.68/5.95 ! [B: num,A: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.antisym
% 5.68/5.95 thf(fact_3779_dual__order_Oantisym,axiom,
% 5.68/5.95 ! [B: nat,A: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.antisym
% 5.68/5.95 thf(fact_3780_dual__order_Oantisym,axiom,
% 5.68/5.95 ! [B: int,A: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.antisym
% 5.68/5.95 thf(fact_3781_dual__order_Oeq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: set_int,Z5: set_int] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: set_int,B3: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.68/5.95 & ( ord_less_eq_set_int @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.eq_iff
% 5.68/5.95 thf(fact_3782_dual__order_Oeq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.68/5.95 & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.eq_iff
% 5.68/5.95 thf(fact_3783_dual__order_Oeq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: num,Z5: num] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: num,B3: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.68/5.95 & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.eq_iff
% 5.68/5.95 thf(fact_3784_dual__order_Oeq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.68/5.95 & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.eq_iff
% 5.68/5.95 thf(fact_3785_dual__order_Oeq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [A4: int,B3: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.68/5.95 & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.eq_iff
% 5.68/5.95 thf(fact_3786_linorder__wlog,axiom,
% 5.68/5.95 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.68/5.95 ( ! [A3: rat,B2: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: rat,B2: rat] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_wlog
% 5.68/5.95 thf(fact_3787_linorder__wlog,axiom,
% 5.68/5.95 ! [P: num > num > $o,A: num,B: num] :
% 5.68/5.95 ( ! [A3: num,B2: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: num,B2: num] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_wlog
% 5.68/5.95 thf(fact_3788_linorder__wlog,axiom,
% 5.68/5.95 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.68/5.95 ( ! [A3: nat,B2: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: nat,B2: nat] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_wlog
% 5.68/5.95 thf(fact_3789_linorder__wlog,axiom,
% 5.68/5.95 ! [P: int > int > $o,A: int,B: int] :
% 5.68/5.95 ( ! [A3: int,B2: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: int,B2: int] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_wlog
% 5.68/5.95 thf(fact_3790_order__trans,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int,Z: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_trans
% 5.68/5.95 thf(fact_3791_order__trans,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_rat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_trans
% 5.68/5.95 thf(fact_3792_order__trans,axiom,
% 5.68/5.95 ! [X: num,Y2: num,Z: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_num @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_trans
% 5.68/5.95 thf(fact_3793_order__trans,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,Z: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_nat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_trans
% 5.68/5.95 thf(fact_3794_order__trans,axiom,
% 5.68/5.95 ! [X: int,Y2: int,Z: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_trans
% 5.68/5.95 thf(fact_3795_order_Otrans,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ B @ C )
% 5.68/5.95 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.trans
% 5.68/5.95 thf(fact_3796_order_Otrans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.95 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.trans
% 5.68/5.95 thf(fact_3797_order_Otrans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.95 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.trans
% 5.68/5.95 thf(fact_3798_order_Otrans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.95 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.trans
% 5.68/5.95 thf(fact_3799_order_Otrans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_int @ B @ C )
% 5.68/5.95 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.trans
% 5.68/5.95 thf(fact_3800_order__antisym,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ Y2 @ X )
% 5.68/5.95 => ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_antisym
% 5.68/5.95 thf(fact_3801_order__antisym,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.95 => ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_antisym
% 5.68/5.95 thf(fact_3802_order__antisym,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.95 => ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_antisym
% 5.68/5.95 thf(fact_3803_order__antisym,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.95 => ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_antisym
% 5.68/5.95 thf(fact_3804_order__antisym,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.95 => ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_antisym
% 5.68/5.95 thf(fact_3805_ord__le__eq__trans,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_le_eq_trans
% 5.68/5.95 thf(fact_3806_ord__le__eq__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_le_eq_trans
% 5.68/5.95 thf(fact_3807_ord__le__eq__trans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_le_eq_trans
% 5.68/5.95 thf(fact_3808_ord__le__eq__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_le_eq_trans
% 5.68/5.95 thf(fact_3809_ord__le__eq__trans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_le_eq_trans
% 5.68/5.95 thf(fact_3810_ord__eq__le__trans,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int,C: set_int] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ B @ C )
% 5.68/5.95 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_le_trans
% 5.68/5.95 thf(fact_3811_ord__eq__le__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.95 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_le_trans
% 5.68/5.95 thf(fact_3812_ord__eq__le__trans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.95 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_le_trans
% 5.68/5.95 thf(fact_3813_ord__eq__le__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.95 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_le_trans
% 5.68/5.95 thf(fact_3814_ord__eq__le__trans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_eq_int @ B @ C )
% 5.68/5.95 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_le_trans
% 5.68/5.95 thf(fact_3815_order__class_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: set_int,Z5: set_int] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [X2: set_int,Y: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.68/5.95 & ( ord_less_eq_set_int @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_class.order_eq_iff
% 5.68/5.95 thf(fact_3816_order__class_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [X2: rat,Y: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.68/5.95 & ( ord_less_eq_rat @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_class.order_eq_iff
% 5.68/5.95 thf(fact_3817_order__class_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: num,Z5: num] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [X2: num,Y: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X2 @ Y )
% 5.68/5.95 & ( ord_less_eq_num @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_class.order_eq_iff
% 5.68/5.95 thf(fact_3818_order__class_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [X2: nat,Y: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.68/5.95 & ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_class.order_eq_iff
% 5.68/5.95 thf(fact_3819_order__class_Oorder__eq__iff,axiom,
% 5.68/5.95 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/5.95 = ( ^ [X2: int,Y: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X2 @ Y )
% 5.68/5.95 & ( ord_less_eq_int @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_class.order_eq_iff
% 5.68/5.95 thf(fact_3820_le__cases3,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ Y2 @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_rat @ X @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ Z @ Y2 ) )
% 5.68/5.95 => ( ( ( ord_less_eq_rat @ Z @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ Y2 @ X ) )
% 5.68/5.95 => ( ( ( ord_less_eq_rat @ Y2 @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 5.68/5.95 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 5.68/5.95 => ~ ( ord_less_eq_rat @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % le_cases3
% 5.68/5.95 thf(fact_3821_le__cases3,axiom,
% 5.68/5.95 ! [X: num,Y2: num,Z: num] :
% 5.68/5.95 ( ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_num @ Y2 @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_num @ Z @ Y2 ) )
% 5.68/5.95 => ( ( ( ord_less_eq_num @ Z @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_num @ Y2 @ X ) )
% 5.68/5.95 => ( ( ( ord_less_eq_num @ Y2 @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.68/5.95 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.68/5.95 => ~ ( ord_less_eq_num @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % le_cases3
% 5.68/5.95 thf(fact_3822_le__cases3,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,Z: nat] :
% 5.68/5.95 ( ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ Y2 @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ Z @ Y2 ) )
% 5.68/5.95 => ( ( ( ord_less_eq_nat @ Z @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ Y2 @ X ) )
% 5.68/5.95 => ( ( ( ord_less_eq_nat @ Y2 @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.68/5.95 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.68/5.95 => ~ ( ord_less_eq_nat @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % le_cases3
% 5.68/5.95 thf(fact_3823_le__cases3,axiom,
% 5.68/5.95 ! [X: int,Y2: int,Z: int] :
% 5.68/5.95 ( ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_int @ Y2 @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.68/5.95 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_int @ Z @ Y2 ) )
% 5.68/5.95 => ( ( ( ord_less_eq_int @ Z @ Y2 )
% 5.68/5.95 => ~ ( ord_less_eq_int @ Y2 @ X ) )
% 5.68/5.95 => ( ( ( ord_less_eq_int @ Y2 @ Z )
% 5.68/5.95 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.68/5.95 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.68/5.95 => ~ ( ord_less_eq_int @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % le_cases3
% 5.68/5.95 thf(fact_3824_nle__le,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.68/5.95 = ( ( ord_less_eq_rat @ B @ A )
% 5.68/5.95 & ( B != A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nle_le
% 5.68/5.95 thf(fact_3825_nle__le,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.68/5.95 = ( ( ord_less_eq_num @ B @ A )
% 5.68/5.95 & ( B != A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nle_le
% 5.68/5.95 thf(fact_3826_nle__le,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.68/5.95 = ( ( ord_less_eq_nat @ B @ A )
% 5.68/5.95 & ( B != A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nle_le
% 5.68/5.95 thf(fact_3827_nle__le,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.68/5.95 = ( ( ord_less_eq_int @ B @ A )
% 5.68/5.95 & ( B != A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nle_le
% 5.68/5.95 thf(fact_3828_lt__ex,axiom,
% 5.68/5.95 ! [X: real] :
% 5.68/5.95 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 5.68/5.95
% 5.68/5.95 % lt_ex
% 5.68/5.95 thf(fact_3829_lt__ex,axiom,
% 5.68/5.95 ! [X: rat] :
% 5.68/5.95 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.68/5.95
% 5.68/5.95 % lt_ex
% 5.68/5.95 thf(fact_3830_lt__ex,axiom,
% 5.68/5.95 ! [X: int] :
% 5.68/5.95 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 5.68/5.95
% 5.68/5.95 % lt_ex
% 5.68/5.95 thf(fact_3831_gt__ex,axiom,
% 5.68/5.95 ! [X: real] :
% 5.68/5.95 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.68/5.95
% 5.68/5.95 % gt_ex
% 5.68/5.95 thf(fact_3832_gt__ex,axiom,
% 5.68/5.95 ! [X: rat] :
% 5.68/5.95 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.68/5.95
% 5.68/5.95 % gt_ex
% 5.68/5.95 thf(fact_3833_gt__ex,axiom,
% 5.68/5.95 ! [X: nat] :
% 5.68/5.95 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.68/5.95
% 5.68/5.95 % gt_ex
% 5.68/5.95 thf(fact_3834_gt__ex,axiom,
% 5.68/5.95 ! [X: int] :
% 5.68/5.95 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.68/5.95
% 5.68/5.95 % gt_ex
% 5.68/5.95 thf(fact_3835_dense,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ? [Z3: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Z3 )
% 5.68/5.95 & ( ord_less_real @ Z3 @ Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense
% 5.68/5.95 thf(fact_3836_dense,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ? [Z3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Z3 )
% 5.68/5.95 & ( ord_less_rat @ Z3 @ Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense
% 5.68/5.95 thf(fact_3837_less__imp__neq,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_imp_neq
% 5.68/5.95 thf(fact_3838_less__imp__neq,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_imp_neq
% 5.68/5.95 thf(fact_3839_less__imp__neq,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_imp_neq
% 5.68/5.95 thf(fact_3840_less__imp__neq,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_imp_neq
% 5.68/5.95 thf(fact_3841_less__imp__neq,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_imp_neq
% 5.68/5.95 thf(fact_3842_order_Oasym,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.asym
% 5.68/5.95 thf(fact_3843_order_Oasym,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.asym
% 5.68/5.95 thf(fact_3844_order_Oasym,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.asym
% 5.68/5.95 thf(fact_3845_order_Oasym,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.asym
% 5.68/5.95 thf(fact_3846_order_Oasym,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.asym
% 5.68/5.95 thf(fact_3847_ord__eq__less__trans,axiom,
% 5.68/5.95 ! [A: real,B: real,C: real] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ord_less_real @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_trans
% 5.68/5.95 thf(fact_3848_ord__eq__less__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_trans
% 5.68/5.95 thf(fact_3849_ord__eq__less__trans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ord_less_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_trans
% 5.68/5.95 thf(fact_3850_ord__eq__less__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_trans
% 5.68/5.95 thf(fact_3851_ord__eq__less__trans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( A = B )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ord_less_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_trans
% 5.68/5.95 thf(fact_3852_ord__less__eq__trans,axiom,
% 5.68/5.95 ! [A: real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_real @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_trans
% 5.68/5.95 thf(fact_3853_ord__less__eq__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_trans
% 5.68/5.95 thf(fact_3854_ord__less__eq__trans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_trans
% 5.68/5.95 thf(fact_3855_ord__less__eq__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_trans
% 5.68/5.95 thf(fact_3856_ord__less__eq__trans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ( ( B = C )
% 5.68/5.95 => ( ord_less_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_trans
% 5.68/5.95 thf(fact_3857_less__induct,axiom,
% 5.68/5.95 ! [P: nat > $o,A: nat] :
% 5.68/5.95 ( ! [X3: nat] :
% 5.68/5.95 ( ! [Y4: nat] :
% 5.68/5.95 ( ( ord_less_nat @ Y4 @ X3 )
% 5.68/5.95 => ( P @ Y4 ) )
% 5.68/5.95 => ( P @ X3 ) )
% 5.68/5.95 => ( P @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_induct
% 5.68/5.95 thf(fact_3858_antisym__conv3,axiom,
% 5.68/5.95 ! [Y2: real,X: real] :
% 5.68/5.95 ( ~ ( ord_less_real @ Y2 @ X )
% 5.68/5.95 => ( ( ~ ( ord_less_real @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv3
% 5.68/5.95 thf(fact_3859_antisym__conv3,axiom,
% 5.68/5.95 ! [Y2: rat,X: rat] :
% 5.68/5.95 ( ~ ( ord_less_rat @ Y2 @ X )
% 5.68/5.95 => ( ( ~ ( ord_less_rat @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv3
% 5.68/5.95 thf(fact_3860_antisym__conv3,axiom,
% 5.68/5.95 ! [Y2: num,X: num] :
% 5.68/5.95 ( ~ ( ord_less_num @ Y2 @ X )
% 5.68/5.95 => ( ( ~ ( ord_less_num @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv3
% 5.68/5.95 thf(fact_3861_antisym__conv3,axiom,
% 5.68/5.95 ! [Y2: nat,X: nat] :
% 5.68/5.95 ( ~ ( ord_less_nat @ Y2 @ X )
% 5.68/5.95 => ( ( ~ ( ord_less_nat @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv3
% 5.68/5.95 thf(fact_3862_antisym__conv3,axiom,
% 5.68/5.95 ! [Y2: int,X: int] :
% 5.68/5.95 ( ~ ( ord_less_int @ Y2 @ X )
% 5.68/5.95 => ( ( ~ ( ord_less_int @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv3
% 5.68/5.95 thf(fact_3863_linorder__cases,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ~ ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ( X != Y2 )
% 5.68/5.95 => ( ord_less_real @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_cases
% 5.68/5.95 thf(fact_3864_linorder__cases,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ~ ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ( X != Y2 )
% 5.68/5.95 => ( ord_less_rat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_cases
% 5.68/5.95 thf(fact_3865_linorder__cases,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ~ ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ( X != Y2 )
% 5.68/5.95 => ( ord_less_num @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_cases
% 5.68/5.95 thf(fact_3866_linorder__cases,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ~ ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ( X != Y2 )
% 5.68/5.95 => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_cases
% 5.68/5.95 thf(fact_3867_linorder__cases,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ~ ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ( X != Y2 )
% 5.68/5.95 => ( ord_less_int @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_cases
% 5.68/5.95 thf(fact_3868_dual__order_Oasym,axiom,
% 5.68/5.95 ! [B: real,A: real] :
% 5.68/5.95 ( ( ord_less_real @ B @ A )
% 5.68/5.95 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.asym
% 5.68/5.95 thf(fact_3869_dual__order_Oasym,axiom,
% 5.68/5.95 ! [B: rat,A: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B @ A )
% 5.68/5.95 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.asym
% 5.68/5.95 thf(fact_3870_dual__order_Oasym,axiom,
% 5.68/5.95 ! [B: num,A: num] :
% 5.68/5.95 ( ( ord_less_num @ B @ A )
% 5.68/5.95 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.asym
% 5.68/5.95 thf(fact_3871_dual__order_Oasym,axiom,
% 5.68/5.95 ! [B: nat,A: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B @ A )
% 5.68/5.95 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.asym
% 5.68/5.95 thf(fact_3872_dual__order_Oasym,axiom,
% 5.68/5.95 ! [B: int,A: int] :
% 5.68/5.95 ( ( ord_less_int @ B @ A )
% 5.68/5.95 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.asym
% 5.68/5.95 thf(fact_3873_dual__order_Oirrefl,axiom,
% 5.68/5.95 ! [A: real] :
% 5.68/5.95 ~ ( ord_less_real @ A @ A ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.irrefl
% 5.68/5.95 thf(fact_3874_dual__order_Oirrefl,axiom,
% 5.68/5.95 ! [A: rat] :
% 5.68/5.95 ~ ( ord_less_rat @ A @ A ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.irrefl
% 5.68/5.95 thf(fact_3875_dual__order_Oirrefl,axiom,
% 5.68/5.95 ! [A: num] :
% 5.68/5.95 ~ ( ord_less_num @ A @ A ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.irrefl
% 5.68/5.95 thf(fact_3876_dual__order_Oirrefl,axiom,
% 5.68/5.95 ! [A: nat] :
% 5.68/5.95 ~ ( ord_less_nat @ A @ A ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.irrefl
% 5.68/5.95 thf(fact_3877_dual__order_Oirrefl,axiom,
% 5.68/5.95 ! [A: int] :
% 5.68/5.95 ~ ( ord_less_int @ A @ A ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.irrefl
% 5.68/5.95 thf(fact_3878_exists__least__iff,axiom,
% 5.68/5.95 ( ( ^ [P2: nat > $o] :
% 5.68/5.95 ? [X4: nat] : ( P2 @ X4 ) )
% 5.68/5.95 = ( ^ [P3: nat > $o] :
% 5.68/5.95 ? [N2: nat] :
% 5.68/5.95 ( ( P3 @ N2 )
% 5.68/5.95 & ! [M6: nat] :
% 5.68/5.95 ( ( ord_less_nat @ M6 @ N2 )
% 5.68/5.95 => ~ ( P3 @ M6 ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % exists_least_iff
% 5.68/5.95 thf(fact_3879_linorder__less__wlog,axiom,
% 5.68/5.95 ! [P: real > real > $o,A: real,B: real] :
% 5.68/5.95 ( ! [A3: real,B2: real] :
% 5.68/5.95 ( ( ord_less_real @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.68/5.95 => ( ! [A3: real,B2: real] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_wlog
% 5.68/5.95 thf(fact_3880_linorder__less__wlog,axiom,
% 5.68/5.95 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.68/5.95 ( ! [A3: rat,B2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 5.68/5.95 => ( ! [A3: rat,B2: rat] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_wlog
% 5.68/5.95 thf(fact_3881_linorder__less__wlog,axiom,
% 5.68/5.95 ! [P: num > num > $o,A: num,B: num] :
% 5.68/5.95 ( ! [A3: num,B2: num] :
% 5.68/5.95 ( ( ord_less_num @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.68/5.95 => ( ! [A3: num,B2: num] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_wlog
% 5.68/5.95 thf(fact_3882_linorder__less__wlog,axiom,
% 5.68/5.95 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.68/5.95 ( ! [A3: nat,B2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.68/5.95 => ( ! [A3: nat,B2: nat] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_wlog
% 5.68/5.95 thf(fact_3883_linorder__less__wlog,axiom,
% 5.68/5.95 ! [P: int > int > $o,A: int,B: int] :
% 5.68/5.95 ( ! [A3: int,B2: int] :
% 5.68/5.95 ( ( ord_less_int @ A3 @ B2 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.68/5.95 => ( ! [A3: int,B2: int] :
% 5.68/5.95 ( ( P @ B2 @ A3 )
% 5.68/5.95 => ( P @ A3 @ B2 ) )
% 5.68/5.95 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_wlog
% 5.68/5.95 thf(fact_3884_order_Ostrict__trans,axiom,
% 5.68/5.95 ! [A: real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ord_less_real @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans
% 5.68/5.95 thf(fact_3885_order_Ostrict__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans
% 5.68/5.95 thf(fact_3886_order_Ostrict__trans,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ord_less_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans
% 5.68/5.95 thf(fact_3887_order_Ostrict__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans
% 5.68/5.95 thf(fact_3888_order_Ostrict__trans,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ord_less_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans
% 5.68/5.95 thf(fact_3889_not__less__iff__gr__or__eq,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ~ ( ord_less_real @ X @ Y2 ) )
% 5.68/5.95 = ( ( ord_less_real @ Y2 @ X )
% 5.68/5.95 | ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_less_iff_gr_or_eq
% 5.68/5.95 thf(fact_3890_not__less__iff__gr__or__eq,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ~ ( ord_less_rat @ X @ Y2 ) )
% 5.68/5.95 = ( ( ord_less_rat @ Y2 @ X )
% 5.68/5.95 | ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_less_iff_gr_or_eq
% 5.68/5.95 thf(fact_3891_not__less__iff__gr__or__eq,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ~ ( ord_less_num @ X @ Y2 ) )
% 5.68/5.95 = ( ( ord_less_num @ Y2 @ X )
% 5.68/5.95 | ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_less_iff_gr_or_eq
% 5.68/5.95 thf(fact_3892_not__less__iff__gr__or__eq,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ~ ( ord_less_nat @ X @ Y2 ) )
% 5.68/5.95 = ( ( ord_less_nat @ Y2 @ X )
% 5.68/5.95 | ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_less_iff_gr_or_eq
% 5.68/5.95 thf(fact_3893_not__less__iff__gr__or__eq,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ~ ( ord_less_int @ X @ Y2 ) )
% 5.68/5.95 = ( ( ord_less_int @ Y2 @ X )
% 5.68/5.95 | ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_less_iff_gr_or_eq
% 5.68/5.95 thf(fact_3894_dual__order_Ostrict__trans,axiom,
% 5.68/5.95 ! [B: real,A: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ B @ A )
% 5.68/5.95 => ( ( ord_less_real @ C @ B )
% 5.68/5.95 => ( ord_less_real @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans
% 5.68/5.95 thf(fact_3895_dual__order_Ostrict__trans,axiom,
% 5.68/5.95 ! [B: rat,A: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B @ A )
% 5.68/5.95 => ( ( ord_less_rat @ C @ B )
% 5.68/5.95 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans
% 5.68/5.95 thf(fact_3896_dual__order_Ostrict__trans,axiom,
% 5.68/5.95 ! [B: num,A: num,C: num] :
% 5.68/5.95 ( ( ord_less_num @ B @ A )
% 5.68/5.95 => ( ( ord_less_num @ C @ B )
% 5.68/5.95 => ( ord_less_num @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans
% 5.68/5.95 thf(fact_3897_dual__order_Ostrict__trans,axiom,
% 5.68/5.95 ! [B: nat,A: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B @ A )
% 5.68/5.95 => ( ( ord_less_nat @ C @ B )
% 5.68/5.95 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans
% 5.68/5.95 thf(fact_3898_dual__order_Ostrict__trans,axiom,
% 5.68/5.95 ! [B: int,A: int,C: int] :
% 5.68/5.95 ( ( ord_less_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_int @ C @ B )
% 5.68/5.95 => ( ord_less_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans
% 5.68/5.95 thf(fact_3899_order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3900_order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3901_order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3902_order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3903_order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3904_dual__order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [B: real,A: real] :
% 5.68/5.95 ( ( ord_less_real @ B @ A )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3905_dual__order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [B: rat,A: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B @ A )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3906_dual__order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [B: num,A: num] :
% 5.68/5.95 ( ( ord_less_num @ B @ A )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3907_dual__order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [B: nat,A: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B @ A )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3908_dual__order_Ostrict__implies__not__eq,axiom,
% 5.68/5.95 ! [B: int,A: int] :
% 5.68/5.95 ( ( ord_less_int @ B @ A )
% 5.68/5.95 => ( A != B ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_not_eq
% 5.68/5.95 thf(fact_3909_linorder__neqE,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 => ( ~ ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ord_less_real @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neqE
% 5.68/5.95 thf(fact_3910_linorder__neqE,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 => ( ~ ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_rat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neqE
% 5.68/5.95 thf(fact_3911_linorder__neqE,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 => ( ~ ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ord_less_num @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neqE
% 5.68/5.95 thf(fact_3912_linorder__neqE,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 => ( ~ ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neqE
% 5.68/5.95 thf(fact_3913_linorder__neqE,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 => ( ~ ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ord_less_int @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neqE
% 5.68/5.95 thf(fact_3914_order__less__asym,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym
% 5.68/5.95 thf(fact_3915_order__less__asym,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym
% 5.68/5.95 thf(fact_3916_order__less__asym,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym
% 5.68/5.95 thf(fact_3917_order__less__asym,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym
% 5.68/5.95 thf(fact_3918_order__less__asym,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym
% 5.68/5.95 thf(fact_3919_linorder__neq__iff,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 = ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 | ( ord_less_real @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neq_iff
% 5.68/5.95 thf(fact_3920_linorder__neq__iff,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 = ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 | ( ord_less_rat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neq_iff
% 5.68/5.95 thf(fact_3921_linorder__neq__iff,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 = ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 | ( ord_less_num @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neq_iff
% 5.68/5.95 thf(fact_3922_linorder__neq__iff,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 = ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 | ( ord_less_nat @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neq_iff
% 5.68/5.95 thf(fact_3923_linorder__neq__iff,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( X != Y2 )
% 5.68/5.95 = ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 | ( ord_less_int @ Y2 @ X ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_neq_iff
% 5.68/5.95 thf(fact_3924_order__less__asym_H,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym'
% 5.68/5.95 thf(fact_3925_order__less__asym_H,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym'
% 5.68/5.95 thf(fact_3926_order__less__asym_H,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym'
% 5.68/5.95 thf(fact_3927_order__less__asym_H,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym'
% 5.68/5.95 thf(fact_3928_order__less__asym_H,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_asym'
% 5.68/5.95 thf(fact_3929_order__less__trans,axiom,
% 5.68/5.95 ! [X: real,Y2: real,Z: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_real @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_trans
% 5.68/5.95 thf(fact_3930_order__less__trans,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_rat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_trans
% 5.68/5.95 thf(fact_3931_order__less__trans,axiom,
% 5.68/5.95 ! [X: num,Y2: num,Z: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_num @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_trans
% 5.68/5.95 thf(fact_3932_order__less__trans,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,Z: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_nat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_trans
% 5.68/5.95 thf(fact_3933_order__less__trans,axiom,
% 5.68/5.95 ! [X: int,Y2: int,Z: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_trans
% 5.68/5.95 thf(fact_3934_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: real,F: real > real,B: real,C: real] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3935_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3936_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: num,F: real > num,B: real,C: real] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3937_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3938_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: int,F: real > int,B: real,C: real] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3939_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3940_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3941_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3942_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3943_ord__eq__less__subst,axiom,
% 5.68/5.95 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.68/5.95 ( ( A
% 5.68/5.95 = ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_eq_less_subst
% 5.68/5.95 thf(fact_3944_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3945_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3946_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > num,C: num] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3947_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3948_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > int,C: int] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3949_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3950_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3951_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3952_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3953_ord__less__eq__subst,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ( F @ B )
% 5.68/5.95 = C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % ord_less_eq_subst
% 5.68/5.95 thf(fact_3954_order__less__irrefl,axiom,
% 5.68/5.95 ! [X: real] :
% 5.68/5.95 ~ ( ord_less_real @ X @ X ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_irrefl
% 5.68/5.95 thf(fact_3955_order__less__irrefl,axiom,
% 5.68/5.95 ! [X: rat] :
% 5.68/5.95 ~ ( ord_less_rat @ X @ X ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_irrefl
% 5.68/5.95 thf(fact_3956_order__less__irrefl,axiom,
% 5.68/5.95 ! [X: num] :
% 5.68/5.95 ~ ( ord_less_num @ X @ X ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_irrefl
% 5.68/5.95 thf(fact_3957_order__less__irrefl,axiom,
% 5.68/5.95 ! [X: nat] :
% 5.68/5.95 ~ ( ord_less_nat @ X @ X ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_irrefl
% 5.68/5.95 thf(fact_3958_order__less__irrefl,axiom,
% 5.68/5.95 ! [X: int] :
% 5.68/5.95 ~ ( ord_less_int @ X @ X ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_irrefl
% 5.68/5.95 thf(fact_3959_order__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: real > real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3960_order__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3961_order__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: num > real,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ! [X3: num,Y3: num] :
% 5.68/5.95 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3962_order__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3963_order__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: int > real,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ! [X3: int,Y3: int] :
% 5.68/5.95 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3964_order__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3965_order__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3966_order__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ! [X3: num,Y3: num] :
% 5.68/5.95 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3967_order__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3968_order__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ! [X3: int,Y3: int] :
% 5.68/5.95 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst1
% 5.68/5.95 thf(fact_3969_order__less__subst2,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3970_order__less__subst2,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3971_order__less__subst2,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > num,C: num] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3972_order__less__subst2,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3973_order__less__subst2,axiom,
% 5.68/5.95 ! [A: real,B: real,F: real > int,C: int] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3974_order__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3975_order__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3976_order__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3977_order__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3978_order__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_subst2
% 5.68/5.95 thf(fact_3979_order__less__not__sym,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_not_sym
% 5.68/5.95 thf(fact_3980_order__less__not__sym,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_not_sym
% 5.68/5.95 thf(fact_3981_order__less__not__sym,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_not_sym
% 5.68/5.95 thf(fact_3982_order__less__not__sym,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_not_sym
% 5.68/5.95 thf(fact_3983_order__less__not__sym,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_not_sym
% 5.68/5.95 thf(fact_3984_order__less__imp__triv,axiom,
% 5.68/5.95 ! [X: real,Y2: real,P: $o] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_real @ Y2 @ X )
% 5.68/5.95 => P ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_triv
% 5.68/5.95 thf(fact_3985_order__less__imp__triv,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,P: $o] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_rat @ Y2 @ X )
% 5.68/5.95 => P ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_triv
% 5.68/5.95 thf(fact_3986_order__less__imp__triv,axiom,
% 5.68/5.95 ! [X: num,Y2: num,P: $o] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_num @ Y2 @ X )
% 5.68/5.95 => P ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_triv
% 5.68/5.95 thf(fact_3987_order__less__imp__triv,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,P: $o] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_nat @ Y2 @ X )
% 5.68/5.95 => P ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_triv
% 5.68/5.95 thf(fact_3988_order__less__imp__triv,axiom,
% 5.68/5.95 ! [X: int,Y2: int,P: $o] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_int @ Y2 @ X )
% 5.68/5.95 => P ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_triv
% 5.68/5.95 thf(fact_3989_linorder__less__linear,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 | ( X = Y2 )
% 5.68/5.95 | ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_linear
% 5.68/5.95 thf(fact_3990_linorder__less__linear,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 | ( X = Y2 )
% 5.68/5.95 | ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_linear
% 5.68/5.95 thf(fact_3991_linorder__less__linear,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 | ( X = Y2 )
% 5.68/5.95 | ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_linear
% 5.68/5.95 thf(fact_3992_linorder__less__linear,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 | ( X = Y2 )
% 5.68/5.95 | ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_linear
% 5.68/5.95 thf(fact_3993_linorder__less__linear,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 | ( X = Y2 )
% 5.68/5.95 | ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_less_linear
% 5.68/5.95 thf(fact_3994_order__less__imp__not__eq,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq
% 5.68/5.95 thf(fact_3995_order__less__imp__not__eq,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq
% 5.68/5.95 thf(fact_3996_order__less__imp__not__eq,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq
% 5.68/5.95 thf(fact_3997_order__less__imp__not__eq,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq
% 5.68/5.95 thf(fact_3998_order__less__imp__not__eq,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( X != Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq
% 5.68/5.95 thf(fact_3999_order__less__imp__not__eq2,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( Y2 != X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq2
% 5.68/5.95 thf(fact_4000_order__less__imp__not__eq2,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( Y2 != X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq2
% 5.68/5.95 thf(fact_4001_order__less__imp__not__eq2,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( Y2 != X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq2
% 5.68/5.95 thf(fact_4002_order__less__imp__not__eq2,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( Y2 != X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq2
% 5.68/5.95 thf(fact_4003_order__less__imp__not__eq2,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( Y2 != X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_eq2
% 5.68/5.95 thf(fact_4004_order__less__imp__not__less,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_less
% 5.68/5.95 thf(fact_4005_order__less__imp__not__less,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_less
% 5.68/5.95 thf(fact_4006_order__less__imp__not__less,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_less
% 5.68/5.95 thf(fact_4007_order__less__imp__not__less,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_less
% 5.68/5.95 thf(fact_4008_order__less__imp__not__less,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ~ ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_not_less
% 5.68/5.95 thf(fact_4009_full__exhaustive__int_H_Ocases,axiom,
% 5.68/5.95 ! [X: produc2285326912895808259nt_int] :
% 5.68/5.95 ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I4: int] :
% 5.68/5.95 ( X
% 5.68/5.95 != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % full_exhaustive_int'.cases
% 5.68/5.95 thf(fact_4010_exhaustive__int_H_Ocases,axiom,
% 5.68/5.95 ! [X: produc7773217078559923341nt_int] :
% 5.68/5.95 ~ ! [F2: int > option6357759511663192854e_term,D3: int,I4: int] :
% 5.68/5.95 ( X
% 5.68/5.95 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % exhaustive_int'.cases
% 5.68/5.95 thf(fact_4011_small__lazy_H_Ocases,axiom,
% 5.68/5.95 ! [X: product_prod_int_int] :
% 5.68/5.95 ~ ! [D3: int,I4: int] :
% 5.68/5.95 ( X
% 5.68/5.95 != ( product_Pair_int_int @ D3 @ I4 ) ) ).
% 5.68/5.95
% 5.68/5.95 % small_lazy'.cases
% 5.68/5.95 thf(fact_4012_leD,axiom,
% 5.68/5.95 ! [Y2: real,X: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_real @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4013_leD,axiom,
% 5.68/5.95 ! [Y2: set_int,X: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_set_int @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4014_leD,axiom,
% 5.68/5.95 ! [Y2: rat,X: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_rat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4015_leD,axiom,
% 5.68/5.95 ! [Y2: num,X: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_num @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4016_leD,axiom,
% 5.68/5.95 ! [Y2: nat,X: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_nat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4017_leD,axiom,
% 5.68/5.95 ! [Y2: int,X: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.95 => ~ ( ord_less_int @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % leD
% 5.68/5.95 thf(fact_4018_leI,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ~ ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % leI
% 5.68/5.95 thf(fact_4019_leI,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ~ ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % leI
% 5.68/5.95 thf(fact_4020_leI,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ~ ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % leI
% 5.68/5.95 thf(fact_4021_leI,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ~ ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % leI
% 5.68/5.95 thf(fact_4022_leI,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ~ ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % leI
% 5.68/5.95 thf(fact_4023_nless__le,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4024_nless__le,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int] :
% 5.68/5.95 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4025_nless__le,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4026_nless__le,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4027_nless__le,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4028_nless__le,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.68/5.95 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.68/5.95 | ( A = B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % nless_le
% 5.68/5.95 thf(fact_4029_antisym__conv1,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ~ ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4030_antisym__conv1,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int] :
% 5.68/5.95 ( ~ ( ord_less_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4031_antisym__conv1,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ~ ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4032_antisym__conv1,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ~ ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4033_antisym__conv1,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ~ ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4034_antisym__conv1,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ~ ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv1
% 5.68/5.95 thf(fact_4035_antisym__conv2,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_real @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4036_antisym__conv2,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_set_int @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4037_antisym__conv2,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_rat @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4038_antisym__conv2,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_num @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4039_antisym__conv2,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_nat @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4040_antisym__conv2,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 => ( ( ~ ( ord_less_int @ X @ Y2 ) )
% 5.68/5.95 = ( X = Y2 ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % antisym_conv2
% 5.68/5.95 thf(fact_4041_dense__ge,axiom,
% 5.68/5.95 ! [Z: real,Y2: real] :
% 5.68/5.95 ( ! [X3: real] :
% 5.68/5.95 ( ( ord_less_real @ Z @ X3 )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ X3 ) )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ Z ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_ge
% 5.68/5.95 thf(fact_4042_dense__ge,axiom,
% 5.68/5.95 ! [Z: rat,Y2: rat] :
% 5.68/5.95 ( ! [X3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ Z @ X3 )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ X3 ) )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ Z ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_ge
% 5.68/5.95 thf(fact_4043_dense__le,axiom,
% 5.68/5.95 ! [Y2: real,Z: real] :
% 5.68/5.95 ( ! [X3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y2 )
% 5.68/5.95 => ( ord_less_eq_real @ X3 @ Z ) )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ Z ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_le
% 5.68/5.95 thf(fact_4044_dense__le,axiom,
% 5.68/5.95 ! [Y2: rat,Z: rat] :
% 5.68/5.95 ( ! [X3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y2 )
% 5.68/5.95 => ( ord_less_eq_rat @ X3 @ Z ) )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ Z ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_le
% 5.68/5.95 thf(fact_4045_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [X2: real,Y: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_real @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4046_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [X2: set_int,Y: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_set_int @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4047_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [X2: rat,Y: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_rat @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4048_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [X2: num,Y: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_num @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4049_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [X2: nat,Y: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_nat @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4050_less__le__not__le,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [X2: int,Y: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X2 @ Y )
% 5.68/5.95 & ~ ( ord_less_eq_int @ Y @ X2 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % less_le_not_le
% 5.68/5.95 thf(fact_4051_not__le__imp__less,axiom,
% 5.68/5.95 ! [Y2: real,X: real] :
% 5.68/5.95 ( ~ ( ord_less_eq_real @ Y2 @ X )
% 5.68/5.95 => ( ord_less_real @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_le_imp_less
% 5.68/5.95 thf(fact_4052_not__le__imp__less,axiom,
% 5.68/5.95 ! [Y2: rat,X: rat] :
% 5.68/5.95 ( ~ ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.95 => ( ord_less_rat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_le_imp_less
% 5.68/5.95 thf(fact_4053_not__le__imp__less,axiom,
% 5.68/5.95 ! [Y2: num,X: num] :
% 5.68/5.95 ( ~ ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.95 => ( ord_less_num @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_le_imp_less
% 5.68/5.95 thf(fact_4054_not__le__imp__less,axiom,
% 5.68/5.95 ! [Y2: nat,X: nat] :
% 5.68/5.95 ( ~ ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.95 => ( ord_less_nat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_le_imp_less
% 5.68/5.95 thf(fact_4055_not__le__imp__less,axiom,
% 5.68/5.95 ! [Y2: int,X: int] :
% 5.68/5.95 ( ~ ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.95 => ( ord_less_int @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % not_le_imp_less
% 5.68/5.95 thf(fact_4056_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_real
% 5.68/5.95 = ( ^ [A4: real,B3: real] :
% 5.68/5.95 ( ( ord_less_real @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4057_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_set_int
% 5.68/5.95 = ( ^ [A4: set_int,B3: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4058_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_rat
% 5.68/5.95 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4059_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_num
% 5.68/5.95 = ( ^ [A4: num,B3: num] :
% 5.68/5.95 ( ( ord_less_num @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4060_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_nat
% 5.68/5.95 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4061_order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_int
% 5.68/5.95 = ( ^ [A4: int,B3: int] :
% 5.68/5.95 ( ( ord_less_int @ A4 @ B3 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.order_iff_strict
% 5.68/5.95 thf(fact_4062_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [A4: real,B3: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4063_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [A4: set_int,B3: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4064_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4065_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [A4: num,B3: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4066_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4067_order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [A4: int,B3: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_order
% 5.68/5.95 thf(fact_4068_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ord_less_real @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4069_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_set_int @ B @ C )
% 5.68/5.95 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4070_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4071_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ord_less_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4072_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4073_order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ord_less_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans1
% 5.68/5.95 thf(fact_4074_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_real @ B @ C )
% 5.68/5.95 => ( ord_less_real @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4075_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ B @ C )
% 5.68/5.95 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4076_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.95 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4077_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: num,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.95 => ( ord_less_num @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4078_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: nat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_nat @ B @ C )
% 5.68/5.95 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4079_order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [A: int,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ( ( ord_less_eq_int @ B @ C )
% 5.68/5.95 => ( ord_less_int @ A @ C ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_trans2
% 5.68/5.95 thf(fact_4080_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [A4: real,B3: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4081_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [A4: set_int,B3: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_set_int @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4082_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4083_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [A4: num,B3: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4084_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4085_order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [A4: int,B3: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.68/5.95 & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_iff_not
% 5.68/5.95 thf(fact_4086_dense__ge__bounded,axiom,
% 5.68/5.95 ! [Z: real,X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ Z @ X )
% 5.68/5.95 => ( ! [W2: real] :
% 5.68/5.95 ( ( ord_less_real @ Z @ W2 )
% 5.68/5.95 => ( ( ord_less_real @ W2 @ X )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ W2 ) ) )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_ge_bounded
% 5.68/5.95 thf(fact_4087_dense__ge__bounded,axiom,
% 5.68/5.95 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ Z @ X )
% 5.68/5.95 => ( ! [W2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ Z @ W2 )
% 5.68/5.95 => ( ( ord_less_rat @ W2 @ X )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ W2 ) ) )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_ge_bounded
% 5.68/5.95 thf(fact_4088_dense__le__bounded,axiom,
% 5.68/5.95 ! [X: real,Y2: real,Z: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ! [W2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ W2 )
% 5.68/5.95 => ( ( ord_less_real @ W2 @ Y2 )
% 5.68/5.95 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.68/5.95 => ( ord_less_eq_real @ Y2 @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_le_bounded
% 5.68/5.95 thf(fact_4089_dense__le__bounded,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ! [W2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ W2 )
% 5.68/5.95 => ( ( ord_less_rat @ W2 @ Y2 )
% 5.68/5.95 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.68/5.95 => ( ord_less_eq_rat @ Y2 @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dense_le_bounded
% 5.68/5.95 thf(fact_4090_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_real
% 5.68/5.95 = ( ^ [B3: real,A4: real] :
% 5.68/5.95 ( ( ord_less_real @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4091_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_set_int
% 5.68/5.95 = ( ^ [B3: set_int,A4: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4092_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_rat
% 5.68/5.95 = ( ^ [B3: rat,A4: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4093_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_num
% 5.68/5.95 = ( ^ [B3: num,A4: num] :
% 5.68/5.95 ( ( ord_less_num @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4094_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_nat
% 5.68/5.95 = ( ^ [B3: nat,A4: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4095_dual__order_Oorder__iff__strict,axiom,
% 5.68/5.95 ( ord_less_eq_int
% 5.68/5.95 = ( ^ [B3: int,A4: int] :
% 5.68/5.95 ( ( ord_less_int @ B3 @ A4 )
% 5.68/5.95 | ( A4 = B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.order_iff_strict
% 5.68/5.95 thf(fact_4096_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [B3: real,A4: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4097_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [B3: set_int,A4: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4098_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [B3: rat,A4: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4099_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [B3: num,A4: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4100_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [B3: nat,A4: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4101_dual__order_Ostrict__iff__order,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [B3: int,A4: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.68/5.95 & ( A4 != B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_order
% 5.68/5.95 thf(fact_4102_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: real,A: real,C: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ B @ A )
% 5.68/5.95 => ( ( ord_less_real @ C @ B )
% 5.68/5.95 => ( ord_less_real @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4103_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: set_int,A: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_set_int @ C @ B )
% 5.68/5.95 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4104_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: rat,A: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B @ A )
% 5.68/5.95 => ( ( ord_less_rat @ C @ B )
% 5.68/5.95 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4105_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: num,A: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B @ A )
% 5.68/5.95 => ( ( ord_less_num @ C @ B )
% 5.68/5.95 => ( ord_less_num @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4106_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: nat,A: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B @ A )
% 5.68/5.95 => ( ( ord_less_nat @ C @ B )
% 5.68/5.95 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4107_dual__order_Ostrict__trans1,axiom,
% 5.68/5.95 ! [B: int,A: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_int @ C @ B )
% 5.68/5.95 => ( ord_less_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans1
% 5.68/5.95 thf(fact_4108_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: real,A: real,C: real] :
% 5.68/5.95 ( ( ord_less_real @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_real @ C @ B )
% 5.68/5.95 => ( ord_less_real @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4109_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: set_int,A: set_int,C: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ C @ B )
% 5.68/5.95 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4110_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: rat,A: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_rat @ C @ B )
% 5.68/5.95 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4111_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: num,A: num,C: num] :
% 5.68/5.95 ( ( ord_less_num @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_num @ C @ B )
% 5.68/5.95 => ( ord_less_num @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4112_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: nat,A: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_nat @ C @ B )
% 5.68/5.95 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4113_dual__order_Ostrict__trans2,axiom,
% 5.68/5.95 ! [B: int,A: int,C: int] :
% 5.68/5.95 ( ( ord_less_int @ B @ A )
% 5.68/5.95 => ( ( ord_less_eq_int @ C @ B )
% 5.68/5.95 => ( ord_less_int @ C @ A ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_trans2
% 5.68/5.95 thf(fact_4114_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [B3: real,A4: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4115_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [B3: set_int,A4: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_set_int @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4116_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [B3: rat,A4: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4117_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [B3: num,A4: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4118_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [B3: nat,A4: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4119_dual__order_Ostrict__iff__not,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [B3: int,A4: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.68/5.95 & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_iff_not
% 5.68/5.95 thf(fact_4120_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ord_less_real @ A @ B )
% 5.68/5.95 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4121_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ A @ B )
% 5.68/5.95 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4122_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_rat @ A @ B )
% 5.68/5.95 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4123_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_num @ A @ B )
% 5.68/5.95 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4124_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_nat @ A @ B )
% 5.68/5.95 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4125_order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_int @ A @ B )
% 5.68/5.95 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.68/5.95
% 5.68/5.95 % order.strict_implies_order
% 5.68/5.95 thf(fact_4126_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: real,A: real] :
% 5.68/5.95 ( ( ord_less_real @ B @ A )
% 5.68/5.95 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4127_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: set_int,A: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ B @ A )
% 5.68/5.95 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4128_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: rat,A: rat] :
% 5.68/5.95 ( ( ord_less_rat @ B @ A )
% 5.68/5.95 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4129_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: num,A: num] :
% 5.68/5.95 ( ( ord_less_num @ B @ A )
% 5.68/5.95 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4130_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: nat,A: nat] :
% 5.68/5.95 ( ( ord_less_nat @ B @ A )
% 5.68/5.95 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4131_dual__order_Ostrict__implies__order,axiom,
% 5.68/5.95 ! [B: int,A: int] :
% 5.68/5.95 ( ( ord_less_int @ B @ A )
% 5.68/5.95 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.68/5.95
% 5.68/5.95 % dual_order.strict_implies_order
% 5.68/5.95 thf(fact_4132_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_real
% 5.68/5.95 = ( ^ [X2: real,Y: real] :
% 5.68/5.95 ( ( ord_less_real @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4133_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_set_int
% 5.68/5.95 = ( ^ [X2: set_int,Y: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4134_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_rat
% 5.68/5.95 = ( ^ [X2: rat,Y: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4135_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_num
% 5.68/5.95 = ( ^ [X2: num,Y: num] :
% 5.68/5.95 ( ( ord_less_num @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4136_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_nat
% 5.68/5.95 = ( ^ [X2: nat,Y: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4137_order__le__less,axiom,
% 5.68/5.95 ( ord_less_eq_int
% 5.68/5.95 = ( ^ [X2: int,Y: int] :
% 5.68/5.95 ( ( ord_less_int @ X2 @ Y )
% 5.68/5.95 | ( X2 = Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less
% 5.68/5.95 thf(fact_4138_order__less__le,axiom,
% 5.68/5.95 ( ord_less_real
% 5.68/5.95 = ( ^ [X2: real,Y: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4139_order__less__le,axiom,
% 5.68/5.95 ( ord_less_set_int
% 5.68/5.95 = ( ^ [X2: set_int,Y: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4140_order__less__le,axiom,
% 5.68/5.95 ( ord_less_rat
% 5.68/5.95 = ( ^ [X2: rat,Y: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4141_order__less__le,axiom,
% 5.68/5.95 ( ord_less_num
% 5.68/5.95 = ( ^ [X2: num,Y: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4142_order__less__le,axiom,
% 5.68/5.95 ( ord_less_nat
% 5.68/5.95 = ( ^ [X2: nat,Y: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4143_order__less__le,axiom,
% 5.68/5.95 ( ord_less_int
% 5.68/5.95 = ( ^ [X2: int,Y: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X2 @ Y )
% 5.68/5.95 & ( X2 != Y ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le
% 5.68/5.95 thf(fact_4144_linorder__not__le,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_real @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_le
% 5.68/5.95 thf(fact_4145_linorder__not__le,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_rat @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_le
% 5.68/5.95 thf(fact_4146_linorder__not__le,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_num @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_le
% 5.68/5.95 thf(fact_4147_linorder__not__le,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_nat @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_le
% 5.68/5.95 thf(fact_4148_linorder__not__le,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ~ ( ord_less_eq_int @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_le
% 5.68/5.95 thf(fact_4149_linorder__not__less,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ~ ( ord_less_real @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_eq_real @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_less
% 5.68/5.95 thf(fact_4150_linorder__not__less,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ~ ( ord_less_rat @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_eq_rat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_less
% 5.68/5.95 thf(fact_4151_linorder__not__less,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ~ ( ord_less_num @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_eq_num @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_less
% 5.68/5.95 thf(fact_4152_linorder__not__less,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ~ ( ord_less_nat @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_eq_nat @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_less
% 5.68/5.95 thf(fact_4153_linorder__not__less,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ~ ( ord_less_int @ X @ Y2 ) )
% 5.68/5.95 = ( ord_less_eq_int @ Y2 @ X ) ) ).
% 5.68/5.95
% 5.68/5.95 % linorder_not_less
% 5.68/5.95 thf(fact_4154_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: real,Y2: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4155_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4156_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4157_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: num,Y2: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_num @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4158_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4159_order__less__imp__le,axiom,
% 5.68/5.95 ! [X: int,Y2: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ord_less_eq_int @ X @ Y2 ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_imp_le
% 5.68/5.95 thf(fact_4160_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_real @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4161_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4162_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4163_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_num @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4164_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4165_order__le__neq__trans,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ( A != B )
% 5.68/5.95 => ( ord_less_int @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_neq_trans
% 5.68/5.95 thf(fact_4166_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: real,B: real] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_real @ A @ B )
% 5.68/5.95 => ( ord_less_real @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4167_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: set_int,B: set_int] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ A @ B )
% 5.68/5.95 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4168_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: rat,B: rat] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4169_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: num,B: num] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_num @ A @ B )
% 5.68/5.95 => ( ord_less_num @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4170_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: nat,B: nat] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_nat @ A @ B )
% 5.68/5.95 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4171_order__neq__le__trans,axiom,
% 5.68/5.95 ! [A: int,B: int] :
% 5.68/5.95 ( ( A != B )
% 5.68/5.95 => ( ( ord_less_eq_int @ A @ B )
% 5.68/5.95 => ( ord_less_int @ A @ B ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_neq_le_trans
% 5.68/5.95 thf(fact_4172_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: real,Y2: real,Z: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_real @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4173_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int,Z: set_int] :
% 5.68/5.95 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_set_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4174_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_rat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4175_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: num,Y2: num,Z: num] :
% 5.68/5.95 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_num @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4176_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,Z: nat] :
% 5.68/5.95 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_nat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4177_order__le__less__trans,axiom,
% 5.68/5.95 ! [X: int,Y2: int,Z: int] :
% 5.68/5.95 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_trans
% 5.68/5.95 thf(fact_4178_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: real,Y2: real,Z: real] :
% 5.68/5.95 ( ( ord_less_real @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_real @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4179_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: set_int,Y2: set_int,Z: set_int] :
% 5.68/5.95 ( ( ord_less_set_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_set_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4180_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: rat,Y2: rat,Z: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_rat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4181_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: num,Y2: num,Z: num] :
% 5.68/5.95 ( ( ord_less_num @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_num @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4182_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: nat,Y2: nat,Z: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_nat @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4183_order__less__le__trans,axiom,
% 5.68/5.95 ! [X: int,Y2: int,Z: int] :
% 5.68/5.95 ( ( ord_less_int @ X @ Y2 )
% 5.68/5.95 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.68/5.95 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_less_le_trans
% 5.68/5.95 thf(fact_4184_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: real > real,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4185_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4186_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: num > real,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ! [X3: num,Y3: num] :
% 5.68/5.95 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4187_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4188_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: real,F: int > real,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ! [X3: int,Y3: int] :
% 5.68/5.95 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4189_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_real @ B @ C )
% 5.68/5.95 => ( ! [X3: real,Y3: real] :
% 5.68/5.95 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4190_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_rat @ B @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4191_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_num @ B @ C )
% 5.68/5.95 => ( ! [X3: num,Y3: num] :
% 5.68/5.95 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4192_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_nat @ B @ C )
% 5.68/5.95 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.95 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4193_order__le__less__subst1,axiom,
% 5.68/5.95 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.68/5.95 => ( ( ord_less_int @ B @ C )
% 5.68/5.95 => ( ! [X3: int,Y3: int] :
% 5.68/5.95 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst1
% 5.68/5.95 thf(fact_4194_order__le__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst2
% 5.68/5.95 thf(fact_4195_order__le__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst2
% 5.68/5.95 thf(fact_4196_order__le__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst2
% 5.68/5.95 thf(fact_4197_order__le__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst2
% 5.68/5.95 thf(fact_4198_order__le__less__subst2,axiom,
% 5.68/5.95 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.68/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.95 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.68/5.95 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.95 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.95 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.95 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.95
% 5.68/5.95 % order_le_less_subst2
% 5.68/5.95 thf(fact_4199_order__le__less__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > real,C: real] :
% 5.68/5.96 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_less_subst2
% 5.68/5.96 thf(fact_4200_order__le__less__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_less_subst2
% 5.68/5.96 thf(fact_4201_order__le__less__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > num,C: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_less_subst2
% 5.68/5.96 thf(fact_4202_order__le__less__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.68/5.96 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_less_subst2
% 5.68/5.96 thf(fact_4203_order__le__less__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > int,C: int] :
% 5.68/5.96 ( ( ord_less_eq_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_less_subst2
% 5.68/5.96 thf(fact_4204_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.68/5.96 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4205_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.68/5.96 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4206_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.68/5.96 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4207_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.68/5.96 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4208_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.68/5.96 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_rat @ B @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4209_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: real,F: num > real,B: num,C: num] :
% 5.68/5.96 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4210_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.68/5.96 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4211_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: num,F: num > num,B: num,C: num] :
% 5.68/5.96 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4212_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.68/5.96 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4213_order__less__le__subst1,axiom,
% 5.68/5.96 ! [A: int,F: num > int,B: num,C: num] :
% 5.68/5.96 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.68/5.96 => ( ( ord_less_eq_num @ B @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst1
% 5.68/5.96 thf(fact_4214_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: real,B: real,F: real > real,C: real] :
% 5.68/5.96 ( ( ord_less_real @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: real,Y3: real] :
% 5.68/5.96 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4215_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.68/5.96 ( ( ord_less_rat @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4216_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > real,C: real] :
% 5.68/5.96 ( ( ord_less_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4217_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.68/5.96 ( ( ord_less_nat @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.96 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4218_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: int,B: int,F: int > real,C: real] :
% 5.68/5.96 ( ( ord_less_int @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: int,Y3: int] :
% 5.68/5.96 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4219_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_real @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: real,Y3: real] :
% 5.68/5.96 ( ( ord_less_real @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4220_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_rat @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: rat,Y3: rat] :
% 5.68/5.96 ( ( ord_less_rat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4221_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_num @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: num,Y3: num] :
% 5.68/5.96 ( ( ord_less_num @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4222_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_nat @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: nat,Y3: nat] :
% 5.68/5.96 ( ( ord_less_nat @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4223_order__less__le__subst2,axiom,
% 5.68/5.96 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.68/5.96 ( ( ord_less_int @ A @ B )
% 5.68/5.96 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.68/5.96 => ( ! [X3: int,Y3: int] :
% 5.68/5.96 ( ( ord_less_int @ X3 @ Y3 )
% 5.68/5.96 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.68/5.96 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_less_le_subst2
% 5.68/5.96 thf(fact_4224_linorder__le__less__linear,axiom,
% 5.68/5.96 ! [X: real,Y2: real] :
% 5.68/5.96 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.96 | ( ord_less_real @ Y2 @ X ) ) ).
% 5.68/5.96
% 5.68/5.96 % linorder_le_less_linear
% 5.68/5.96 thf(fact_4225_linorder__le__less__linear,axiom,
% 5.68/5.96 ! [X: rat,Y2: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.96 | ( ord_less_rat @ Y2 @ X ) ) ).
% 5.68/5.96
% 5.68/5.96 % linorder_le_less_linear
% 5.68/5.96 thf(fact_4226_linorder__le__less__linear,axiom,
% 5.68/5.96 ! [X: num,Y2: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.96 | ( ord_less_num @ Y2 @ X ) ) ).
% 5.68/5.96
% 5.68/5.96 % linorder_le_less_linear
% 5.68/5.96 thf(fact_4227_linorder__le__less__linear,axiom,
% 5.68/5.96 ! [X: nat,Y2: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.96 | ( ord_less_nat @ Y2 @ X ) ) ).
% 5.68/5.96
% 5.68/5.96 % linorder_le_less_linear
% 5.68/5.96 thf(fact_4228_linorder__le__less__linear,axiom,
% 5.68/5.96 ! [X: int,Y2: int] :
% 5.68/5.96 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.96 | ( ord_less_int @ Y2 @ X ) ) ).
% 5.68/5.96
% 5.68/5.96 % linorder_le_less_linear
% 5.68/5.96 thf(fact_4229_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: real,Y2: real] :
% 5.68/5.96 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_real @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4230_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: set_int,Y2: set_int] :
% 5.68/5.96 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_set_int @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4231_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: rat,Y2: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_rat @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4232_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: num,Y2: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_num @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4233_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: nat,Y2: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_nat @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4234_order__le__imp__less__or__eq,axiom,
% 5.68/5.96 ! [X: int,Y2: int] :
% 5.68/5.96 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_int @ X @ Y2 )
% 5.68/5.96 | ( X = Y2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % order_le_imp_less_or_eq
% 5.68/5.96 thf(fact_4235_bot_Oextremum__uniqueI,axiom,
% 5.68/5.96 ! [A: set_nat] :
% 5.68/5.96 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.68/5.96 => ( A = bot_bot_set_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_uniqueI
% 5.68/5.96 thf(fact_4236_bot_Oextremum__uniqueI,axiom,
% 5.68/5.96 ! [A: extended_enat] :
% 5.68/5.96 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.68/5.96 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_uniqueI
% 5.68/5.96 thf(fact_4237_bot_Oextremum__uniqueI,axiom,
% 5.68/5.96 ! [A: set_real] :
% 5.68/5.96 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.68/5.96 => ( A = bot_bot_set_real ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_uniqueI
% 5.68/5.96 thf(fact_4238_bot_Oextremum__uniqueI,axiom,
% 5.68/5.96 ! [A: set_int] :
% 5.68/5.96 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.68/5.96 => ( A = bot_bot_set_int ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_uniqueI
% 5.68/5.96 thf(fact_4239_bot_Oextremum__uniqueI,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.68/5.96 => ( A = bot_bot_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_uniqueI
% 5.68/5.96 thf(fact_4240_bot_Oextremum__unique,axiom,
% 5.68/5.96 ! [A: set_nat] :
% 5.68/5.96 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.68/5.96 = ( A = bot_bot_set_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_unique
% 5.68/5.96 thf(fact_4241_bot_Oextremum__unique,axiom,
% 5.68/5.96 ! [A: extended_enat] :
% 5.68/5.96 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.68/5.96 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_unique
% 5.68/5.96 thf(fact_4242_bot_Oextremum__unique,axiom,
% 5.68/5.96 ! [A: set_real] :
% 5.68/5.96 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.68/5.96 = ( A = bot_bot_set_real ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_unique
% 5.68/5.96 thf(fact_4243_bot_Oextremum__unique,axiom,
% 5.68/5.96 ! [A: set_int] :
% 5.68/5.96 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.68/5.96 = ( A = bot_bot_set_int ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_unique
% 5.68/5.96 thf(fact_4244_bot_Oextremum__unique,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.68/5.96 = ( A = bot_bot_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_unique
% 5.68/5.96 thf(fact_4245_bot_Oextremum,axiom,
% 5.68/5.96 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum
% 5.68/5.96 thf(fact_4246_bot_Oextremum,axiom,
% 5.68/5.96 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum
% 5.68/5.96 thf(fact_4247_bot_Oextremum,axiom,
% 5.68/5.96 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum
% 5.68/5.96 thf(fact_4248_bot_Oextremum,axiom,
% 5.68/5.96 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum
% 5.68/5.96 thf(fact_4249_bot_Oextremum,axiom,
% 5.68/5.96 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum
% 5.68/5.96 thf(fact_4250_bot_Oextremum__strict,axiom,
% 5.68/5.96 ! [A: set_nat] :
% 5.68/5.96 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_strict
% 5.68/5.96 thf(fact_4251_bot_Oextremum__strict,axiom,
% 5.68/5.96 ! [A: extended_enat] :
% 5.68/5.96 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_strict
% 5.68/5.96 thf(fact_4252_bot_Oextremum__strict,axiom,
% 5.68/5.96 ! [A: set_int] :
% 5.68/5.96 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_strict
% 5.68/5.96 thf(fact_4253_bot_Oextremum__strict,axiom,
% 5.68/5.96 ! [A: set_real] :
% 5.68/5.96 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_strict
% 5.68/5.96 thf(fact_4254_bot_Oextremum__strict,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.68/5.96
% 5.68/5.96 % bot.extremum_strict
% 5.68/5.96 thf(fact_4255_bot_Onot__eq__extremum,axiom,
% 5.68/5.96 ! [A: set_nat] :
% 5.68/5.96 ( ( A != bot_bot_set_nat )
% 5.68/5.96 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.not_eq_extremum
% 5.68/5.96 thf(fact_4256_bot_Onot__eq__extremum,axiom,
% 5.68/5.96 ! [A: extended_enat] :
% 5.68/5.96 ( ( A != bot_bo4199563552545308370d_enat )
% 5.68/5.96 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.not_eq_extremum
% 5.68/5.96 thf(fact_4257_bot_Onot__eq__extremum,axiom,
% 5.68/5.96 ! [A: set_int] :
% 5.68/5.96 ( ( A != bot_bot_set_int )
% 5.68/5.96 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.not_eq_extremum
% 5.68/5.96 thf(fact_4258_bot_Onot__eq__extremum,axiom,
% 5.68/5.96 ! [A: set_real] :
% 5.68/5.96 ( ( A != bot_bot_set_real )
% 5.68/5.96 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.not_eq_extremum
% 5.68/5.96 thf(fact_4259_bot_Onot__eq__extremum,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( A != bot_bot_nat )
% 5.68/5.96 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % bot.not_eq_extremum
% 5.68/5.96 thf(fact_4260_Euclid__induct,axiom,
% 5.68/5.96 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.68/5.96 ( ! [A3: nat,B2: nat] :
% 5.68/5.96 ( ( P @ A3 @ B2 )
% 5.68/5.96 = ( P @ B2 @ A3 ) )
% 5.68/5.96 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.68/5.96 => ( ! [A3: nat,B2: nat] :
% 5.68/5.96 ( ( P @ A3 @ B2 )
% 5.68/5.96 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 5.68/5.96 => ( P @ A @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % Euclid_induct
% 5.68/5.96 thf(fact_4261_max__absorb2,axiom,
% 5.68/5.96 ! [X: extended_enat,Y2: extended_enat] :
% 5.68/5.96 ( ( ord_le2932123472753598470d_enat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_ma741700101516333627d_enat @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4262_max__absorb2,axiom,
% 5.68/5.96 ! [X: set_int,Y2: set_int] :
% 5.68/5.96 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.96 => ( ( ord_max_set_int @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4263_max__absorb2,axiom,
% 5.68/5.96 ! [X: rat,Y2: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_max_rat @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4264_max__absorb2,axiom,
% 5.68/5.96 ! [X: num,Y2: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ X @ Y2 )
% 5.68/5.96 => ( ( ord_max_num @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4265_max__absorb2,axiom,
% 5.68/5.96 ! [X: nat,Y2: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_max_nat @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4266_max__absorb2,axiom,
% 5.68/5.96 ! [X: int,Y2: int] :
% 5.68/5.96 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/5.96 => ( ( ord_max_int @ X @ Y2 )
% 5.68/5.96 = Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb2
% 5.68/5.96 thf(fact_4267_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: extended_enat,X: extended_enat] :
% 5.68/5.96 ( ( ord_le2932123472753598470d_enat @ Y2 @ X )
% 5.68/5.96 => ( ( ord_ma741700101516333627d_enat @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4268_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: set_int,X: set_int] :
% 5.68/5.96 ( ( ord_less_eq_set_int @ Y2 @ X )
% 5.68/5.96 => ( ( ord_max_set_int @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4269_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: rat,X: rat] :
% 5.68/5.96 ( ( ord_less_eq_rat @ Y2 @ X )
% 5.68/5.96 => ( ( ord_max_rat @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4270_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: num,X: num] :
% 5.68/5.96 ( ( ord_less_eq_num @ Y2 @ X )
% 5.68/5.96 => ( ( ord_max_num @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4271_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: nat,X: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/5.96 => ( ( ord_max_nat @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4272_max__absorb1,axiom,
% 5.68/5.96 ! [Y2: int,X: int] :
% 5.68/5.96 ( ( ord_less_eq_int @ Y2 @ X )
% 5.68/5.96 => ( ( ord_max_int @ X @ Y2 )
% 5.68/5.96 = X ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_absorb1
% 5.68/5.96 thf(fact_4273_max__def,axiom,
% 5.68/5.96 ( ord_ma741700101516333627d_enat
% 5.68/5.96 = ( ^ [A4: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4274_max__def,axiom,
% 5.68/5.96 ( ord_max_set_int
% 5.68/5.96 = ( ^ [A4: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4275_max__def,axiom,
% 5.68/5.96 ( ord_max_rat
% 5.68/5.96 = ( ^ [A4: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4276_max__def,axiom,
% 5.68/5.96 ( ord_max_num
% 5.68/5.96 = ( ^ [A4: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4277_max__def,axiom,
% 5.68/5.96 ( ord_max_nat
% 5.68/5.96 = ( ^ [A4: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4278_max__def,axiom,
% 5.68/5.96 ( ord_max_int
% 5.68/5.96 = ( ^ [A4: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % max_def
% 5.68/5.96 thf(fact_4279_infinite__growing,axiom,
% 5.68/5.96 ! [X8: set_real] :
% 5.68/5.96 ( ( X8 != bot_bot_set_real )
% 5.68/5.96 => ( ! [X3: real] :
% 5.68/5.96 ( ( member_real @ X3 @ X8 )
% 5.68/5.96 => ? [Xa: real] :
% 5.68/5.96 ( ( member_real @ Xa @ X8 )
% 5.68/5.96 & ( ord_less_real @ X3 @ Xa ) ) )
% 5.68/5.96 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % infinite_growing
% 5.68/5.96 thf(fact_4280_infinite__growing,axiom,
% 5.68/5.96 ! [X8: set_rat] :
% 5.68/5.96 ( ( X8 != bot_bot_set_rat )
% 5.68/5.96 => ( ! [X3: rat] :
% 5.68/5.96 ( ( member_rat @ X3 @ X8 )
% 5.68/5.96 => ? [Xa: rat] :
% 5.68/5.96 ( ( member_rat @ Xa @ X8 )
% 5.68/5.96 & ( ord_less_rat @ X3 @ Xa ) ) )
% 5.68/5.96 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % infinite_growing
% 5.68/5.96 thf(fact_4281_infinite__growing,axiom,
% 5.68/5.96 ! [X8: set_num] :
% 5.68/5.96 ( ( X8 != bot_bot_set_num )
% 5.68/5.96 => ( ! [X3: num] :
% 5.68/5.96 ( ( member_num @ X3 @ X8 )
% 5.68/5.96 => ? [Xa: num] :
% 5.68/5.96 ( ( member_num @ Xa @ X8 )
% 5.68/5.96 & ( ord_less_num @ X3 @ Xa ) ) )
% 5.68/5.96 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % infinite_growing
% 5.68/5.96 thf(fact_4282_infinite__growing,axiom,
% 5.68/5.96 ! [X8: set_nat] :
% 5.68/5.96 ( ( X8 != bot_bot_set_nat )
% 5.68/5.96 => ( ! [X3: nat] :
% 5.68/5.96 ( ( member_nat @ X3 @ X8 )
% 5.68/5.96 => ? [Xa: nat] :
% 5.68/5.96 ( ( member_nat @ Xa @ X8 )
% 5.68/5.96 & ( ord_less_nat @ X3 @ Xa ) ) )
% 5.68/5.96 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % infinite_growing
% 5.68/5.96 thf(fact_4283_infinite__growing,axiom,
% 5.68/5.96 ! [X8: set_int] :
% 5.68/5.96 ( ( X8 != bot_bot_set_int )
% 5.68/5.96 => ( ! [X3: int] :
% 5.68/5.96 ( ( member_int @ X3 @ X8 )
% 5.68/5.96 => ? [Xa: int] :
% 5.68/5.96 ( ( member_int @ Xa @ X8 )
% 5.68/5.96 & ( ord_less_int @ X3 @ Xa ) ) )
% 5.68/5.96 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % infinite_growing
% 5.68/5.96 thf(fact_4284_ex__min__if__finite,axiom,
% 5.68/5.96 ! [S3: set_real] :
% 5.68/5.96 ( ( finite_finite_real @ S3 )
% 5.68/5.96 => ( ( S3 != bot_bot_set_real )
% 5.68/5.96 => ? [X3: real] :
% 5.68/5.96 ( ( member_real @ X3 @ S3 )
% 5.68/5.96 & ~ ? [Xa: real] :
% 5.68/5.96 ( ( member_real @ Xa @ S3 )
% 5.68/5.96 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ex_min_if_finite
% 5.68/5.96 thf(fact_4285_ex__min__if__finite,axiom,
% 5.68/5.96 ! [S3: set_rat] :
% 5.68/5.96 ( ( finite_finite_rat @ S3 )
% 5.68/5.96 => ( ( S3 != bot_bot_set_rat )
% 5.68/5.96 => ? [X3: rat] :
% 5.68/5.96 ( ( member_rat @ X3 @ S3 )
% 5.68/5.96 & ~ ? [Xa: rat] :
% 5.68/5.96 ( ( member_rat @ Xa @ S3 )
% 5.68/5.96 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ex_min_if_finite
% 5.68/5.96 thf(fact_4286_ex__min__if__finite,axiom,
% 5.68/5.96 ! [S3: set_num] :
% 5.68/5.96 ( ( finite_finite_num @ S3 )
% 5.68/5.96 => ( ( S3 != bot_bot_set_num )
% 5.68/5.96 => ? [X3: num] :
% 5.68/5.96 ( ( member_num @ X3 @ S3 )
% 5.68/5.96 & ~ ? [Xa: num] :
% 5.68/5.96 ( ( member_num @ Xa @ S3 )
% 5.68/5.96 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ex_min_if_finite
% 5.68/5.96 thf(fact_4287_ex__min__if__finite,axiom,
% 5.68/5.96 ! [S3: set_nat] :
% 5.68/5.96 ( ( finite_finite_nat @ S3 )
% 5.68/5.96 => ( ( S3 != bot_bot_set_nat )
% 5.68/5.96 => ? [X3: nat] :
% 5.68/5.96 ( ( member_nat @ X3 @ S3 )
% 5.68/5.96 & ~ ? [Xa: nat] :
% 5.68/5.96 ( ( member_nat @ Xa @ S3 )
% 5.68/5.96 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ex_min_if_finite
% 5.68/5.96 thf(fact_4288_ex__min__if__finite,axiom,
% 5.68/5.96 ! [S3: set_int] :
% 5.68/5.96 ( ( finite_finite_int @ S3 )
% 5.68/5.96 => ( ( S3 != bot_bot_set_int )
% 5.68/5.96 => ? [X3: int] :
% 5.68/5.96 ( ( member_int @ X3 @ S3 )
% 5.68/5.96 & ~ ? [Xa: int] :
% 5.68/5.96 ( ( member_int @ Xa @ S3 )
% 5.68/5.96 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ex_min_if_finite
% 5.68/5.96 thf(fact_4289_even__succ__mod__exp,axiom,
% 5.68/5.96 ! [A: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_mod_exp
% 5.68/5.96 thf(fact_4290_even__succ__mod__exp,axiom,
% 5.68/5.96 ! [A: int,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_mod_exp
% 5.68/5.96 thf(fact_4291_even__succ__mod__exp,axiom,
% 5.68/5.96 ! [A: code_integer,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_mod_exp
% 5.68/5.96 thf(fact_4292_option_Osize__gen_I2_J,axiom,
% 5.68/5.96 ! [X: nat > nat,X22: nat] :
% 5.68/5.96 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.68/5.96 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % option.size_gen(2)
% 5.68/5.96 thf(fact_4293_option_Osize__gen_I2_J,axiom,
% 5.68/5.96 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.68/5.96 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.68/5.96 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % option.size_gen(2)
% 5.68/5.96 thf(fact_4294_option_Osize__gen_I2_J,axiom,
% 5.68/5.96 ! [X: num > nat,X22: num] :
% 5.68/5.96 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.68/5.96 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % option.size_gen(2)
% 5.68/5.96 thf(fact_4295_even__succ__div__exp,axiom,
% 5.68/5.96 ! [A: code_integer,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_exp
% 5.68/5.96 thf(fact_4296_even__succ__div__exp,axiom,
% 5.68/5.96 ! [A: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_exp
% 5.68/5.96 thf(fact_4297_even__succ__div__exp,axiom,
% 5.68/5.96 ! [A: int,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.96 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_exp
% 5.68/5.96 thf(fact_4298_signed__take__bit__Suc,axiom,
% 5.68/5.96 ! [N: nat,A: code_integer] :
% 5.68/5.96 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_Suc
% 5.68/5.96 thf(fact_4299_signed__take__bit__Suc,axiom,
% 5.68/5.96 ! [N: nat,A: int] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.68/5.96 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_Suc
% 5.68/5.96 thf(fact_4300_diff__shunt__var,axiom,
% 5.68/5.96 ! [X: set_real,Y2: set_real] :
% 5.68/5.96 ( ( ( minus_minus_set_real @ X @ Y2 )
% 5.68/5.96 = bot_bot_set_real )
% 5.68/5.96 = ( ord_less_eq_set_real @ X @ Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % diff_shunt_var
% 5.68/5.96 thf(fact_4301_diff__shunt__var,axiom,
% 5.68/5.96 ! [X: set_nat,Y2: set_nat] :
% 5.68/5.96 ( ( ( minus_minus_set_nat @ X @ Y2 )
% 5.68/5.96 = bot_bot_set_nat )
% 5.68/5.96 = ( ord_less_eq_set_nat @ X @ Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % diff_shunt_var
% 5.68/5.96 thf(fact_4302_diff__shunt__var,axiom,
% 5.68/5.96 ! [X: set_int,Y2: set_int] :
% 5.68/5.96 ( ( ( minus_minus_set_int @ X @ Y2 )
% 5.68/5.96 = bot_bot_set_int )
% 5.68/5.96 = ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 5.68/5.96
% 5.68/5.96 % diff_shunt_var
% 5.68/5.96 thf(fact_4303_add__scale__eq__noteq,axiom,
% 5.68/5.96 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.68/5.96 ( ( R2 != zero_zero_complex )
% 5.68/5.96 => ( ( ( A = B )
% 5.68/5.96 & ( C != D ) )
% 5.68/5.96 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.68/5.96 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % add_scale_eq_noteq
% 5.68/5.96 thf(fact_4304_add__scale__eq__noteq,axiom,
% 5.68/5.96 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.68/5.96 ( ( R2 != zero_zero_real )
% 5.68/5.96 => ( ( ( A = B )
% 5.68/5.96 & ( C != D ) )
% 5.68/5.96 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.68/5.96 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % add_scale_eq_noteq
% 5.68/5.96 thf(fact_4305_add__scale__eq__noteq,axiom,
% 5.68/5.96 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.68/5.96 ( ( R2 != zero_zero_rat )
% 5.68/5.96 => ( ( ( A = B )
% 5.68/5.96 & ( C != D ) )
% 5.68/5.96 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.68/5.96 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % add_scale_eq_noteq
% 5.68/5.96 thf(fact_4306_add__scale__eq__noteq,axiom,
% 5.68/5.96 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.68/5.96 ( ( R2 != zero_zero_nat )
% 5.68/5.96 => ( ( ( A = B )
% 5.68/5.96 & ( C != D ) )
% 5.68/5.96 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.68/5.96 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % add_scale_eq_noteq
% 5.68/5.96 thf(fact_4307_add__scale__eq__noteq,axiom,
% 5.68/5.96 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.68/5.96 ( ( R2 != zero_zero_int )
% 5.68/5.96 => ( ( ( A = B )
% 5.68/5.96 & ( C != D ) )
% 5.68/5.96 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.68/5.96 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % add_scale_eq_noteq
% 5.68/5.96 thf(fact_4308_artanh__def,axiom,
% 5.68/5.96 ( artanh_real
% 5.68/5.96 = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % artanh_def
% 5.68/5.96 thf(fact_4309_nat__dvd__1__iff__1,axiom,
% 5.68/5.96 ! [M: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.68/5.96 = ( M = one_one_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % nat_dvd_1_iff_1
% 5.68/5.96 thf(fact_4310_dvd__add__triv__left__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_left_iff
% 5.68/5.96 thf(fact_4311_dvd__add__triv__left__iff,axiom,
% 5.68/5.96 ! [A: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_left_iff
% 5.68/5.96 thf(fact_4312_dvd__add__triv__left__iff,axiom,
% 5.68/5.96 ! [A: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_left_iff
% 5.68/5.96 thf(fact_4313_dvd__add__triv__left__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_left_iff
% 5.68/5.96 thf(fact_4314_dvd__add__triv__left__iff,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_left_iff
% 5.68/5.96 thf(fact_4315_dvd__add__triv__right__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_right_iff
% 5.68/5.96 thf(fact_4316_dvd__add__triv__right__iff,axiom,
% 5.68/5.96 ! [A: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_right_iff
% 5.68/5.96 thf(fact_4317_dvd__add__triv__right__iff,axiom,
% 5.68/5.96 ! [A: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_right_iff
% 5.68/5.96 thf(fact_4318_dvd__add__triv__right__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_right_iff
% 5.68/5.96 thf(fact_4319_dvd__add__triv__right__iff,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_triv_right_iff
% 5.68/5.96 thf(fact_4320_dvd__1__iff__1,axiom,
% 5.68/5.96 ! [M: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.68/5.96 = ( M
% 5.68/5.96 = ( suc @ zero_zero_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_1_iff_1
% 5.68/5.96 thf(fact_4321_dvd__1__left,axiom,
% 5.68/5.96 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_1_left
% 5.68/5.96 thf(fact_4322_div__dvd__div,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_dvd_div
% 5.68/5.96 thf(fact_4323_div__dvd__div,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_dvd_div
% 5.68/5.96 thf(fact_4324_div__dvd__div,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_dvd_div
% 5.68/5.96 thf(fact_4325_nat__mult__dvd__cancel__disj,axiom,
% 5.68/5.96 ! [K: nat,M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.68/5.96 = ( ( K = zero_zero_nat )
% 5.68/5.96 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % nat_mult_dvd_cancel_disj
% 5.68/5.96 thf(fact_4326_signed__take__bit__of__0,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.68/5.96 = zero_zero_int ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_of_0
% 5.68/5.96 thf(fact_4327_dvd__times__right__cancel__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_right_cancel_iff
% 5.68/5.96 thf(fact_4328_dvd__times__right__cancel__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( A != zero_zero_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_right_cancel_iff
% 5.68/5.96 thf(fact_4329_dvd__times__right__cancel__iff,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( A != zero_zero_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.68/5.96 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_right_cancel_iff
% 5.68/5.96 thf(fact_4330_dvd__times__left__cancel__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_left_cancel_iff
% 5.68/5.96 thf(fact_4331_dvd__times__left__cancel__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( A != zero_zero_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.68/5.96 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_left_cancel_iff
% 5.68/5.96 thf(fact_4332_dvd__times__left__cancel__iff,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( A != zero_zero_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.68/5.96 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_times_left_cancel_iff
% 5.68/5.96 thf(fact_4333_dvd__mult__cancel__right,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.68/5.96 = ( ( C = zero_z3403309356797280102nteger )
% 5.68/5.96 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_right
% 5.68/5.96 thf(fact_4334_dvd__mult__cancel__right,axiom,
% 5.68/5.96 ! [A: complex,C: complex,B: complex] :
% 5.68/5.96 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.68/5.96 = ( ( C = zero_zero_complex )
% 5.68/5.96 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_right
% 5.68/5.96 thf(fact_4335_dvd__mult__cancel__right,axiom,
% 5.68/5.96 ! [A: real,C: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.68/5.96 = ( ( C = zero_zero_real )
% 5.68/5.96 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_right
% 5.68/5.96 thf(fact_4336_dvd__mult__cancel__right,axiom,
% 5.68/5.96 ! [A: rat,C: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.68/5.96 = ( ( C = zero_zero_rat )
% 5.68/5.96 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_right
% 5.68/5.96 thf(fact_4337_dvd__mult__cancel__right,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.68/5.96 = ( ( C = zero_zero_int )
% 5.68/5.96 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_right
% 5.68/5.96 thf(fact_4338_dvd__mult__cancel__left,axiom,
% 5.68/5.96 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.68/5.96 = ( ( C = zero_z3403309356797280102nteger )
% 5.68/5.96 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_left
% 5.68/5.96 thf(fact_4339_dvd__mult__cancel__left,axiom,
% 5.68/5.96 ! [C: complex,A: complex,B: complex] :
% 5.68/5.96 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.68/5.96 = ( ( C = zero_zero_complex )
% 5.68/5.96 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_left
% 5.68/5.96 thf(fact_4340_dvd__mult__cancel__left,axiom,
% 5.68/5.96 ! [C: real,A: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.68/5.96 = ( ( C = zero_zero_real )
% 5.68/5.96 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_left
% 5.68/5.96 thf(fact_4341_dvd__mult__cancel__left,axiom,
% 5.68/5.96 ! [C: rat,A: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.68/5.96 = ( ( C = zero_zero_rat )
% 5.68/5.96 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_left
% 5.68/5.96 thf(fact_4342_dvd__mult__cancel__left,axiom,
% 5.68/5.96 ! [C: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.68/5.96 = ( ( C = zero_zero_int )
% 5.68/5.96 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_cancel_left
% 5.68/5.96 thf(fact_4343_unit__prod,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_prod
% 5.68/5.96 thf(fact_4344_unit__prod,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_prod
% 5.68/5.96 thf(fact_4345_unit__prod,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_prod
% 5.68/5.96 thf(fact_4346_dvd__add__times__triv__right__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_right_iff
% 5.68/5.96 thf(fact_4347_dvd__add__times__triv__right__iff,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_right_iff
% 5.68/5.96 thf(fact_4348_dvd__add__times__triv__right__iff,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_right_iff
% 5.68/5.96 thf(fact_4349_dvd__add__times__triv__right__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_right_iff
% 5.68/5.96 thf(fact_4350_dvd__add__times__triv__right__iff,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_right_iff
% 5.68/5.96 thf(fact_4351_dvd__add__times__triv__left__iff,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_left_iff
% 5.68/5.96 thf(fact_4352_dvd__add__times__triv__left__iff,axiom,
% 5.68/5.96 ! [A: real,C: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_left_iff
% 5.68/5.96 thf(fact_4353_dvd__add__times__triv__left__iff,axiom,
% 5.68/5.96 ! [A: rat,C: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_left_iff
% 5.68/5.96 thf(fact_4354_dvd__add__times__triv__left__iff,axiom,
% 5.68/5.96 ! [A: nat,C: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_left_iff
% 5.68/5.96 thf(fact_4355_dvd__add__times__triv__left__iff,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_times_triv_left_iff
% 5.68/5.96 thf(fact_4356_dvd__mult__div__cancel,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_div_cancel
% 5.68/5.96 thf(fact_4357_dvd__mult__div__cancel,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_div_cancel
% 5.68/5.96 thf(fact_4358_dvd__mult__div__cancel,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_div_cancel
% 5.68/5.96 thf(fact_4359_dvd__div__mult__self,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult_self
% 5.68/5.96 thf(fact_4360_dvd__div__mult__self,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult_self
% 5.68/5.96 thf(fact_4361_dvd__div__mult__self,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult_self
% 5.68/5.96 thf(fact_4362_unit__div__1__div__1,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_div_1
% 5.68/5.96 thf(fact_4363_unit__div__1__div__1,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_div_1
% 5.68/5.96 thf(fact_4364_unit__div__1__div__1,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_div_1
% 5.68/5.96 thf(fact_4365_unit__div__1__unit,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_unit
% 5.68/5.96 thf(fact_4366_unit__div__1__unit,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_unit
% 5.68/5.96 thf(fact_4367_unit__div__1__unit,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_1_unit
% 5.68/5.96 thf(fact_4368_unit__div,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div
% 5.68/5.96 thf(fact_4369_unit__div,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div
% 5.68/5.96 thf(fact_4370_unit__div,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div
% 5.68/5.96 thf(fact_4371_div__add,axiom,
% 5.68/5.96 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_add
% 5.68/5.96 thf(fact_4372_div__add,axiom,
% 5.68/5.96 ! [C: nat,A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_add
% 5.68/5.96 thf(fact_4373_div__add,axiom,
% 5.68/5.96 ! [C: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_add
% 5.68/5.96 thf(fact_4374_div__diff,axiom,
% 5.68/5.96 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.68/5.96 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_diff
% 5.68/5.96 thf(fact_4375_div__diff,axiom,
% 5.68/5.96 ! [C: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.68/5.96 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_diff
% 5.68/5.96 thf(fact_4376_ln__le__cancel__iff,axiom,
% 5.68/5.96 ! [X: real,Y2: real] :
% 5.68/5.96 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.96 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 5.68/5.96 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ln_le_cancel_iff
% 5.68/5.96 thf(fact_4377_signed__take__bit__Suc__1,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.68/5.96 = one_one_int ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_Suc_1
% 5.68/5.96 thf(fact_4378_signed__take__bit__numeral__of__1,axiom,
% 5.68/5.96 ! [K: num] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.68/5.96 = one_one_int ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_numeral_of_1
% 5.68/5.96 thf(fact_4379_unit__div__mult__self,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_mult_self
% 5.68/5.96 thf(fact_4380_unit__div__mult__self,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_mult_self
% 5.68/5.96 thf(fact_4381_unit__div__mult__self,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.68/5.96 = B ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_mult_self
% 5.68/5.96 thf(fact_4382_unit__mult__div__div,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_div_div
% 5.68/5.96 thf(fact_4383_unit__mult__div__div,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.68/5.96 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_div_div
% 5.68/5.96 thf(fact_4384_unit__mult__div__div,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.68/5.96 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_div_div
% 5.68/5.96 thf(fact_4385_even__Suc__Suc__iff,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.68/5.96 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_Suc_Suc_iff
% 5.68/5.96 thf(fact_4386_even__Suc,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_Suc
% 5.68/5.96 thf(fact_4387_pow__divides__pow__iff,axiom,
% 5.68/5.96 ! [N: nat,A: nat,B: nat] :
% 5.68/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pow_divides_pow_iff
% 5.68/5.96 thf(fact_4388_pow__divides__pow__iff,axiom,
% 5.68/5.96 ! [N: nat,A: int,B: int] :
% 5.68/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pow_divides_pow_iff
% 5.68/5.96 thf(fact_4389_ln__ge__zero__iff,axiom,
% 5.68/5.96 ! [X: real] :
% 5.68/5.96 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.96 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.68/5.96 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ln_ge_zero_iff
% 5.68/5.96 thf(fact_4390_ln__le__zero__iff,axiom,
% 5.68/5.96 ! [X: real] :
% 5.68/5.96 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.96 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.68/5.96 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % ln_le_zero_iff
% 5.68/5.96 thf(fact_4391_even__mult__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mult_iff
% 5.68/5.96 thf(fact_4392_even__mult__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mult_iff
% 5.68/5.96 thf(fact_4393_even__mult__iff,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mult_iff
% 5.68/5.96 thf(fact_4394_even__add,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_add
% 5.68/5.96 thf(fact_4395_even__add,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_add
% 5.68/5.96 thf(fact_4396_even__add,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.68/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_add
% 5.68/5.96 thf(fact_4397_odd__add,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.68/5.96 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.96 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_add
% 5.68/5.96 thf(fact_4398_odd__add,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.68/5.96 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.96 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_add
% 5.68/5.96 thf(fact_4399_odd__add,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.68/5.96 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.96 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_add
% 5.68/5.96 thf(fact_4400_even__mod__2__iff,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.96 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mod_2_iff
% 5.68/5.96 thf(fact_4401_even__mod__2__iff,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.68/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mod_2_iff
% 5.68/5.96 thf(fact_4402_even__mod__2__iff,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_mod_2_iff
% 5.68/5.96 thf(fact_4403_even__Suc__div__two,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_Suc_div_two
% 5.68/5.96 thf(fact_4404_odd__Suc__div__two,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_Suc_div_two
% 5.68/5.96 thf(fact_4405_signed__take__bit__Suc__bit0,axiom,
% 5.68/5.96 ! [N: nat,K: num] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.68/5.96 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_Suc_bit0
% 5.68/5.96 thf(fact_4406_zero__le__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: real,W: num] :
% 5.68/5.96 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_le_power_eq_numeral
% 5.68/5.96 thf(fact_4407_zero__le__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: rat,W: num] :
% 5.68/5.96 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_le_power_eq_numeral
% 5.68/5.96 thf(fact_4408_zero__le__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: int,W: num] :
% 5.68/5.96 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_le_power_eq_numeral
% 5.68/5.96 thf(fact_4409_power__less__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: real,W: num] :
% 5.68/5.96 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq_numeral
% 5.68/5.96 thf(fact_4410_power__less__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: rat,W: num] :
% 5.68/5.96 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq_numeral
% 5.68/5.96 thf(fact_4411_power__less__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: int,W: num] :
% 5.68/5.96 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq_numeral
% 5.68/5.96 thf(fact_4412_power__less__zero__eq,axiom,
% 5.68/5.96 ! [A: real,N: nat] :
% 5.68/5.96 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq
% 5.68/5.96 thf(fact_4413_power__less__zero__eq,axiom,
% 5.68/5.96 ! [A: rat,N: nat] :
% 5.68/5.96 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq
% 5.68/5.96 thf(fact_4414_power__less__zero__eq,axiom,
% 5.68/5.96 ! [A: int,N: nat] :
% 5.68/5.96 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_less_zero_eq
% 5.68/5.96 thf(fact_4415_even__plus__one__iff,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_plus_one_iff
% 5.68/5.96 thf(fact_4416_even__plus__one__iff,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_plus_one_iff
% 5.68/5.96 thf(fact_4417_even__plus__one__iff,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_plus_one_iff
% 5.68/5.96 thf(fact_4418_even__diff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_diff
% 5.68/5.96 thf(fact_4419_even__diff,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_diff
% 5.68/5.96 thf(fact_4420_odd__Suc__minus__one,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.68/5.96 = N ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_Suc_minus_one
% 5.68/5.96 thf(fact_4421_even__diff__nat,axiom,
% 5.68/5.96 ! [M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.68/5.96 = ( ( ord_less_nat @ M @ N )
% 5.68/5.96 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_diff_nat
% 5.68/5.96 thf(fact_4422_zero__less__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: real,W: num] :
% 5.68/5.96 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( ( numeral_numeral_nat @ W )
% 5.68/5.96 = zero_zero_nat )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A != zero_zero_real ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_less_power_eq_numeral
% 5.68/5.96 thf(fact_4423_zero__less__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: rat,W: num] :
% 5.68/5.96 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( ( numeral_numeral_nat @ W )
% 5.68/5.96 = zero_zero_nat )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A != zero_zero_rat ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_less_power_eq_numeral
% 5.68/5.96 thf(fact_4424_zero__less__power__eq__numeral,axiom,
% 5.68/5.96 ! [A: int,W: num] :
% 5.68/5.96 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.68/5.96 = ( ( ( numeral_numeral_nat @ W )
% 5.68/5.96 = zero_zero_nat )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A != zero_zero_int ) )
% 5.68/5.96 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zero_less_power_eq_numeral
% 5.68/5.96 thf(fact_4425_even__succ__div__2,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_2
% 5.68/5.96 thf(fact_4426_even__succ__div__2,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_2
% 5.68/5.96 thf(fact_4427_even__succ__div__2,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_2
% 5.68/5.96 thf(fact_4428_even__succ__div__two,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_two
% 5.68/5.96 thf(fact_4429_even__succ__div__two,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_two
% 5.68/5.96 thf(fact_4430_even__succ__div__two,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_succ_div_two
% 5.68/5.96 thf(fact_4431_odd__succ__div__two,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_succ_div_two
% 5.68/5.96 thf(fact_4432_odd__succ__div__two,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_succ_div_two
% 5.68/5.96 thf(fact_4433_odd__succ__div__two,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.96 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_succ_div_two
% 5.68/5.96 thf(fact_4434_even__power,axiom,
% 5.68/5.96 ! [A: code_integer,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.68/5.96 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_power
% 5.68/5.96 thf(fact_4435_even__power,axiom,
% 5.68/5.96 ! [A: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.68/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_power
% 5.68/5.96 thf(fact_4436_even__power,axiom,
% 5.68/5.96 ! [A: int,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.68/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_power
% 5.68/5.96 thf(fact_4437_odd__two__times__div__two__nat,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.96 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.96 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_two_times_div_two_nat
% 5.68/5.96 thf(fact_4438_odd__two__times__div__two__succ,axiom,
% 5.68/5.96 ! [A: code_integer] :
% 5.68/5.96 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_two_times_div_two_succ
% 5.68/5.96 thf(fact_4439_odd__two__times__div__two__succ,axiom,
% 5.68/5.96 ! [A: nat] :
% 5.68/5.96 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_two_times_div_two_succ
% 5.68/5.96 thf(fact_4440_odd__two__times__div__two__succ,axiom,
% 5.68/5.96 ! [A: int] :
% 5.68/5.96 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.96 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.68/5.96 = A ) ) ).
% 5.68/5.96
% 5.68/5.96 % odd_two_times_div_two_succ
% 5.68/5.96 thf(fact_4441_power__le__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: real,W: num] :
% 5.68/5.96 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.68/5.96 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_zero_eq_numeral
% 5.68/5.96 thf(fact_4442_power__le__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: rat,W: num] :
% 5.68/5.96 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.68/5.96 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_zero_eq_numeral
% 5.68/5.96 thf(fact_4443_power__le__zero__eq__numeral,axiom,
% 5.68/5.96 ! [A: int,W: num] :
% 5.68/5.96 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.68/5.96 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.68/5.96 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.96 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_zero_eq_numeral
% 5.68/5.96 thf(fact_4444_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.68/5.96 = ( N = zero_zero_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % semiring_parity_class.even_mask_iff
% 5.68/5.96 thf(fact_4445_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.68/5.96 = ( N = zero_zero_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % semiring_parity_class.even_mask_iff
% 5.68/5.96 thf(fact_4446_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.68/5.96 ! [N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.68/5.96 = ( N = zero_zero_nat ) ) ).
% 5.68/5.96
% 5.68/5.96 % semiring_parity_class.even_mask_iff
% 5.68/5.96 thf(fact_4447_bot__nat__def,axiom,
% 5.68/5.96 bot_bot_nat = zero_zero_nat ).
% 5.68/5.96
% 5.68/5.96 % bot_nat_def
% 5.68/5.96 thf(fact_4448_dvd__field__iff,axiom,
% 5.68/5.96 ( dvd_dvd_complex
% 5.68/5.96 = ( ^ [A4: complex,B3: complex] :
% 5.68/5.96 ( ( A4 = zero_zero_complex )
% 5.68/5.96 => ( B3 = zero_zero_complex ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_field_iff
% 5.68/5.96 thf(fact_4449_dvd__field__iff,axiom,
% 5.68/5.96 ( dvd_dvd_real
% 5.68/5.96 = ( ^ [A4: real,B3: real] :
% 5.68/5.96 ( ( A4 = zero_zero_real )
% 5.68/5.96 => ( B3 = zero_zero_real ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_field_iff
% 5.68/5.96 thf(fact_4450_dvd__field__iff,axiom,
% 5.68/5.96 ( dvd_dvd_rat
% 5.68/5.96 = ( ^ [A4: rat,B3: rat] :
% 5.68/5.96 ( ( A4 = zero_zero_rat )
% 5.68/5.96 => ( B3 = zero_zero_rat ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_field_iff
% 5.68/5.96 thf(fact_4451_dvdE,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ~ ! [K2: code_integer] :
% 5.68/5.96 ( A
% 5.68/5.96 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdE
% 5.68/5.96 thf(fact_4452_dvdE,axiom,
% 5.68/5.96 ! [B: real,A: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ B @ A )
% 5.68/5.96 => ~ ! [K2: real] :
% 5.68/5.96 ( A
% 5.68/5.96 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdE
% 5.68/5.96 thf(fact_4453_dvdE,axiom,
% 5.68/5.96 ! [B: rat,A: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ B @ A )
% 5.68/5.96 => ~ ! [K2: rat] :
% 5.68/5.96 ( A
% 5.68/5.96 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdE
% 5.68/5.96 thf(fact_4454_dvdE,axiom,
% 5.68/5.96 ! [B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ~ ! [K2: nat] :
% 5.68/5.96 ( A
% 5.68/5.96 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdE
% 5.68/5.96 thf(fact_4455_dvdE,axiom,
% 5.68/5.96 ! [B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ~ ! [K2: int] :
% 5.68/5.96 ( A
% 5.68/5.96 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdE
% 5.68/5.96 thf(fact_4456_dvdI,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdI
% 5.68/5.96 thf(fact_4457_dvdI,axiom,
% 5.68/5.96 ! [A: real,B: real,K: real] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_real @ B @ K ) )
% 5.68/5.96 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdI
% 5.68/5.96 thf(fact_4458_dvdI,axiom,
% 5.68/5.96 ! [A: rat,B: rat,K: rat] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_rat @ B @ K ) )
% 5.68/5.96 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdI
% 5.68/5.96 thf(fact_4459_dvdI,axiom,
% 5.68/5.96 ! [A: nat,B: nat,K: nat] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_nat @ B @ K ) )
% 5.68/5.96 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdI
% 5.68/5.96 thf(fact_4460_dvdI,axiom,
% 5.68/5.96 ! [A: int,B: int,K: int] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_int @ B @ K ) )
% 5.68/5.96 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvdI
% 5.68/5.96 thf(fact_4461_dvd__def,axiom,
% 5.68/5.96 ( dvd_dvd_Code_integer
% 5.68/5.96 = ( ^ [B3: code_integer,A4: code_integer] :
% 5.68/5.96 ? [K3: code_integer] :
% 5.68/5.96 ( A4
% 5.68/5.96 = ( times_3573771949741848930nteger @ B3 @ K3 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_def
% 5.68/5.96 thf(fact_4462_dvd__def,axiom,
% 5.68/5.96 ( dvd_dvd_real
% 5.68/5.96 = ( ^ [B3: real,A4: real] :
% 5.68/5.96 ? [K3: real] :
% 5.68/5.96 ( A4
% 5.68/5.96 = ( times_times_real @ B3 @ K3 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_def
% 5.68/5.96 thf(fact_4463_dvd__def,axiom,
% 5.68/5.96 ( dvd_dvd_rat
% 5.68/5.96 = ( ^ [B3: rat,A4: rat] :
% 5.68/5.96 ? [K3: rat] :
% 5.68/5.96 ( A4
% 5.68/5.96 = ( times_times_rat @ B3 @ K3 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_def
% 5.68/5.96 thf(fact_4464_dvd__def,axiom,
% 5.68/5.96 ( dvd_dvd_nat
% 5.68/5.96 = ( ^ [B3: nat,A4: nat] :
% 5.68/5.96 ? [K3: nat] :
% 5.68/5.96 ( A4
% 5.68/5.96 = ( times_times_nat @ B3 @ K3 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_def
% 5.68/5.96 thf(fact_4465_dvd__def,axiom,
% 5.68/5.96 ( dvd_dvd_int
% 5.68/5.96 = ( ^ [B3: int,A4: int] :
% 5.68/5.96 ? [K3: int] :
% 5.68/5.96 ( A4
% 5.68/5.96 = ( times_times_int @ B3 @ K3 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_def
% 5.68/5.96 thf(fact_4466_dvd__mult,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult
% 5.68/5.96 thf(fact_4467_dvd__mult,axiom,
% 5.68/5.96 ! [A: real,C: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ C )
% 5.68/5.96 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult
% 5.68/5.96 thf(fact_4468_dvd__mult,axiom,
% 5.68/5.96 ! [A: rat,C: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ C )
% 5.68/5.96 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult
% 5.68/5.96 thf(fact_4469_dvd__mult,axiom,
% 5.68/5.96 ! [A: nat,C: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ C )
% 5.68/5.96 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult
% 5.68/5.96 thf(fact_4470_dvd__mult,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ C )
% 5.68/5.96 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult
% 5.68/5.96 thf(fact_4471_dvd__mult2,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult2
% 5.68/5.96 thf(fact_4472_dvd__mult2,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ B )
% 5.68/5.96 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult2
% 5.68/5.96 thf(fact_4473_dvd__mult2,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ B )
% 5.68/5.96 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult2
% 5.68/5.96 thf(fact_4474_dvd__mult2,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult2
% 5.68/5.96 thf(fact_4475_dvd__mult2,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult2
% 5.68/5.96 thf(fact_4476_dvd__mult__left,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_left
% 5.68/5.96 thf(fact_4477_dvd__mult__left,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_left
% 5.68/5.96 thf(fact_4478_dvd__mult__left,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_left
% 5.68/5.96 thf(fact_4479_dvd__mult__left,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_left
% 5.68/5.96 thf(fact_4480_dvd__mult__left,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_left
% 5.68/5.96 thf(fact_4481_dvd__triv__left,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_left
% 5.68/5.96 thf(fact_4482_dvd__triv__left,axiom,
% 5.68/5.96 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_left
% 5.68/5.96 thf(fact_4483_dvd__triv__left,axiom,
% 5.68/5.96 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_left
% 5.68/5.96 thf(fact_4484_dvd__triv__left,axiom,
% 5.68/5.96 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_left
% 5.68/5.96 thf(fact_4485_dvd__triv__left,axiom,
% 5.68/5.96 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_left
% 5.68/5.96 thf(fact_4486_mult__dvd__mono,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_dvd_mono
% 5.68/5.96 thf(fact_4487_mult__dvd__mono,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real,D: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_real @ C @ D )
% 5.68/5.96 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_dvd_mono
% 5.68/5.96 thf(fact_4488_mult__dvd__mono,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_rat @ C @ D )
% 5.68/5.96 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_dvd_mono
% 5.68/5.96 thf(fact_4489_mult__dvd__mono,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ C @ D )
% 5.68/5.96 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_dvd_mono
% 5.68/5.96 thf(fact_4490_mult__dvd__mono,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int,D: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ D )
% 5.68/5.96 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_dvd_mono
% 5.68/5.96 thf(fact_4491_dvd__mult__right,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_right
% 5.68/5.96 thf(fact_4492_dvd__mult__right,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_right
% 5.68/5.96 thf(fact_4493_dvd__mult__right,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_right
% 5.68/5.96 thf(fact_4494_dvd__mult__right,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_right
% 5.68/5.96 thf(fact_4495_dvd__mult__right,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.68/5.96 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_right
% 5.68/5.96 thf(fact_4496_dvd__triv__right,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_right
% 5.68/5.96 thf(fact_4497_dvd__triv__right,axiom,
% 5.68/5.96 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_right
% 5.68/5.96 thf(fact_4498_dvd__triv__right,axiom,
% 5.68/5.96 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_right
% 5.68/5.96 thf(fact_4499_dvd__triv__right,axiom,
% 5.68/5.96 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_right
% 5.68/5.96 thf(fact_4500_dvd__triv__right,axiom,
% 5.68/5.96 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_triv_right
% 5.68/5.96 thf(fact_4501_dvd__productE,axiom,
% 5.68/5.96 ! [P4: nat,A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 5.68/5.96 => ~ ! [X3: nat,Y3: nat] :
% 5.68/5.96 ( ( P4
% 5.68/5.96 = ( times_times_nat @ X3 @ Y3 ) )
% 5.68/5.96 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.68/5.96 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_productE
% 5.68/5.96 thf(fact_4502_dvd__productE,axiom,
% 5.68/5.96 ! [P4: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 5.68/5.96 => ~ ! [X3: int,Y3: int] :
% 5.68/5.96 ( ( P4
% 5.68/5.96 = ( times_times_int @ X3 @ Y3 ) )
% 5.68/5.96 => ( ( dvd_dvd_int @ X3 @ A )
% 5.68/5.96 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_productE
% 5.68/5.96 thf(fact_4503_division__decomp,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.68/5.96 => ? [B7: nat,C5: nat] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_nat @ B7 @ C5 ) )
% 5.68/5.96 & ( dvd_dvd_nat @ B7 @ B )
% 5.68/5.96 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % division_decomp
% 5.68/5.96 thf(fact_4504_division__decomp,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.68/5.96 => ? [B7: int,C5: int] :
% 5.68/5.96 ( ( A
% 5.68/5.96 = ( times_times_int @ B7 @ C5 ) )
% 5.68/5.96 & ( dvd_dvd_int @ B7 @ B )
% 5.68/5.96 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % division_decomp
% 5.68/5.96 thf(fact_4505_dvd__add,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add
% 5.68/5.96 thf(fact_4506_dvd__add,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_real @ A @ C )
% 5.68/5.96 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add
% 5.68/5.96 thf(fact_4507_dvd__add,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_rat @ A @ C )
% 5.68/5.96 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add
% 5.68/5.96 thf(fact_4508_dvd__add,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ C )
% 5.68/5.96 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add
% 5.68/5.96 thf(fact_4509_dvd__add,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ C )
% 5.68/5.96 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add
% 5.68/5.96 thf(fact_4510_dvd__add__left__iff,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_left_iff
% 5.68/5.96 thf(fact_4511_dvd__add__left__iff,axiom,
% 5.68/5.96 ! [A: real,C: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_left_iff
% 5.68/5.96 thf(fact_4512_dvd__add__left__iff,axiom,
% 5.68/5.96 ! [A: rat,C: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_left_iff
% 5.68/5.96 thf(fact_4513_dvd__add__left__iff,axiom,
% 5.68/5.96 ! [A: nat,C: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_left_iff
% 5.68/5.96 thf(fact_4514_dvd__add__left__iff,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ C )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_left_iff
% 5.68/5.96 thf(fact_4515_dvd__add__right__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_right_iff
% 5.68/5.96 thf(fact_4516_dvd__add__right__iff,axiom,
% 5.68/5.96 ! [A: real,B: real,C: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_right_iff
% 5.68/5.96 thf(fact_4517_dvd__add__right__iff,axiom,
% 5.68/5.96 ! [A: rat,B: rat,C: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_right_iff
% 5.68/5.96 thf(fact_4518_dvd__add__right__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_right_iff
% 5.68/5.96 thf(fact_4519_dvd__add__right__iff,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_add_right_iff
% 5.68/5.96 thf(fact_4520_dvd__diff__commute,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_diff_commute
% 5.68/5.96 thf(fact_4521_dvd__diff__commute,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_diff_commute
% 5.68/5.96 thf(fact_4522_div__div__div__same,axiom,
% 5.68/5.96 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_div_same
% 5.68/5.96 thf(fact_4523_div__div__div__same,axiom,
% 5.68/5.96 ! [D: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ D @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.68/5.96 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_div_same
% 5.68/5.96 thf(fact_4524_div__div__div__same,axiom,
% 5.68/5.96 ! [D: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ D @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.68/5.96 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_div_same
% 5.68/5.96 thf(fact_4525_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.68/5.96 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4526_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: complex,C: complex,B: complex] :
% 5.68/5.96 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.68/5.96 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_complex @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_complex @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4527_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: real,C: real,B: real] :
% 5.68/5.96 ( ( ( divide_divide_real @ A @ C )
% 5.68/5.96 = ( divide_divide_real @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_real @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_real @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4528_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: rat,C: rat,B: rat] :
% 5.68/5.96 ( ( ( divide_divide_rat @ A @ C )
% 5.68/5.96 = ( divide_divide_rat @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_rat @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_rat @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4529_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: nat,C: nat,B: nat] :
% 5.68/5.96 ( ( ( divide_divide_nat @ A @ C )
% 5.68/5.96 = ( divide_divide_nat @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_nat @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4530_dvd__div__eq__cancel,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( ( divide_divide_int @ A @ C )
% 5.68/5.96 = ( divide_divide_int @ B @ C ) )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_cancel
% 5.68/5.96 thf(fact_4531_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.68/5.96 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4532_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: complex,A: complex,B: complex] :
% 5.68/5.96 ( ( dvd_dvd_complex @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_complex @ C @ B )
% 5.68/5.96 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.68/5.96 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4533_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: real,A: real,B: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_real @ C @ B )
% 5.68/5.96 => ( ( ( divide_divide_real @ A @ C )
% 5.68/5.96 = ( divide_divide_real @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4534_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: rat,A: rat,B: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_rat @ C @ B )
% 5.68/5.96 => ( ( ( divide_divide_rat @ A @ C )
% 5.68/5.96 = ( divide_divide_rat @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4535_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: nat,A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( ( divide_divide_nat @ A @ C )
% 5.68/5.96 = ( divide_divide_nat @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4536_dvd__div__eq__iff,axiom,
% 5.68/5.96 ! [C: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ A )
% 5.68/5.96 => ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( ( divide_divide_int @ A @ C )
% 5.68/5.96 = ( divide_divide_int @ B @ C ) )
% 5.68/5.96 = ( A = B ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_iff
% 5.68/5.96 thf(fact_4537_dvd__power__same,axiom,
% 5.68/5.96 ! [X: code_integer,Y2: code_integer,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_same
% 5.68/5.96 thf(fact_4538_dvd__power__same,axiom,
% 5.68/5.96 ! [X: nat,Y2: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ X @ Y2 )
% 5.68/5.96 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_same
% 5.68/5.96 thf(fact_4539_dvd__power__same,axiom,
% 5.68/5.96 ! [X: real,Y2: real,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_real @ X @ Y2 )
% 5.68/5.96 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_same
% 5.68/5.96 thf(fact_4540_dvd__power__same,axiom,
% 5.68/5.96 ! [X: int,Y2: int,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ X @ Y2 )
% 5.68/5.96 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_same
% 5.68/5.96 thf(fact_4541_dvd__power__same,axiom,
% 5.68/5.96 ! [X: complex,Y2: complex,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_complex @ X @ Y2 )
% 5.68/5.96 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_same
% 5.68/5.96 thf(fact_4542_mod__mod__cancel,axiom,
% 5.68/5.96 ! [C: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.68/5.96 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mod_mod_cancel
% 5.68/5.96 thf(fact_4543_mod__mod__cancel,axiom,
% 5.68/5.96 ! [C: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.68/5.96 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mod_mod_cancel
% 5.68/5.96 thf(fact_4544_mod__mod__cancel,axiom,
% 5.68/5.96 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.68/5.96 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mod_mod_cancel
% 5.68/5.96 thf(fact_4545_dvd__mod,axiom,
% 5.68/5.96 ! [K: nat,M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ K @ M )
% 5.68/5.96 => ( ( dvd_dvd_nat @ K @ N )
% 5.68/5.96 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mod
% 5.68/5.96 thf(fact_4546_dvd__mod,axiom,
% 5.68/5.96 ! [K: int,M: int,N: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ K @ M )
% 5.68/5.96 => ( ( dvd_dvd_int @ K @ N )
% 5.68/5.96 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mod
% 5.68/5.96 thf(fact_4547_dvd__mod,axiom,
% 5.68/5.96 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mod
% 5.68/5.96 thf(fact_4548_signed__take__bit__mult,axiom,
% 5.68/5.96 ! [N: nat,K: int,L2: int] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.68/5.96 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_mult
% 5.68/5.96 thf(fact_4549_signed__take__bit__add,axiom,
% 5.68/5.96 ! [N: nat,K: int,L2: int] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.68/5.96 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_add
% 5.68/5.96 thf(fact_4550_dvd__diff__nat,axiom,
% 5.68/5.96 ! [K: nat,M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ K @ M )
% 5.68/5.96 => ( ( dvd_dvd_nat @ K @ N )
% 5.68/5.96 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_diff_nat
% 5.68/5.96 thf(fact_4551_signed__take__bit__diff,axiom,
% 5.68/5.96 ! [N: nat,K: int,L2: int] :
% 5.68/5.96 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.68/5.96 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % signed_take_bit_diff
% 5.68/5.96 thf(fact_4552_bot__enat__def,axiom,
% 5.68/5.96 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.68/5.96
% 5.68/5.96 % bot_enat_def
% 5.68/5.96 thf(fact_4553_subset__divisors__dvd,axiom,
% 5.68/5.96 ! [A: complex,B: complex] :
% 5.68/5.96 ( ( ord_le211207098394363844omplex
% 5.68/5.96 @ ( collect_complex
% 5.68/5.96 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.68/5.96 @ ( collect_complex
% 5.68/5.96 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.68/5.96 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % subset_divisors_dvd
% 5.68/5.96 thf(fact_4554_subset__divisors__dvd,axiom,
% 5.68/5.96 ! [A: real,B: real] :
% 5.68/5.96 ( ( ord_less_eq_set_real
% 5.68/5.96 @ ( collect_real
% 5.68/5.96 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.68/5.96 @ ( collect_real
% 5.68/5.96 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.68/5.96 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % subset_divisors_dvd
% 5.68/5.96 thf(fact_4555_subset__divisors__dvd,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( ord_less_eq_set_nat
% 5.68/5.96 @ ( collect_nat
% 5.68/5.96 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.68/5.96 @ ( collect_nat
% 5.68/5.96 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % subset_divisors_dvd
% 5.68/5.96 thf(fact_4556_subset__divisors__dvd,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( ord_le7084787975880047091nteger
% 5.68/5.96 @ ( collect_Code_integer
% 5.68/5.96 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.68/5.96 @ ( collect_Code_integer
% 5.68/5.96 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % subset_divisors_dvd
% 5.68/5.96 thf(fact_4557_subset__divisors__dvd,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( ord_less_eq_set_int
% 5.68/5.96 @ ( collect_int
% 5.68/5.96 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.68/5.96 @ ( collect_int
% 5.68/5.96 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.68/5.96
% 5.68/5.96 % subset_divisors_dvd
% 5.68/5.96 thf(fact_4558_even__signed__take__bit__iff,axiom,
% 5.68/5.96 ! [M: nat,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_signed_take_bit_iff
% 5.68/5.96 thf(fact_4559_even__signed__take__bit__iff,axiom,
% 5.68/5.96 ! [M: nat,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.68/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.96
% 5.68/5.96 % even_signed_take_bit_iff
% 5.68/5.96 thf(fact_4560_pinf_I9_J,axiom,
% 5.68/5.96 ! [D: code_integer,S2: code_integer] :
% 5.68/5.96 ? [Z3: code_integer] :
% 5.68/5.96 ! [X5: code_integer] :
% 5.68/5.96 ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(9)
% 5.68/5.96 thf(fact_4561_pinf_I9_J,axiom,
% 5.68/5.96 ! [D: real,S2: real] :
% 5.68/5.96 ? [Z3: real] :
% 5.68/5.96 ! [X5: real] :
% 5.68/5.96 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.96 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(9)
% 5.68/5.96 thf(fact_4562_pinf_I9_J,axiom,
% 5.68/5.96 ! [D: rat,S2: rat] :
% 5.68/5.96 ? [Z3: rat] :
% 5.68/5.96 ! [X5: rat] :
% 5.68/5.96 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.96 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(9)
% 5.68/5.96 thf(fact_4563_pinf_I9_J,axiom,
% 5.68/5.96 ! [D: nat,S2: nat] :
% 5.68/5.96 ? [Z3: nat] :
% 5.68/5.96 ! [X5: nat] :
% 5.68/5.96 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.96 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(9)
% 5.68/5.96 thf(fact_4564_pinf_I9_J,axiom,
% 5.68/5.96 ! [D: int,S2: int] :
% 5.68/5.96 ? [Z3: int] :
% 5.68/5.96 ! [X5: int] :
% 5.68/5.96 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.96 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(9)
% 5.68/5.96 thf(fact_4565_pinf_I10_J,axiom,
% 5.68/5.96 ! [D: code_integer,S2: code_integer] :
% 5.68/5.96 ? [Z3: code_integer] :
% 5.68/5.96 ! [X5: code_integer] :
% 5.68/5.96 ( ( ord_le6747313008572928689nteger @ Z3 @ X5 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(10)
% 5.68/5.96 thf(fact_4566_pinf_I10_J,axiom,
% 5.68/5.96 ! [D: real,S2: real] :
% 5.68/5.96 ? [Z3: real] :
% 5.68/5.96 ! [X5: real] :
% 5.68/5.96 ( ( ord_less_real @ Z3 @ X5 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(10)
% 5.68/5.96 thf(fact_4567_pinf_I10_J,axiom,
% 5.68/5.96 ! [D: rat,S2: rat] :
% 5.68/5.96 ? [Z3: rat] :
% 5.68/5.96 ! [X5: rat] :
% 5.68/5.96 ( ( ord_less_rat @ Z3 @ X5 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(10)
% 5.68/5.96 thf(fact_4568_pinf_I10_J,axiom,
% 5.68/5.96 ! [D: nat,S2: nat] :
% 5.68/5.96 ? [Z3: nat] :
% 5.68/5.96 ! [X5: nat] :
% 5.68/5.96 ( ( ord_less_nat @ Z3 @ X5 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(10)
% 5.68/5.96 thf(fact_4569_pinf_I10_J,axiom,
% 5.68/5.96 ! [D: int,S2: int] :
% 5.68/5.96 ? [Z3: int] :
% 5.68/5.96 ! [X5: int] :
% 5.68/5.96 ( ( ord_less_int @ Z3 @ X5 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % pinf(10)
% 5.68/5.96 thf(fact_4570_minf_I9_J,axiom,
% 5.68/5.96 ! [D: code_integer,S2: code_integer] :
% 5.68/5.96 ? [Z3: code_integer] :
% 5.68/5.96 ! [X5: code_integer] :
% 5.68/5.96 ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(9)
% 5.68/5.96 thf(fact_4571_minf_I9_J,axiom,
% 5.68/5.96 ! [D: real,S2: real] :
% 5.68/5.96 ? [Z3: real] :
% 5.68/5.96 ! [X5: real] :
% 5.68/5.96 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.96 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(9)
% 5.68/5.96 thf(fact_4572_minf_I9_J,axiom,
% 5.68/5.96 ! [D: rat,S2: rat] :
% 5.68/5.96 ? [Z3: rat] :
% 5.68/5.96 ! [X5: rat] :
% 5.68/5.96 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.96 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(9)
% 5.68/5.96 thf(fact_4573_minf_I9_J,axiom,
% 5.68/5.96 ! [D: nat,S2: nat] :
% 5.68/5.96 ? [Z3: nat] :
% 5.68/5.96 ! [X5: nat] :
% 5.68/5.96 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.96 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(9)
% 5.68/5.96 thf(fact_4574_minf_I9_J,axiom,
% 5.68/5.96 ! [D: int,S2: int] :
% 5.68/5.96 ? [Z3: int] :
% 5.68/5.96 ! [X5: int] :
% 5.68/5.96 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.96 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.68/5.96 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(9)
% 5.68/5.96 thf(fact_4575_minf_I10_J,axiom,
% 5.68/5.96 ! [D: code_integer,S2: code_integer] :
% 5.68/5.96 ? [Z3: code_integer] :
% 5.68/5.96 ! [X5: code_integer] :
% 5.68/5.96 ( ( ord_le6747313008572928689nteger @ X5 @ Z3 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(10)
% 5.68/5.96 thf(fact_4576_minf_I10_J,axiom,
% 5.68/5.96 ! [D: real,S2: real] :
% 5.68/5.96 ? [Z3: real] :
% 5.68/5.96 ! [X5: real] :
% 5.68/5.96 ( ( ord_less_real @ X5 @ Z3 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(10)
% 5.68/5.96 thf(fact_4577_minf_I10_J,axiom,
% 5.68/5.96 ! [D: rat,S2: rat] :
% 5.68/5.96 ? [Z3: rat] :
% 5.68/5.96 ! [X5: rat] :
% 5.68/5.96 ( ( ord_less_rat @ X5 @ Z3 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(10)
% 5.68/5.96 thf(fact_4578_minf_I10_J,axiom,
% 5.68/5.96 ! [D: nat,S2: nat] :
% 5.68/5.96 ? [Z3: nat] :
% 5.68/5.96 ! [X5: nat] :
% 5.68/5.96 ( ( ord_less_nat @ X5 @ Z3 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(10)
% 5.68/5.96 thf(fact_4579_minf_I10_J,axiom,
% 5.68/5.96 ! [D: int,S2: int] :
% 5.68/5.96 ? [Z3: int] :
% 5.68/5.96 ! [X5: int] :
% 5.68/5.96 ( ( ord_less_int @ X5 @ Z3 )
% 5.68/5.96 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.68/5.96 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % minf(10)
% 5.68/5.96 thf(fact_4580_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.68/5.96 = zero_z3403309356797280102nteger )
% 5.68/5.96 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4581_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: complex,A: complex] :
% 5.68/5.96 ( ( dvd_dvd_complex @ B @ A )
% 5.68/5.96 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.68/5.96 = zero_zero_complex )
% 5.68/5.96 = ( A = zero_zero_complex ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4582_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: real,A: real] :
% 5.68/5.96 ( ( dvd_dvd_real @ B @ A )
% 5.68/5.96 => ( ( ( divide_divide_real @ A @ B )
% 5.68/5.96 = zero_zero_real )
% 5.68/5.96 = ( A = zero_zero_real ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4583_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: rat,A: rat] :
% 5.68/5.96 ( ( dvd_dvd_rat @ B @ A )
% 5.68/5.96 => ( ( ( divide_divide_rat @ A @ B )
% 5.68/5.96 = zero_zero_rat )
% 5.68/5.96 = ( A = zero_zero_rat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4584_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ( ( ( divide_divide_nat @ A @ B )
% 5.68/5.96 = zero_zero_nat )
% 5.68/5.96 = ( A = zero_zero_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4585_dvd__div__eq__0__iff,axiom,
% 5.68/5.96 ! [B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ( ( ( divide_divide_int @ A @ B )
% 5.68/5.96 = zero_zero_int )
% 5.68/5.96 = ( A = zero_zero_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_eq_0_iff
% 5.68/5.96 thf(fact_4586_unit__mult__right__cancel,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.68/5.96 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_right_cancel
% 5.68/5.96 thf(fact_4587_unit__mult__right__cancel,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( ( times_times_nat @ B @ A )
% 5.68/5.96 = ( times_times_nat @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_right_cancel
% 5.68/5.96 thf(fact_4588_unit__mult__right__cancel,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( ( times_times_int @ B @ A )
% 5.68/5.96 = ( times_times_int @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_right_cancel
% 5.68/5.96 thf(fact_4589_unit__mult__left__cancel,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.68/5.96 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_left_cancel
% 5.68/5.96 thf(fact_4590_unit__mult__left__cancel,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( ( times_times_nat @ A @ B )
% 5.68/5.96 = ( times_times_nat @ A @ C ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_left_cancel
% 5.68/5.96 thf(fact_4591_unit__mult__left__cancel,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( ( times_times_int @ A @ B )
% 5.68/5.96 = ( times_times_int @ A @ C ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_mult_left_cancel
% 5.68/5.96 thf(fact_4592_mult__unit__dvd__iff_H,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff'
% 5.68/5.96 thf(fact_4593_mult__unit__dvd__iff_H,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff'
% 5.68/5.96 thf(fact_4594_mult__unit__dvd__iff_H,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff'
% 5.68/5.96 thf(fact_4595_dvd__mult__unit__iff_H,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff'
% 5.68/5.96 thf(fact_4596_dvd__mult__unit__iff_H,axiom,
% 5.68/5.96 ! [B: nat,A: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff'
% 5.68/5.96 thf(fact_4597_dvd__mult__unit__iff_H,axiom,
% 5.68/5.96 ! [B: int,A: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff'
% 5.68/5.96 thf(fact_4598_mult__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff
% 5.68/5.96 thf(fact_4599_mult__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: nat,A: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff
% 5.68/5.96 thf(fact_4600_mult__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: int,A: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mult_unit_dvd_iff
% 5.68/5.96 thf(fact_4601_dvd__mult__unit__iff,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff
% 5.68/5.96 thf(fact_4602_dvd__mult__unit__iff,axiom,
% 5.68/5.96 ! [B: nat,A: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff
% 5.68/5.96 thf(fact_4603_dvd__mult__unit__iff,axiom,
% 5.68/5.96 ! [B: int,A: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_unit_iff
% 5.68/5.96 thf(fact_4604_is__unit__mult__iff,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.68/5.96 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % is_unit_mult_iff
% 5.68/5.96 thf(fact_4605_is__unit__mult__iff,axiom,
% 5.68/5.96 ! [A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.68/5.96 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % is_unit_mult_iff
% 5.68/5.96 thf(fact_4606_is__unit__mult__iff,axiom,
% 5.68/5.96 ! [A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.68/5.96 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % is_unit_mult_iff
% 5.68/5.96 thf(fact_4607_div__mult__div__if__dvd,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_div_if_dvd
% 5.68/5.96 thf(fact_4608_div__mult__div__if__dvd,axiom,
% 5.68/5.96 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ( ( dvd_dvd_nat @ D @ C )
% 5.68/5.96 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.68/5.96 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_div_if_dvd
% 5.68/5.96 thf(fact_4609_div__mult__div__if__dvd,axiom,
% 5.68/5.96 ! [B: int,A: int,D: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ( ( dvd_dvd_int @ D @ C )
% 5.68/5.96 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.68/5.96 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_div_if_dvd
% 5.68/5.96 thf(fact_4610_dvd__mult__imp__div,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_imp_div
% 5.68/5.96 thf(fact_4611_dvd__mult__imp__div,axiom,
% 5.68/5.96 ! [A: nat,C: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.68/5.96 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_imp_div
% 5.68/5.96 thf(fact_4612_dvd__mult__imp__div,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.68/5.96 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_mult_imp_div
% 5.68/5.96 thf(fact_4613_dvd__div__mult2__eq,axiom,
% 5.68/5.96 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult2_eq
% 5.68/5.96 thf(fact_4614_dvd__div__mult2__eq,axiom,
% 5.68/5.96 ! [B: nat,C: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.68/5.96 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult2_eq
% 5.68/5.96 thf(fact_4615_dvd__div__mult2__eq,axiom,
% 5.68/5.96 ! [B: int,C: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.68/5.96 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.68/5.96 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult2_eq
% 5.68/5.96 thf(fact_4616_div__div__eq__right,axiom,
% 5.68/5.96 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.96 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_eq_right
% 5.68/5.96 thf(fact_4617_div__div__eq__right,axiom,
% 5.68/5.96 ! [C: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.68/5.96 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_eq_right
% 5.68/5.96 thf(fact_4618_div__div__eq__right,axiom,
% 5.68/5.96 ! [C: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.68/5.96 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_div_eq_right
% 5.68/5.96 thf(fact_4619_div__mult__swap,axiom,
% 5.68/5.96 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.96 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_swap
% 5.68/5.96 thf(fact_4620_div__mult__swap,axiom,
% 5.68/5.96 ! [C: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.68/5.96 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_swap
% 5.68/5.96 thf(fact_4621_div__mult__swap,axiom,
% 5.68/5.96 ! [C: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.68/5.96 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_mult_swap
% 5.68/5.96 thf(fact_4622_dvd__div__mult,axiom,
% 5.68/5.96 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.68/5.96 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult
% 5.68/5.96 thf(fact_4623_dvd__div__mult,axiom,
% 5.68/5.96 ! [C: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.68/5.96 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult
% 5.68/5.96 thf(fact_4624_dvd__div__mult,axiom,
% 5.68/5.96 ! [C: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.68/5.96 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_mult
% 5.68/5.96 thf(fact_4625_dvd__div__unit__iff,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_unit_iff
% 5.68/5.96 thf(fact_4626_dvd__div__unit__iff,axiom,
% 5.68/5.96 ! [B: nat,A: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_unit_iff
% 5.68/5.96 thf(fact_4627_dvd__div__unit__iff,axiom,
% 5.68/5.96 ! [B: int,A: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_div_unit_iff
% 5.68/5.96 thf(fact_4628_div__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.96 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_unit_dvd_iff
% 5.68/5.96 thf(fact_4629_div__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: nat,A: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.96 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_unit_dvd_iff
% 5.68/5.96 thf(fact_4630_div__unit__dvd__iff,axiom,
% 5.68/5.96 ! [B: int,A: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.68/5.96 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_unit_dvd_iff
% 5.68/5.96 thf(fact_4631_unit__div__cancel,axiom,
% 5.68/5.96 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.96 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.68/5.96 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_cancel
% 5.68/5.96 thf(fact_4632_unit__div__cancel,axiom,
% 5.68/5.96 ! [A: nat,B: nat,C: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.96 => ( ( ( divide_divide_nat @ B @ A )
% 5.68/5.96 = ( divide_divide_nat @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_cancel
% 5.68/5.96 thf(fact_4633_unit__div__cancel,axiom,
% 5.68/5.96 ! [A: int,B: int,C: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.96 => ( ( ( divide_divide_int @ B @ A )
% 5.68/5.96 = ( divide_divide_int @ C @ A ) )
% 5.68/5.96 = ( B = C ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % unit_div_cancel
% 5.68/5.96 thf(fact_4634_div__plus__div__distrib__dvd__left,axiom,
% 5.68/5.96 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_left
% 5.68/5.96 thf(fact_4635_div__plus__div__distrib__dvd__left,axiom,
% 5.68/5.96 ! [C: nat,A: nat,B: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ A )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_left
% 5.68/5.96 thf(fact_4636_div__plus__div__distrib__dvd__left,axiom,
% 5.68/5.96 ! [C: int,A: int,B: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ A )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_left
% 5.68/5.96 thf(fact_4637_div__plus__div__distrib__dvd__right,axiom,
% 5.68/5.96 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.96 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.68/5.96 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_right
% 5.68/5.96 thf(fact_4638_div__plus__div__distrib__dvd__right,axiom,
% 5.68/5.96 ! [C: nat,B: nat,A: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.96 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_right
% 5.68/5.96 thf(fact_4639_div__plus__div__distrib__dvd__right,axiom,
% 5.68/5.96 ! [C: int,B: int,A: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ C @ B )
% 5.68/5.96 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.68/5.96 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_plus_div_distrib_dvd_right
% 5.68/5.96 thf(fact_4640_div__power,axiom,
% 5.68/5.96 ! [B: code_integer,A: code_integer,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.96 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.68/5.96 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_power
% 5.68/5.96 thf(fact_4641_div__power,axiom,
% 5.68/5.96 ! [B: nat,A: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.96 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.68/5.96 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_power
% 5.68/5.96 thf(fact_4642_div__power,axiom,
% 5.68/5.96 ! [B: int,A: int,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.96 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.68/5.96 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % div_power
% 5.68/5.96 thf(fact_4643_dvd__power__le,axiom,
% 5.68/5.96 ! [X: code_integer,Y2: code_integer,N: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y2 @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_le
% 5.68/5.96 thf(fact_4644_dvd__power__le,axiom,
% 5.68/5.96 ! [X: nat,Y2: nat,N: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y2 @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_le
% 5.68/5.96 thf(fact_4645_dvd__power__le,axiom,
% 5.68/5.96 ! [X: real,Y2: real,N: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_real @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_le
% 5.68/5.96 thf(fact_4646_dvd__power__le,axiom,
% 5.68/5.96 ! [X: int,Y2: int,N: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_le
% 5.68/5.96 thf(fact_4647_dvd__power__le,axiom,
% 5.68/5.96 ! [X: complex,Y2: complex,N: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_complex @ X @ Y2 )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_power_le
% 5.68/5.96 thf(fact_4648_power__le__dvd,axiom,
% 5.68/5.96 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.68/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_dvd
% 5.68/5.96 thf(fact_4649_power__le__dvd,axiom,
% 5.68/5.96 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.68/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_dvd
% 5.68/5.96 thf(fact_4650_power__le__dvd,axiom,
% 5.68/5.96 ! [A: real,N: nat,B: real,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.68/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_dvd
% 5.68/5.96 thf(fact_4651_power__le__dvd,axiom,
% 5.68/5.96 ! [A: int,N: nat,B: int,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.68/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_dvd
% 5.68/5.96 thf(fact_4652_power__le__dvd,axiom,
% 5.68/5.96 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.68/5.96 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.68/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % power_le_dvd
% 5.68/5.96 thf(fact_4653_le__imp__power__dvd,axiom,
% 5.68/5.96 ! [M: nat,N: nat,A: code_integer] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % le_imp_power_dvd
% 5.68/5.96 thf(fact_4654_le__imp__power__dvd,axiom,
% 5.68/5.96 ! [M: nat,N: nat,A: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % le_imp_power_dvd
% 5.68/5.96 thf(fact_4655_le__imp__power__dvd,axiom,
% 5.68/5.96 ! [M: nat,N: nat,A: real] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % le_imp_power_dvd
% 5.68/5.96 thf(fact_4656_le__imp__power__dvd,axiom,
% 5.68/5.96 ! [M: nat,N: nat,A: int] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % le_imp_power_dvd
% 5.68/5.96 thf(fact_4657_le__imp__power__dvd,axiom,
% 5.68/5.96 ! [M: nat,N: nat,A: complex] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % le_imp_power_dvd
% 5.68/5.96 thf(fact_4658_mod__eq__dvd__iff,axiom,
% 5.68/5.96 ! [A: int,C: int,B: int] :
% 5.68/5.96 ( ( ( modulo_modulo_int @ A @ C )
% 5.68/5.96 = ( modulo_modulo_int @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mod_eq_dvd_iff
% 5.68/5.96 thf(fact_4659_mod__eq__dvd__iff,axiom,
% 5.68/5.96 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.68/5.96 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.68/5.96 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.68/5.96 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % mod_eq_dvd_iff
% 5.68/5.96 thf(fact_4660_nat__dvd__not__less,axiom,
% 5.68/5.96 ! [M: nat,N: nat] :
% 5.68/5.96 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/5.96 => ( ( ord_less_nat @ M @ N )
% 5.68/5.96 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % nat_dvd_not_less
% 5.68/5.96 thf(fact_4661_dvd__pos__nat,axiom,
% 5.68/5.96 ! [N: nat,M: nat] :
% 5.68/5.96 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.96 => ( ( dvd_dvd_nat @ M @ N )
% 5.68/5.96 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_pos_nat
% 5.68/5.96 thf(fact_4662_dvd__minus__self,axiom,
% 5.68/5.96 ! [M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.68/5.96 = ( ( ord_less_nat @ N @ M )
% 5.68/5.96 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_minus_self
% 5.68/5.96 thf(fact_4663_zdvd__antisym__nonneg,axiom,
% 5.68/5.96 ! [M: int,N: int] :
% 5.68/5.96 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.68/5.96 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.68/5.96 => ( ( dvd_dvd_int @ M @ N )
% 5.68/5.96 => ( ( dvd_dvd_int @ N @ M )
% 5.68/5.96 => ( M = N ) ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zdvd_antisym_nonneg
% 5.68/5.96 thf(fact_4664_less__eq__dvd__minus,axiom,
% 5.68/5.96 ! [M: nat,N: nat] :
% 5.68/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.96 => ( ( dvd_dvd_nat @ M @ N )
% 5.68/5.96 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % less_eq_dvd_minus
% 5.68/5.96 thf(fact_4665_dvd__diffD1,axiom,
% 5.68/5.96 ! [K: nat,M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.68/5.96 => ( ( dvd_dvd_nat @ K @ M )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_diffD1
% 5.68/5.96 thf(fact_4666_dvd__diffD,axiom,
% 5.68/5.96 ! [K: nat,M: nat,N: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.68/5.96 => ( ( dvd_dvd_nat @ K @ N )
% 5.68/5.96 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.96 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % dvd_diffD
% 5.68/5.96 thf(fact_4667_zdvd__mono,axiom,
% 5.68/5.96 ! [K: int,M: int,T: int] :
% 5.68/5.96 ( ( K != zero_zero_int )
% 5.68/5.96 => ( ( dvd_dvd_int @ M @ T )
% 5.68/5.96 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zdvd_mono
% 5.68/5.96 thf(fact_4668_zdvd__mult__cancel,axiom,
% 5.68/5.96 ! [K: int,M: int,N: int] :
% 5.68/5.96 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.68/5.96 => ( ( K != zero_zero_int )
% 5.68/5.96 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.68/5.96
% 5.68/5.96 % zdvd_mult_cancel
% 5.68/5.96 thf(fact_4669_bezout__lemma__nat,axiom,
% 5.68/5.96 ! [D: nat,A: nat,B: nat,X: nat,Y2: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ D @ A )
% 5.68/5.96 => ( ( dvd_dvd_nat @ D @ B )
% 5.68/5.96 => ( ( ( ( times_times_nat @ A @ X )
% 5.68/5.96 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D ) )
% 5.68/5.96 | ( ( times_times_nat @ B @ X )
% 5.68/5.96 = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) )
% 5.68/5.96 => ? [X3: nat,Y3: nat] :
% 5.68/5.96 ( ( dvd_dvd_nat @ D @ A )
% 5.68/5.97 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.68/5.97 & ( ( ( times_times_nat @ A @ X3 )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.68/5.97 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bezout_lemma_nat
% 5.68/5.97 thf(fact_4670_bezout__add__nat,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ? [D3: nat,X3: nat,Y3: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ D3 @ A )
% 5.68/5.97 & ( dvd_dvd_nat @ D3 @ B )
% 5.68/5.97 & ( ( ( times_times_nat @ A @ X3 )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.68/5.97 | ( ( times_times_nat @ B @ X3 )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bezout_add_nat
% 5.68/5.97 thf(fact_4671_bezout1__nat,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ? [D3: nat,X3: nat,Y3: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ D3 @ A )
% 5.68/5.97 & ( dvd_dvd_nat @ D3 @ B )
% 5.68/5.97 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.68/5.97 = D3 )
% 5.68/5.97 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.68/5.97 = D3 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bezout1_nat
% 5.68/5.97 thf(fact_4672_zdvd__reduce,axiom,
% 5.68/5.97 ! [K: int,N: int,M: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.68/5.97 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % zdvd_reduce
% 5.68/5.97 thf(fact_4673_zdvd__period,axiom,
% 5.68/5.97 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ A @ D )
% 5.68/5.97 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.68/5.97 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zdvd_period
% 5.68/5.97 thf(fact_4674_ln__bound,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_bound
% 5.68/5.97 thf(fact_4675_ln__ge__zero,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_ge_zero
% 5.68/5.97 thf(fact_4676_div2__even__ext__nat,axiom,
% 5.68/5.97 ! [X: nat,Y2: nat] :
% 5.68/5.97 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.97 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.68/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 5.68/5.97 => ( X = Y2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div2_even_ext_nat
% 5.68/5.97 thf(fact_4677_unit__dvdE,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.97 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ! [C2: code_integer] :
% 5.68/5.97 ( B
% 5.68/5.97 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_dvdE
% 5.68/5.97 thf(fact_4678_unit__dvdE,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.97 => ~ ( ( A != zero_zero_nat )
% 5.68/5.97 => ! [C2: nat] :
% 5.68/5.97 ( B
% 5.68/5.97 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_dvdE
% 5.68/5.97 thf(fact_4679_unit__dvdE,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.97 => ~ ( ( A != zero_zero_int )
% 5.68/5.97 => ! [C2: int] :
% 5.68/5.97 ( B
% 5.68/5.97 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_dvdE
% 5.68/5.97 thf(fact_4680_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: code_integer > $o,L2: code_integer] :
% 5.68/5.97 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4681_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: complex > $o,L2: complex] :
% 5.68/5.97 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: complex] :
% 5.68/5.97 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4682_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: real > $o,L2: real] :
% 5.68/5.97 ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: real] :
% 5.68/5.97 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4683_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: rat > $o,L2: rat] :
% 5.68/5.97 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: rat] :
% 5.68/5.97 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4684_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: nat > $o,L2: nat] :
% 5.68/5.97 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4685_unity__coeff__ex,axiom,
% 5.68/5.97 ! [P: int > $o,L2: int] :
% 5.68/5.97 ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 5.68/5.97 = ( ? [X2: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.68/5.97 & ( P @ X2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unity_coeff_ex
% 5.68/5.97 thf(fact_4686_dvd__div__div__eq__mult,axiom,
% 5.68/5.97 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.68/5.97 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( C != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.68/5.97 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.68/5.97 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.68/5.97 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_div_eq_mult
% 5.68/5.97 thf(fact_4687_dvd__div__div__eq__mult,axiom,
% 5.68/5.97 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.68/5.97 ( ( A != zero_zero_nat )
% 5.68/5.97 => ( ( C != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.97 => ( ( dvd_dvd_nat @ C @ D )
% 5.68/5.97 => ( ( ( divide_divide_nat @ B @ A )
% 5.68/5.97 = ( divide_divide_nat @ D @ C ) )
% 5.68/5.97 = ( ( times_times_nat @ B @ C )
% 5.68/5.97 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_div_eq_mult
% 5.68/5.97 thf(fact_4688_dvd__div__div__eq__mult,axiom,
% 5.68/5.97 ! [A: int,C: int,B: int,D: int] :
% 5.68/5.97 ( ( A != zero_zero_int )
% 5.68/5.97 => ( ( C != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ A @ B )
% 5.68/5.97 => ( ( dvd_dvd_int @ C @ D )
% 5.68/5.97 => ( ( ( divide_divide_int @ B @ A )
% 5.68/5.97 = ( divide_divide_int @ D @ C ) )
% 5.68/5.97 = ( ( times_times_int @ B @ C )
% 5.68/5.97 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_div_eq_mult
% 5.68/5.97 thf(fact_4689_dvd__div__iff__mult,axiom,
% 5.68/5.97 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( C != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.97 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_iff_mult
% 5.68/5.97 thf(fact_4690_dvd__div__iff__mult,axiom,
% 5.68/5.97 ! [C: nat,B: nat,A: nat] :
% 5.68/5.97 ( ( C != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ C @ B )
% 5.68/5.97 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.68/5.97 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_iff_mult
% 5.68/5.97 thf(fact_4691_dvd__div__iff__mult,axiom,
% 5.68/5.97 ! [C: int,B: int,A: int] :
% 5.68/5.97 ( ( C != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ C @ B )
% 5.68/5.97 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.68/5.97 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_iff_mult
% 5.68/5.97 thf(fact_4692_div__dvd__iff__mult,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.97 ( ( B != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.68/5.97 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_dvd_iff_mult
% 5.68/5.97 thf(fact_4693_div__dvd__iff__mult,axiom,
% 5.68/5.97 ! [B: nat,A: nat,C: nat] :
% 5.68/5.97 ( ( B != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.68/5.97 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_dvd_iff_mult
% 5.68/5.97 thf(fact_4694_div__dvd__iff__mult,axiom,
% 5.68/5.97 ! [B: int,A: int,C: int] :
% 5.68/5.97 ( ( B != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ B @ A )
% 5.68/5.97 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.68/5.97 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_dvd_iff_mult
% 5.68/5.97 thf(fact_4695_dvd__div__eq__mult,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.68/5.97 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.68/5.97 = C )
% 5.68/5.97 = ( B
% 5.68/5.97 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_eq_mult
% 5.68/5.97 thf(fact_4696_dvd__div__eq__mult,axiom,
% 5.68/5.97 ! [A: nat,B: nat,C: nat] :
% 5.68/5.97 ( ( A != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ A @ B )
% 5.68/5.97 => ( ( ( divide_divide_nat @ B @ A )
% 5.68/5.97 = C )
% 5.68/5.97 = ( B
% 5.68/5.97 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_eq_mult
% 5.68/5.97 thf(fact_4697_dvd__div__eq__mult,axiom,
% 5.68/5.97 ! [A: int,B: int,C: int] :
% 5.68/5.97 ( ( A != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ A @ B )
% 5.68/5.97 => ( ( ( divide_divide_int @ B @ A )
% 5.68/5.97 = C )
% 5.68/5.97 = ( B
% 5.68/5.97 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_div_eq_mult
% 5.68/5.97 thf(fact_4698_unit__div__eq__0__iff,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.68/5.97 = zero_z3403309356797280102nteger )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_eq_0_iff
% 5.68/5.97 thf(fact_4699_unit__div__eq__0__iff,axiom,
% 5.68/5.97 ! [B: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( ( divide_divide_nat @ A @ B )
% 5.68/5.97 = zero_zero_nat )
% 5.68/5.97 = ( A = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_eq_0_iff
% 5.68/5.97 thf(fact_4700_unit__div__eq__0__iff,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( ( divide_divide_int @ A @ B )
% 5.68/5.97 = zero_zero_int )
% 5.68/5.97 = ( A = zero_zero_int ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_eq_0_iff
% 5.68/5.97 thf(fact_4701_even__numeral,axiom,
% 5.68/5.97 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_numeral
% 5.68/5.97 thf(fact_4702_even__numeral,axiom,
% 5.68/5.97 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_numeral
% 5.68/5.97 thf(fact_4703_even__numeral,axiom,
% 5.68/5.97 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_numeral
% 5.68/5.97 thf(fact_4704_inf__period_I3_J,axiom,
% 5.68/5.97 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.68/5.97 => ! [X5: code_integer,K4: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.68/5.97 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(3)
% 5.68/5.97 thf(fact_4705_inf__period_I3_J,axiom,
% 5.68/5.97 ! [D: real,D4: real,T: real] :
% 5.68/5.97 ( ( dvd_dvd_real @ D @ D4 )
% 5.68/5.97 => ! [X5: real,K4: real] :
% 5.68/5.97 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.68/5.97 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(3)
% 5.68/5.97 thf(fact_4706_inf__period_I3_J,axiom,
% 5.68/5.97 ! [D: rat,D4: rat,T: rat] :
% 5.68/5.97 ( ( dvd_dvd_rat @ D @ D4 )
% 5.68/5.97 => ! [X5: rat,K4: rat] :
% 5.68/5.97 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.68/5.97 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(3)
% 5.68/5.97 thf(fact_4707_inf__period_I3_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int,K4: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.68/5.97 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(3)
% 5.68/5.97 thf(fact_4708_inf__period_I4_J,axiom,
% 5.68/5.97 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.68/5.97 => ! [X5: code_integer,K4: code_integer] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.68/5.97 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(4)
% 5.68/5.97 thf(fact_4709_inf__period_I4_J,axiom,
% 5.68/5.97 ! [D: real,D4: real,T: real] :
% 5.68/5.97 ( ( dvd_dvd_real @ D @ D4 )
% 5.68/5.97 => ! [X5: real,K4: real] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.68/5.97 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(4)
% 5.68/5.97 thf(fact_4710_inf__period_I4_J,axiom,
% 5.68/5.97 ! [D: rat,D4: rat,T: rat] :
% 5.68/5.97 ( ( dvd_dvd_rat @ D @ D4 )
% 5.68/5.97 => ! [X5: rat,K4: rat] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.68/5.97 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(4)
% 5.68/5.97 thf(fact_4711_inf__period_I4_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int,K4: int] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.68/5.97 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % inf_period(4)
% 5.68/5.97 thf(fact_4712_is__unit__div__mult2__eq,axiom,
% 5.68/5.97 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.68/5.97 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult2_eq
% 5.68/5.97 thf(fact_4713_is__unit__div__mult2__eq,axiom,
% 5.68/5.97 ! [B: nat,C: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.68/5.97 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.68/5.97 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult2_eq
% 5.68/5.97 thf(fact_4714_is__unit__div__mult2__eq,axiom,
% 5.68/5.97 ! [B: int,C: int,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.68/5.97 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.68/5.97 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult2_eq
% 5.68/5.97 thf(fact_4715_unit__div__mult__swap,axiom,
% 5.68/5.97 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.68/5.97 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_mult_swap
% 5.68/5.97 thf(fact_4716_unit__div__mult__swap,axiom,
% 5.68/5.97 ! [C: nat,A: nat,B: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.68/5.97 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.68/5.97 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_mult_swap
% 5.68/5.97 thf(fact_4717_unit__div__mult__swap,axiom,
% 5.68/5.97 ! [C: int,A: int,B: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.68/5.97 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.68/5.97 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_mult_swap
% 5.68/5.97 thf(fact_4718_unit__div__commute,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.68/5.97 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_commute
% 5.68/5.97 thf(fact_4719_unit__div__commute,axiom,
% 5.68/5.97 ! [B: nat,A: nat,C: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.68/5.97 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_commute
% 5.68/5.97 thf(fact_4720_unit__div__commute,axiom,
% 5.68/5.97 ! [B: int,A: int,C: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.68/5.97 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_div_commute
% 5.68/5.97 thf(fact_4721_div__mult__unit2,axiom,
% 5.68/5.97 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.97 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_mult_unit2
% 5.68/5.97 thf(fact_4722_div__mult__unit2,axiom,
% 5.68/5.97 ! [C: nat,B: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ B @ A )
% 5.68/5.97 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.68/5.97 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_mult_unit2
% 5.68/5.97 thf(fact_4723_div__mult__unit2,axiom,
% 5.68/5.97 ! [C: int,B: int,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ B @ A )
% 5.68/5.97 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.68/5.97 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_mult_unit2
% 5.68/5.97 thf(fact_4724_unit__eq__div2,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( A
% 5.68/5.97 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.68/5.97 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.68/5.97 = C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div2
% 5.68/5.97 thf(fact_4725_unit__eq__div2,axiom,
% 5.68/5.97 ! [B: nat,A: nat,C: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( A
% 5.68/5.97 = ( divide_divide_nat @ C @ B ) )
% 5.68/5.97 = ( ( times_times_nat @ A @ B )
% 5.68/5.97 = C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div2
% 5.68/5.97 thf(fact_4726_unit__eq__div2,axiom,
% 5.68/5.97 ! [B: int,A: int,C: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( A
% 5.68/5.97 = ( divide_divide_int @ C @ B ) )
% 5.68/5.97 = ( ( times_times_int @ A @ B )
% 5.68/5.97 = C ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div2
% 5.68/5.97 thf(fact_4727_unit__eq__div1,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.68/5.97 = C )
% 5.68/5.97 = ( A
% 5.68/5.97 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div1
% 5.68/5.97 thf(fact_4728_unit__eq__div1,axiom,
% 5.68/5.97 ! [B: nat,A: nat,C: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( ( divide_divide_nat @ A @ B )
% 5.68/5.97 = C )
% 5.68/5.97 = ( A
% 5.68/5.97 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div1
% 5.68/5.97 thf(fact_4729_unit__eq__div1,axiom,
% 5.68/5.97 ! [B: int,A: int,C: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( ( divide_divide_int @ A @ B )
% 5.68/5.97 = C )
% 5.68/5.97 = ( A
% 5.68/5.97 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_eq_div1
% 5.68/5.97 thf(fact_4730_unit__imp__mod__eq__0,axiom,
% 5.68/5.97 ! [B: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( modulo_modulo_nat @ A @ B )
% 5.68/5.97 = zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_imp_mod_eq_0
% 5.68/5.97 thf(fact_4731_unit__imp__mod__eq__0,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( modulo_modulo_int @ A @ B )
% 5.68/5.97 = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_imp_mod_eq_0
% 5.68/5.97 thf(fact_4732_unit__imp__mod__eq__0,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % unit_imp_mod_eq_0
% 5.68/5.97 thf(fact_4733_is__unit__power__iff,axiom,
% 5.68/5.97 ! [A: code_integer,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.68/5.97 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_power_iff
% 5.68/5.97 thf(fact_4734_is__unit__power__iff,axiom,
% 5.68/5.97 ! [A: nat,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.68/5.97 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_power_iff
% 5.68/5.97 thf(fact_4735_is__unit__power__iff,axiom,
% 5.68/5.97 ! [A: int,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.68/5.97 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_power_iff
% 5.68/5.97 thf(fact_4736_dvd__imp__le,axiom,
% 5.68/5.97 ! [K: nat,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ K @ N )
% 5.68/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_imp_le
% 5.68/5.97 thf(fact_4737_nat__mult__dvd__cancel1,axiom,
% 5.68/5.97 ! [K: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.68/5.97 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % nat_mult_dvd_cancel1
% 5.68/5.97 thf(fact_4738_dvd__mult__cancel,axiom,
% 5.68/5.97 ! [K: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.68/5.97 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/5.97 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_mult_cancel
% 5.68/5.97 thf(fact_4739_bezout__add__strong__nat,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ( ( A != zero_zero_nat )
% 5.68/5.97 => ? [D3: nat,X3: nat,Y3: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ D3 @ A )
% 5.68/5.97 & ( dvd_dvd_nat @ D3 @ B )
% 5.68/5.97 & ( ( times_times_nat @ A @ X3 )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bezout_add_strong_nat
% 5.68/5.97 thf(fact_4740_zdvd__imp__le,axiom,
% 5.68/5.97 ! [Z: int,N: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ Z @ N )
% 5.68/5.97 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.68/5.97 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zdvd_imp_le
% 5.68/5.97 thf(fact_4741_mod__greater__zero__iff__not__dvd,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.68/5.97 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_greater_zero_iff_not_dvd
% 5.68/5.97 thf(fact_4742_mod__eq__dvd__iff__nat,axiom,
% 5.68/5.97 ! [N: nat,M: nat,Q2: nat] :
% 5.68/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.68/5.97 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.68/5.97 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.68/5.97 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_eq_dvd_iff_nat
% 5.68/5.97 thf(fact_4743_prod__decode__aux_Ocases,axiom,
% 5.68/5.97 ! [X: product_prod_nat_nat] :
% 5.68/5.97 ~ ! [K2: nat,M5: nat] :
% 5.68/5.97 ( X
% 5.68/5.97 != ( product_Pair_nat_nat @ K2 @ M5 ) ) ).
% 5.68/5.97
% 5.68/5.97 % prod_decode_aux.cases
% 5.68/5.97 thf(fact_4744_finite__divisors__nat,axiom,
% 5.68/5.97 ! [M: nat] :
% 5.68/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/5.97 => ( finite_finite_nat
% 5.68/5.97 @ ( collect_nat
% 5.68/5.97 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % finite_divisors_nat
% 5.68/5.97 thf(fact_4745_ln__ge__zero__imp__ge__one,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.68/5.97 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_ge_zero_imp_ge_one
% 5.68/5.97 thf(fact_4746_ln__add__one__self__le__self,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_add_one_self_le_self
% 5.68/5.97 thf(fact_4747_ln__mult,axiom,
% 5.68/5.97 ! [X: real,Y2: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/5.97 => ( ( ln_ln_real @ ( times_times_real @ X @ Y2 ) )
% 5.68/5.97 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_mult
% 5.68/5.97 thf(fact_4748_even__zero,axiom,
% 5.68/5.97 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.68/5.97
% 5.68/5.97 % even_zero
% 5.68/5.97 thf(fact_4749_even__zero,axiom,
% 5.68/5.97 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.68/5.97
% 5.68/5.97 % even_zero
% 5.68/5.97 thf(fact_4750_even__zero,axiom,
% 5.68/5.97 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.68/5.97
% 5.68/5.97 % even_zero
% 5.68/5.97 thf(fact_4751_is__unitE,axiom,
% 5.68/5.97 ! [A: code_integer,C: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.68/5.97 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ! [B2: code_integer] :
% 5.68/5.97 ( ( B2 != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.68/5.97 = B2 )
% 5.68/5.97 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 5.68/5.97 = A )
% 5.68/5.97 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.68/5.97 = one_one_Code_integer )
% 5.68/5.97 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.68/5.97 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unitE
% 5.68/5.97 thf(fact_4752_is__unitE,axiom,
% 5.68/5.97 ! [A: nat,C: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.68/5.97 => ~ ( ( A != zero_zero_nat )
% 5.68/5.97 => ! [B2: nat] :
% 5.68/5.97 ( ( B2 != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.68/5.97 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.68/5.97 = B2 )
% 5.68/5.97 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 5.68/5.97 = A )
% 5.68/5.97 => ( ( ( times_times_nat @ A @ B2 )
% 5.68/5.97 = one_one_nat )
% 5.68/5.97 => ( ( divide_divide_nat @ C @ A )
% 5.68/5.97 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unitE
% 5.68/5.97 thf(fact_4753_is__unitE,axiom,
% 5.68/5.97 ! [A: int,C: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.68/5.97 => ~ ( ( A != zero_zero_int )
% 5.68/5.97 => ! [B2: int] :
% 5.68/5.97 ( ( B2 != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.68/5.97 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.68/5.97 = B2 )
% 5.68/5.97 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 5.68/5.97 = A )
% 5.68/5.97 => ( ( ( times_times_int @ A @ B2 )
% 5.68/5.97 = one_one_int )
% 5.68/5.97 => ( ( divide_divide_int @ C @ A )
% 5.68/5.97 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unitE
% 5.68/5.97 thf(fact_4754_is__unit__div__mult__cancel__left,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_left
% 5.68/5.97 thf(fact_4755_is__unit__div__mult__cancel__left,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ( ( A != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.68/5.97 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_left
% 5.68/5.97 thf(fact_4756_is__unit__div__mult__cancel__left,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( A != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.68/5.97 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_left
% 5.68/5.97 thf(fact_4757_is__unit__div__mult__cancel__right,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.68/5.97 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_right
% 5.68/5.97 thf(fact_4758_is__unit__div__mult__cancel__right,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ( ( A != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.68/5.97 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.68/5.97 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_right
% 5.68/5.97 thf(fact_4759_is__unit__div__mult__cancel__right,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( A != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.68/5.97 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.68/5.97 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % is_unit_div_mult_cancel_right
% 5.68/5.97 thf(fact_4760_evenE,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: code_integer] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % evenE
% 5.68/5.97 thf(fact_4761_evenE,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: nat] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % evenE
% 5.68/5.97 thf(fact_4762_evenE,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: int] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % evenE
% 5.68/5.97 thf(fact_4763_odd__one,axiom,
% 5.68/5.97 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.68/5.97
% 5.68/5.97 % odd_one
% 5.68/5.97 thf(fact_4764_odd__one,axiom,
% 5.68/5.97 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.68/5.97
% 5.68/5.97 % odd_one
% 5.68/5.97 thf(fact_4765_odd__one,axiom,
% 5.68/5.97 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.68/5.97
% 5.68/5.97 % odd_one
% 5.68/5.97 thf(fact_4766_odd__even__add,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.68/5.97 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_even_add
% 5.68/5.97 thf(fact_4767_odd__even__add,axiom,
% 5.68/5.97 ! [A: nat,B: nat] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.68/5.97 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_even_add
% 5.68/5.97 thf(fact_4768_odd__even__add,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.68/5.97 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_even_add
% 5.68/5.97 thf(fact_4769_bit__eq__rec,axiom,
% 5.68/5.97 ( ( ^ [Y5: code_integer,Z5: code_integer] : ( Y5 = Z5 ) )
% 5.68/5.97 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.68/5.97 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.68/5.97 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.68/5.97 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bit_eq_rec
% 5.68/5.97 thf(fact_4770_bit__eq__rec,axiom,
% 5.68/5.97 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/5.97 = ( ^ [A4: nat,B3: nat] :
% 5.68/5.97 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.68/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.68/5.97 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bit_eq_rec
% 5.68/5.97 thf(fact_4771_bit__eq__rec,axiom,
% 5.68/5.97 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/5.97 = ( ^ [A4: int,B3: int] :
% 5.68/5.97 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.68/5.97 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.68/5.97 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bit_eq_rec
% 5.68/5.97 thf(fact_4772_dvd__power__iff,axiom,
% 5.68/5.97 ! [X: code_integer,M: nat,N: nat] :
% 5.68/5.97 ( ( X != zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power_iff
% 5.68/5.97 thf(fact_4773_dvd__power__iff,axiom,
% 5.68/5.97 ! [X: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( X != zero_zero_nat )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power_iff
% 5.68/5.97 thf(fact_4774_dvd__power__iff,axiom,
% 5.68/5.97 ! [X: int,M: nat,N: nat] :
% 5.68/5.97 ( ( X != zero_zero_int )
% 5.68/5.97 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power_iff
% 5.68/5.97 thf(fact_4775_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: code_integer] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_Code_integer ) )
% 5.68/5.97 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4776_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: rat] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_rat ) )
% 5.68/5.97 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4777_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: nat] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_nat ) )
% 5.68/5.97 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4778_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: real] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_real ) )
% 5.68/5.97 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4779_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: int] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_int ) )
% 5.68/5.97 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4780_dvd__power,axiom,
% 5.68/5.97 ! [N: nat,X: complex] :
% 5.68/5.97 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 | ( X = one_one_complex ) )
% 5.68/5.97 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power
% 5.68/5.97 thf(fact_4781_even__even__mod__4__iff,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_even_mod_4_iff
% 5.68/5.97 thf(fact_4782_dvd__mult__cancel1,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.68/5.97 = ( N = one_one_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_mult_cancel1
% 5.68/5.97 thf(fact_4783_dvd__mult__cancel2,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.68/5.97 = ( N = one_one_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_mult_cancel2
% 5.68/5.97 thf(fact_4784_dvd__minus__add,axiom,
% 5.68/5.97 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 5.68/5.97 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.68/5.97 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.68/5.97 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.68/5.97 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_minus_add
% 5.68/5.97 thf(fact_4785_power__dvd__imp__le,axiom,
% 5.68/5.97 ! [I2: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 5.68/5.97 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.68/5.97 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_dvd_imp_le
% 5.68/5.97 thf(fact_4786_mod__nat__eqI,axiom,
% 5.68/5.97 ! [R2: nat,N: nat,M: nat] :
% 5.68/5.97 ( ( ord_less_nat @ R2 @ N )
% 5.68/5.97 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.68/5.97 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.68/5.97 => ( ( modulo_modulo_nat @ M @ N )
% 5.68/5.97 = R2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_nat_eqI
% 5.68/5.97 thf(fact_4787_mod__int__pos__iff,axiom,
% 5.68/5.97 ! [K: int,L2: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.68/5.97 = ( ( dvd_dvd_int @ L2 @ K )
% 5.68/5.97 | ( ( L2 = zero_zero_int )
% 5.68/5.97 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.68/5.97 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_int_pos_iff
% 5.68/5.97 thf(fact_4788_bset_I9_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int] :
% 5.68/5.97 ( ! [Xa3: int] :
% 5.68/5.97 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.97 => ! [Xb3: int] :
% 5.68/5.97 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.97 => ( X5
% 5.68/5.97 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.97 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.68/5.97 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bset(9)
% 5.68/5.97 thf(fact_4789_bset_I10_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int] :
% 5.68/5.97 ( ! [Xa3: int] :
% 5.68/5.97 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.97 => ! [Xb3: int] :
% 5.68/5.97 ( ( member_int @ Xb3 @ B4 )
% 5.68/5.97 => ( X5
% 5.68/5.97 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.97 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.68/5.97 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % bset(10)
% 5.68/5.97 thf(fact_4790_aset_I9_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int] :
% 5.68/5.97 ( ! [Xa3: int] :
% 5.68/5.97 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.97 => ! [Xb3: int] :
% 5.68/5.97 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.97 => ( X5
% 5.68/5.97 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.97 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.68/5.97 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % aset(9)
% 5.68/5.97 thf(fact_4791_aset_I10_J,axiom,
% 5.68/5.97 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ D @ D4 )
% 5.68/5.97 => ! [X5: int] :
% 5.68/5.97 ( ! [Xa3: int] :
% 5.68/5.97 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.68/5.97 => ! [Xb3: int] :
% 5.68/5.97 ( ( member_int @ Xb3 @ A2 )
% 5.68/5.97 => ( X5
% 5.68/5.97 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.68/5.97 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.68/5.97 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % aset(10)
% 5.68/5.97 thf(fact_4792_ln__le__minus__one,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_le_minus_one
% 5.68/5.97 thf(fact_4793_ln__diff__le,axiom,
% 5.68/5.97 ! [X: real,Y2: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/5.97 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y2 ) @ Y2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_diff_le
% 5.68/5.97 thf(fact_4794_even__two__times__div__two,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_two_times_div_two
% 5.68/5.97 thf(fact_4795_even__two__times__div__two,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_two_times_div_two
% 5.68/5.97 thf(fact_4796_even__two__times__div__two,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_two_times_div_two
% 5.68/5.97 thf(fact_4797_even__iff__mod__2__eq__zero,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_iff_mod_2_eq_zero
% 5.68/5.97 thf(fact_4798_even__iff__mod__2__eq__zero,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_iff_mod_2_eq_zero
% 5.68/5.97 thf(fact_4799_even__iff__mod__2__eq__zero,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_iff_mod_2_eq_zero
% 5.68/5.97 thf(fact_4800_odd__iff__mod__2__eq__one,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.97 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_iff_mod_2_eq_one
% 5.68/5.97 thf(fact_4801_odd__iff__mod__2__eq__one,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.97 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_iff_mod_2_eq_one
% 5.68/5.97 thf(fact_4802_odd__iff__mod__2__eq__one,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.97 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_Code_integer ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_iff_mod_2_eq_one
% 5.68/5.97 thf(fact_4803_power__mono__odd,axiom,
% 5.68/5.97 ! [N: nat,A: real,B: real] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_real @ A @ B )
% 5.68/5.97 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_mono_odd
% 5.68/5.97 thf(fact_4804_power__mono__odd,axiom,
% 5.68/5.97 ! [N: nat,A: rat,B: rat] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.97 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_mono_odd
% 5.68/5.97 thf(fact_4805_power__mono__odd,axiom,
% 5.68/5.97 ! [N: nat,A: int,B: int] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_int @ A @ B )
% 5.68/5.97 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_mono_odd
% 5.68/5.97 thf(fact_4806_odd__pos,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % odd_pos
% 5.68/5.97 thf(fact_4807_dvd__power__iff__le,axiom,
% 5.68/5.97 ! [K: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.68/5.97 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.68/5.97 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dvd_power_iff_le
% 5.68/5.97 thf(fact_4808_signed__take__bit__int__less__exp,axiom,
% 5.68/5.97 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_int_less_exp
% 5.68/5.97 thf(fact_4809_even__unset__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 | ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_unset_bit_iff
% 5.68/5.97 thf(fact_4810_even__unset__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 | ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_unset_bit_iff
% 5.68/5.97 thf(fact_4811_even__unset__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 | ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_unset_bit_iff
% 5.68/5.97 thf(fact_4812_even__set__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 & ( M != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_set_bit_iff
% 5.68/5.97 thf(fact_4813_even__set__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 & ( M != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_set_bit_iff
% 5.68/5.97 thf(fact_4814_even__set__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 & ( M != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_set_bit_iff
% 5.68/5.97 thf(fact_4815_even__flip__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: code_integer] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 != ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_flip_bit_iff
% 5.68/5.97 thf(fact_4816_even__flip__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 != ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_flip_bit_iff
% 5.68/5.97 thf(fact_4817_even__flip__bit__iff,axiom,
% 5.68/5.97 ! [M: nat,A: nat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 != ( M = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_flip_bit_iff
% 5.68/5.97 thf(fact_4818_even__diff__iff,axiom,
% 5.68/5.97 ! [K: int,L2: int] :
% 5.68/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.68/5.97 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_diff_iff
% 5.68/5.97 thf(fact_4819_oddE,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: code_integer] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % oddE
% 5.68/5.97 thf(fact_4820_oddE,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: nat] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % oddE
% 5.68/5.97 thf(fact_4821_oddE,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ~ ! [B2: int] :
% 5.68/5.97 ( A
% 5.68/5.97 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % oddE
% 5.68/5.97 thf(fact_4822_parity__cases,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 != zero_zero_nat ) )
% 5.68/5.97 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 != one_one_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % parity_cases
% 5.68/5.97 thf(fact_4823_parity__cases,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 != zero_zero_int ) )
% 5.68/5.97 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 != one_one_int ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % parity_cases
% 5.68/5.97 thf(fact_4824_parity__cases,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 != zero_z3403309356797280102nteger ) )
% 5.68/5.97 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 != one_one_Code_integer ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % parity_cases
% 5.68/5.97 thf(fact_4825_mod2__eq__if,axiom,
% 5.68/5.97 ! [A: nat] :
% 5.68/5.97 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_zero_nat ) )
% 5.68/5.97 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod2_eq_if
% 5.68/5.97 thf(fact_4826_mod2__eq__if,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_zero_int ) )
% 5.68/5.97 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_int ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod2_eq_if
% 5.68/5.97 thf(fact_4827_mod2__eq__if,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) )
% 5.68/5.97 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.68/5.97 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.97 = one_one_Code_integer ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod2_eq_if
% 5.68/5.97 thf(fact_4828_zero__le__even__power,axiom,
% 5.68/5.97 ! [N: nat,A: real] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_even_power
% 5.68/5.97 thf(fact_4829_zero__le__even__power,axiom,
% 5.68/5.97 ! [N: nat,A: rat] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_even_power
% 5.68/5.97 thf(fact_4830_zero__le__even__power,axiom,
% 5.68/5.97 ! [N: nat,A: int] :
% 5.68/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_even_power
% 5.68/5.97 thf(fact_4831_zero__le__odd__power,axiom,
% 5.68/5.97 ! [N: nat,A: real] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.68/5.97 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_odd_power
% 5.68/5.97 thf(fact_4832_zero__le__odd__power,axiom,
% 5.68/5.97 ! [N: nat,A: rat] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.68/5.97 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_odd_power
% 5.68/5.97 thf(fact_4833_zero__le__odd__power,axiom,
% 5.68/5.97 ! [N: nat,A: int] :
% 5.68/5.97 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.68/5.97 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_odd_power
% 5.68/5.97 thf(fact_4834_zero__le__power__eq,axiom,
% 5.68/5.97 ! [A: real,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_power_eq
% 5.68/5.97 thf(fact_4835_zero__le__power__eq,axiom,
% 5.68/5.97 ! [A: rat,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_power_eq
% 5.68/5.97 thf(fact_4836_zero__le__power__eq,axiom,
% 5.68/5.97 ! [A: int,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.68/5.97 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_power_eq
% 5.68/5.97 thf(fact_4837_signed__take__bit__int__less__self__iff,axiom,
% 5.68/5.97 ! [N: nat,K: int] :
% 5.68/5.97 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.68/5.97 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_int_less_self_iff
% 5.68/5.97 thf(fact_4838_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.68/5.97 ! [K: int,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.68/5.97 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_int_greater_eq_self_iff
% 5.68/5.97 thf(fact_4839_add__0__iff,axiom,
% 5.68/5.97 ! [B: complex,A: complex] :
% 5.68/5.97 ( ( B
% 5.68/5.97 = ( plus_plus_complex @ B @ A ) )
% 5.68/5.97 = ( A = zero_zero_complex ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_0_iff
% 5.68/5.97 thf(fact_4840_add__0__iff,axiom,
% 5.68/5.97 ! [B: real,A: real] :
% 5.68/5.97 ( ( B
% 5.68/5.97 = ( plus_plus_real @ B @ A ) )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_0_iff
% 5.68/5.97 thf(fact_4841_add__0__iff,axiom,
% 5.68/5.97 ! [B: rat,A: rat] :
% 5.68/5.97 ( ( B
% 5.68/5.97 = ( plus_plus_rat @ B @ A ) )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_0_iff
% 5.68/5.97 thf(fact_4842_add__0__iff,axiom,
% 5.68/5.97 ! [B: nat,A: nat] :
% 5.68/5.97 ( ( B
% 5.68/5.97 = ( plus_plus_nat @ B @ A ) )
% 5.68/5.97 = ( A = zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_0_iff
% 5.68/5.97 thf(fact_4843_add__0__iff,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( B
% 5.68/5.97 = ( plus_plus_int @ B @ A ) )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_0_iff
% 5.68/5.97 thf(fact_4844_crossproduct__eq,axiom,
% 5.68/5.97 ! [W: real,Y2: real,X: real,Z: real] :
% 5.68/5.97 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y2 ) @ ( times_times_real @ X @ Z ) )
% 5.68/5.97 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y2 ) ) )
% 5.68/5.97 = ( ( W = X )
% 5.68/5.97 | ( Y2 = Z ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_eq
% 5.68/5.97 thf(fact_4845_crossproduct__eq,axiom,
% 5.68/5.97 ! [W: rat,Y2: rat,X: rat,Z: rat] :
% 5.68/5.97 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y2 ) @ ( times_times_rat @ X @ Z ) )
% 5.68/5.97 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y2 ) ) )
% 5.68/5.97 = ( ( W = X )
% 5.68/5.97 | ( Y2 = Z ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_eq
% 5.68/5.97 thf(fact_4846_crossproduct__eq,axiom,
% 5.68/5.97 ! [W: nat,Y2: nat,X: nat,Z: nat] :
% 5.68/5.97 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y2 ) @ ( times_times_nat @ X @ Z ) )
% 5.68/5.97 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y2 ) ) )
% 5.68/5.97 = ( ( W = X )
% 5.68/5.97 | ( Y2 = Z ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_eq
% 5.68/5.97 thf(fact_4847_crossproduct__eq,axiom,
% 5.68/5.97 ! [W: int,Y2: int,X: int,Z: int] :
% 5.68/5.97 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y2 ) @ ( times_times_int @ X @ Z ) )
% 5.68/5.97 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y2 ) ) )
% 5.68/5.97 = ( ( W = X )
% 5.68/5.97 | ( Y2 = Z ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_eq
% 5.68/5.97 thf(fact_4848_crossproduct__noteq,axiom,
% 5.68/5.97 ! [A: real,B: real,C: real,D: real] :
% 5.68/5.97 ( ( ( A != B )
% 5.68/5.97 & ( C != D ) )
% 5.68/5.97 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.68/5.97 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_noteq
% 5.68/5.97 thf(fact_4849_crossproduct__noteq,axiom,
% 5.68/5.97 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.68/5.97 ( ( ( A != B )
% 5.68/5.97 & ( C != D ) )
% 5.68/5.97 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.68/5.97 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_noteq
% 5.68/5.97 thf(fact_4850_crossproduct__noteq,axiom,
% 5.68/5.97 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.68/5.97 ( ( ( A != B )
% 5.68/5.97 & ( C != D ) )
% 5.68/5.97 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.68/5.97 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_noteq
% 5.68/5.97 thf(fact_4851_crossproduct__noteq,axiom,
% 5.68/5.97 ! [A: int,B: int,C: int,D: int] :
% 5.68/5.97 ( ( ( A != B )
% 5.68/5.97 & ( C != D ) )
% 5.68/5.97 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.68/5.97 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % crossproduct_noteq
% 5.68/5.97 thf(fact_4852_list__decode_Ocases,axiom,
% 5.68/5.97 ! [X: nat] :
% 5.68/5.97 ( ( X != zero_zero_nat )
% 5.68/5.97 => ~ ! [N3: nat] :
% 5.68/5.97 ( X
% 5.68/5.97 != ( suc @ N3 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % list_decode.cases
% 5.68/5.97 thf(fact_4853_zero__less__power__eq,axiom,
% 5.68/5.97 ! [A: real,N: nat] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.68/5.97 = ( ( N = zero_zero_nat )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A != zero_zero_real ) )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_power_eq
% 5.68/5.97 thf(fact_4854_zero__less__power__eq,axiom,
% 5.68/5.97 ! [A: rat,N: nat] :
% 5.68/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.68/5.97 = ( ( N = zero_zero_nat )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A != zero_zero_rat ) )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_power_eq
% 5.68/5.97 thf(fact_4855_zero__less__power__eq,axiom,
% 5.68/5.97 ! [A: int,N: nat] :
% 5.68/5.97 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.68/5.97 = ( ( N = zero_zero_nat )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A != zero_zero_int ) )
% 5.68/5.97 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_power_eq
% 5.68/5.97 thf(fact_4856_signed__take__bit__int__less__eq,axiom,
% 5.68/5.97 ! [N: nat,K: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.68/5.97 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_int_less_eq
% 5.68/5.97 thf(fact_4857_even__mask__div__iff_H,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff'
% 5.68/5.97 thf(fact_4858_even__mask__div__iff_H,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff'
% 5.68/5.97 thf(fact_4859_even__mask__div__iff_H,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff'
% 5.68/5.97 thf(fact_4860_power__le__zero__eq,axiom,
% 5.68/5.97 ! [A: real,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.68/5.97 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_le_zero_eq
% 5.68/5.97 thf(fact_4861_power__le__zero__eq,axiom,
% 5.68/5.97 ! [A: rat,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.68/5.97 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_le_zero_eq
% 5.68/5.97 thf(fact_4862_power__le__zero__eq,axiom,
% 5.68/5.97 ! [A: int,N: nat] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.68/5.97 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/5.97 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.68/5.97 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % power_le_zero_eq
% 5.68/5.97 thf(fact_4863_option_Osize__gen_I1_J,axiom,
% 5.68/5.97 ! [X: nat > nat] :
% 5.68/5.97 ( ( size_option_nat @ X @ none_nat )
% 5.68/5.97 = ( suc @ zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % option.size_gen(1)
% 5.68/5.97 thf(fact_4864_option_Osize__gen_I1_J,axiom,
% 5.68/5.97 ! [X: product_prod_nat_nat > nat] :
% 5.68/5.97 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.68/5.97 = ( suc @ zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % option.size_gen(1)
% 5.68/5.97 thf(fact_4865_option_Osize__gen_I1_J,axiom,
% 5.68/5.97 ! [X: num > nat] :
% 5.68/5.97 ( ( size_option_num @ X @ none_num )
% 5.68/5.97 = ( suc @ zero_zero_nat ) ) ).
% 5.68/5.97
% 5.68/5.97 % option.size_gen(1)
% 5.68/5.97 thf(fact_4866_even__mod__4__div__2,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.97 = ( suc @ zero_zero_nat ) )
% 5.68/5.97 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mod_4_div_2
% 5.68/5.97 thf(fact_4867_ln__one__plus__pos__lower__bound,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/5.97 => ( 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 ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_one_plus_pos_lower_bound
% 5.68/5.97 thf(fact_4868_even__mask__div__iff,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_z3403309356797280102nteger )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff
% 5.68/5.97 thf(fact_4869_even__mask__div__iff,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_zero_nat )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff
% 5.68/5.97 thf(fact_4870_even__mask__div__iff,axiom,
% 5.68/5.97 ! [M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_zero_int )
% 5.68/5.97 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mask_div_iff
% 5.68/5.97 thf(fact_4871_even__mult__exp__div__exp__iff,axiom,
% 5.68/5.97 ! [A: code_integer,M: nat,N: nat] :
% 5.68/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.97 = ( ( ord_less_nat @ N @ M )
% 5.68/5.97 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_z3403309356797280102nteger )
% 5.68/5.97 | ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.97 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mult_exp_div_exp_iff
% 5.68/5.97 thf(fact_4872_even__mult__exp__div__exp__iff,axiom,
% 5.68/5.97 ! [A: nat,M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ( ord_less_nat @ N @ M )
% 5.68/5.97 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_zero_nat )
% 5.68/5.97 | ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.97 & ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mult_exp_div_exp_iff
% 5.68/5.97 thf(fact_4873_even__mult__exp__div__exp__iff,axiom,
% 5.68/5.97 ! [A: int,M: nat,N: nat] :
% 5.68/5.97 ( ( 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 ) ) )
% 5.68/5.97 = ( ( ord_less_nat @ N @ M )
% 5.68/5.97 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.68/5.97 = zero_zero_int )
% 5.68/5.97 | ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.97 & ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % even_mult_exp_div_exp_iff
% 5.68/5.97 thf(fact_4874_ln__2__less__1,axiom,
% 5.68/5.97 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.68/5.97
% 5.68/5.97 % ln_2_less_1
% 5.68/5.97 thf(fact_4875_triangle__def,axiom,
% 5.68/5.97 ( nat_triangle
% 5.68/5.97 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % triangle_def
% 5.68/5.97 thf(fact_4876_vebt__buildup_Oelims,axiom,
% 5.68/5.97 ! [X: nat,Y2: vEBT_VEBT] :
% 5.68/5.97 ( ( ( vEBT_vebt_buildup @ X )
% 5.68/5.97 = Y2 )
% 5.68/5.97 => ( ( ( X = zero_zero_nat )
% 5.68/5.97 => ( Y2
% 5.68/5.97 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.68/5.97 => ( ( ( X
% 5.68/5.97 = ( suc @ zero_zero_nat ) )
% 5.68/5.97 => ( Y2
% 5.68/5.97 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.68/5.97 => ~ ! [Va3: nat] :
% 5.68/5.97 ( ( X
% 5.68/5.97 = ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.97 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.97 => ( Y2
% 5.68/5.97 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.68/5.97 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.97 => ( Y2
% 5.68/5.97 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % vebt_buildup.elims
% 5.68/5.97 thf(fact_4877_tanh__ln__real,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.68/5.97 = ( 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 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % tanh_ln_real
% 5.68/5.97 thf(fact_4878_ln__one__minus__pos__lower__bound,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.97 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/5.97 => ( 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 ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % ln_one_minus_pos_lower_bound
% 5.68/5.97 thf(fact_4879_signed__take__bit__rec,axiom,
% 5.68/5.97 ( bit_ri6519982836138164636nteger
% 5.68/5.97 = ( ^ [N2: nat,A4: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_rec
% 5.68/5.97 thf(fact_4880_signed__take__bit__rec,axiom,
% 5.68/5.97 ( bit_ri631733984087533419it_int
% 5.68/5.97 = ( ^ [N2: nat,A4: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_rec
% 5.68/5.97 thf(fact_4881_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/5.97 => ( 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 ) ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_ln_one_plus_x_minus_x_bound
% 5.68/5.97 thf(fact_4882_intind,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,P: int > $o,X: int] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( P @ X )
% 5.68/5.97 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % intind
% 5.68/5.97 thf(fact_4883_intind,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,P: nat > $o,X: nat] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( P @ X )
% 5.68/5.97 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % intind
% 5.68/5.97 thf(fact_4884_intind,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( P @ X )
% 5.68/5.97 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % intind
% 5.68/5.97 thf(fact_4885_add_Oinverse__inverse,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_inverse
% 5.68/5.97 thf(fact_4886_add_Oinverse__inverse,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_inverse
% 5.68/5.97 thf(fact_4887_add_Oinverse__inverse,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_inverse
% 5.68/5.97 thf(fact_4888_add_Oinverse__inverse,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_inverse
% 5.68/5.97 thf(fact_4889_add_Oinverse__inverse,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_inverse
% 5.68/5.97 thf(fact_4890_neg__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ A )
% 5.68/5.97 = ( uminus_uminus_real @ B ) )
% 5.68/5.97 = ( A = B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_iff_equal
% 5.68/5.97 thf(fact_4891_neg__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ A )
% 5.68/5.97 = ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( A = B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_iff_equal
% 5.68/5.97 thf(fact_4892_neg__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.97 = ( A = B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_iff_equal
% 5.68/5.97 thf(fact_4893_neg__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( A = B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_iff_equal
% 5.68/5.97 thf(fact_4894_neg__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ A )
% 5.68/5.97 = ( uminus_uminus_rat @ B ) )
% 5.68/5.97 = ( A = B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_iff_equal
% 5.68/5.97 thf(fact_4895_Compl__anti__mono,axiom,
% 5.68/5.97 ! [A2: set_int,B4: set_int] :
% 5.68/5.97 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/5.97 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B4 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Compl_anti_mono
% 5.68/5.97 thf(fact_4896_Compl__subset__Compl__iff,axiom,
% 5.68/5.97 ! [A2: set_int,B4: set_int] :
% 5.68/5.97 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B4 ) )
% 5.68/5.97 = ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % Compl_subset_Compl_iff
% 5.68/5.97 thf(fact_4897_abs__idempotent,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.68/5.97 = ( abs_abs_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_idempotent
% 5.68/5.97 thf(fact_4898_abs__idempotent,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.68/5.97 = ( abs_abs_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_idempotent
% 5.68/5.97 thf(fact_4899_abs__idempotent,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.68/5.97 = ( abs_abs_Code_integer @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_idempotent
% 5.68/5.97 thf(fact_4900_abs__idempotent,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.68/5.97 = ( abs_abs_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_idempotent
% 5.68/5.97 thf(fact_4901_neg__le__iff__le,axiom,
% 5.68/5.97 ! [B: real,A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_iff_le
% 5.68/5.97 thf(fact_4902_neg__le__iff__le,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_iff_le
% 5.68/5.97 thf(fact_4903_neg__le__iff__le,axiom,
% 5.68/5.97 ! [B: rat,A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_iff_le
% 5.68/5.97 thf(fact_4904_neg__le__iff__le,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_iff_le
% 5.68/5.97 thf(fact_4905_compl__le__compl__iff,axiom,
% 5.68/5.97 ! [X: set_int,Y2: set_int] :
% 5.68/5.97 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y2 ) )
% 5.68/5.97 = ( ord_less_eq_set_int @ Y2 @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % compl_le_compl_iff
% 5.68/5.97 thf(fact_4906_add_Oinverse__neutral,axiom,
% 5.68/5.97 ( ( uminus_uminus_real @ zero_zero_real )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_neutral
% 5.68/5.97 thf(fact_4907_add_Oinverse__neutral,axiom,
% 5.68/5.97 ( ( uminus_uminus_int @ zero_zero_int )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_neutral
% 5.68/5.97 thf(fact_4908_add_Oinverse__neutral,axiom,
% 5.68/5.97 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_neutral
% 5.68/5.97 thf(fact_4909_add_Oinverse__neutral,axiom,
% 5.68/5.97 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_neutral
% 5.68/5.97 thf(fact_4910_add_Oinverse__neutral,axiom,
% 5.68/5.97 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % add.inverse_neutral
% 5.68/5.97 thf(fact_4911_neg__0__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( zero_zero_real
% 5.68/5.97 = ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( zero_zero_real = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_equal_iff_equal
% 5.68/5.97 thf(fact_4912_neg__0__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( zero_zero_int
% 5.68/5.97 = ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( zero_zero_int = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_equal_iff_equal
% 5.68/5.97 thf(fact_4913_neg__0__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( zero_zero_complex
% 5.68/5.97 = ( uminus1482373934393186551omplex @ A ) )
% 5.68/5.97 = ( zero_zero_complex = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_equal_iff_equal
% 5.68/5.97 thf(fact_4914_neg__0__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( zero_z3403309356797280102nteger
% 5.68/5.97 = ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_equal_iff_equal
% 5.68/5.97 thf(fact_4915_neg__0__equal__iff__equal,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( zero_zero_rat
% 5.68/5.97 = ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( zero_zero_rat = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_equal_iff_equal
% 5.68/5.97 thf(fact_4916_neg__equal__0__iff__equal,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ A )
% 5.68/5.97 = zero_zero_real )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_0_iff_equal
% 5.68/5.97 thf(fact_4917_neg__equal__0__iff__equal,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ A )
% 5.68/5.97 = zero_zero_int )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_0_iff_equal
% 5.68/5.97 thf(fact_4918_neg__equal__0__iff__equal,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.97 = zero_zero_complex )
% 5.68/5.97 = ( A = zero_zero_complex ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_0_iff_equal
% 5.68/5.97 thf(fact_4919_neg__equal__0__iff__equal,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.97 = zero_z3403309356797280102nteger )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_0_iff_equal
% 5.68/5.97 thf(fact_4920_neg__equal__0__iff__equal,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ A )
% 5.68/5.97 = zero_zero_rat )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_0_iff_equal
% 5.68/5.97 thf(fact_4921_equal__neg__zero,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( A
% 5.68/5.97 = ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % equal_neg_zero
% 5.68/5.97 thf(fact_4922_equal__neg__zero,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( A
% 5.68/5.97 = ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % equal_neg_zero
% 5.68/5.97 thf(fact_4923_equal__neg__zero,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( A
% 5.68/5.97 = ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % equal_neg_zero
% 5.68/5.97 thf(fact_4924_equal__neg__zero,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( A
% 5.68/5.97 = ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % equal_neg_zero
% 5.68/5.97 thf(fact_4925_neg__equal__zero,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ A )
% 5.68/5.97 = A )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_zero
% 5.68/5.97 thf(fact_4926_neg__equal__zero,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ A )
% 5.68/5.97 = A )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_zero
% 5.68/5.97 thf(fact_4927_neg__equal__zero,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.97 = A )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_zero
% 5.68/5.97 thf(fact_4928_neg__equal__zero,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ A )
% 5.68/5.97 = A )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_equal_zero
% 5.68/5.97 thf(fact_4929_neg__less__iff__less,axiom,
% 5.68/5.97 ! [B: real,A: real] :
% 5.68/5.97 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_real @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_iff_less
% 5.68/5.97 thf(fact_4930_neg__less__iff__less,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_int @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_iff_less
% 5.68/5.97 thf(fact_4931_neg__less__iff__less,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_iff_less
% 5.68/5.97 thf(fact_4932_neg__less__iff__less,axiom,
% 5.68/5.97 ! [B: rat,A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_rat @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_iff_less
% 5.68/5.97 thf(fact_4933_neg__numeral__eq__iff,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.97 = ( M = N ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_numeral_eq_iff
% 5.68/5.97 thf(fact_4934_neg__numeral__eq__iff,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.97 = ( M = N ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_numeral_eq_iff
% 5.68/5.97 thf(fact_4935_neg__numeral__eq__iff,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.97 = ( M = N ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_numeral_eq_iff
% 5.68/5.97 thf(fact_4936_neg__numeral__eq__iff,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.97 = ( M = N ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_numeral_eq_iff
% 5.68/5.97 thf(fact_4937_neg__numeral__eq__iff,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.97 = ( M = N ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_numeral_eq_iff
% 5.68/5.97 thf(fact_4938_mult__minus__right,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_right
% 5.68/5.97 thf(fact_4939_mult__minus__right,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_right
% 5.68/5.97 thf(fact_4940_mult__minus__right,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_right
% 5.68/5.97 thf(fact_4941_mult__minus__right,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_right
% 5.68/5.97 thf(fact_4942_mult__minus__right,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_right
% 5.68/5.97 thf(fact_4943_minus__mult__minus,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.68/5.97 = ( times_times_real @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mult_minus
% 5.68/5.97 thf(fact_4944_minus__mult__minus,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( times_times_int @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mult_minus
% 5.68/5.97 thf(fact_4945_minus__mult__minus,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.97 = ( times_times_complex @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mult_minus
% 5.68/5.97 thf(fact_4946_minus__mult__minus,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mult_minus
% 5.68/5.97 thf(fact_4947_minus__mult__minus,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.68/5.97 = ( times_times_rat @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mult_minus
% 5.68/5.97 thf(fact_4948_mult__minus__left,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.97 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_left
% 5.68/5.97 thf(fact_4949_mult__minus__left,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.97 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_left
% 5.68/5.97 thf(fact_4950_mult__minus__left,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_left
% 5.68/5.97 thf(fact_4951_mult__minus__left,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_left
% 5.68/5.97 thf(fact_4952_mult__minus__left,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.97 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus_left
% 5.68/5.97 thf(fact_4953_minus__add__distrib,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.68/5.97 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_distrib
% 5.68/5.97 thf(fact_4954_minus__add__distrib,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.68/5.97 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_distrib
% 5.68/5.97 thf(fact_4955_minus__add__distrib,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.68/5.97 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_distrib
% 5.68/5.97 thf(fact_4956_minus__add__distrib,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.97 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_distrib
% 5.68/5.97 thf(fact_4957_minus__add__distrib,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.68/5.97 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_distrib
% 5.68/5.97 thf(fact_4958_minus__add__cancel,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_cancel
% 5.68/5.97 thf(fact_4959_minus__add__cancel,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_cancel
% 5.68/5.97 thf(fact_4960_minus__add__cancel,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_cancel
% 5.68/5.97 thf(fact_4961_minus__add__cancel,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_cancel
% 5.68/5.97 thf(fact_4962_minus__add__cancel,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % minus_add_cancel
% 5.68/5.97 thf(fact_4963_add__minus__cancel,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % add_minus_cancel
% 5.68/5.97 thf(fact_4964_add__minus__cancel,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % add_minus_cancel
% 5.68/5.97 thf(fact_4965_add__minus__cancel,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % add_minus_cancel
% 5.68/5.97 thf(fact_4966_add__minus__cancel,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % add_minus_cancel
% 5.68/5.97 thf(fact_4967_add__minus__cancel,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.68/5.97 = B ) ).
% 5.68/5.97
% 5.68/5.97 % add_minus_cancel
% 5.68/5.97 thf(fact_4968_minus__diff__eq,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.68/5.97 = ( minus_minus_real @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_diff_eq
% 5.68/5.97 thf(fact_4969_minus__diff__eq,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.68/5.97 = ( minus_minus_int @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_diff_eq
% 5.68/5.97 thf(fact_4970_minus__diff__eq,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.68/5.97 = ( minus_minus_complex @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_diff_eq
% 5.68/5.97 thf(fact_4971_minus__diff__eq,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.68/5.97 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_diff_eq
% 5.68/5.97 thf(fact_4972_minus__diff__eq,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.68/5.97 = ( minus_minus_rat @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_diff_eq
% 5.68/5.97 thf(fact_4973_div__minus__minus,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( divide_divide_int @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_minus_minus
% 5.68/5.97 thf(fact_4974_div__minus__minus,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_minus_minus
% 5.68/5.97 thf(fact_4975_abs__0__eq,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( zero_z3403309356797280102nteger
% 5.68/5.97 = ( abs_abs_Code_integer @ A ) )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_0_eq
% 5.68/5.97 thf(fact_4976_abs__0__eq,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( zero_zero_real
% 5.68/5.97 = ( abs_abs_real @ A ) )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_0_eq
% 5.68/5.97 thf(fact_4977_abs__0__eq,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( zero_zero_rat
% 5.68/5.97 = ( abs_abs_rat @ A ) )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_0_eq
% 5.68/5.97 thf(fact_4978_abs__0__eq,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( zero_zero_int
% 5.68/5.97 = ( abs_abs_int @ A ) )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_0_eq
% 5.68/5.97 thf(fact_4979_abs__eq__0,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ( abs_abs_Code_integer @ A )
% 5.68/5.97 = zero_z3403309356797280102nteger )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_eq_0
% 5.68/5.97 thf(fact_4980_abs__eq__0,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ( abs_abs_real @ A )
% 5.68/5.97 = zero_zero_real )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_eq_0
% 5.68/5.97 thf(fact_4981_abs__eq__0,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ( abs_abs_rat @ A )
% 5.68/5.97 = zero_zero_rat )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_eq_0
% 5.68/5.97 thf(fact_4982_abs__eq__0,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ( abs_abs_int @ A )
% 5.68/5.97 = zero_zero_int )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_eq_0
% 5.68/5.97 thf(fact_4983_abs__zero,axiom,
% 5.68/5.97 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % abs_zero
% 5.68/5.97 thf(fact_4984_abs__zero,axiom,
% 5.68/5.97 ( ( abs_abs_real @ zero_zero_real )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % abs_zero
% 5.68/5.97 thf(fact_4985_abs__zero,axiom,
% 5.68/5.97 ( ( abs_abs_rat @ zero_zero_rat )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % abs_zero
% 5.68/5.97 thf(fact_4986_abs__zero,axiom,
% 5.68/5.97 ( ( abs_abs_int @ zero_zero_int )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % abs_zero
% 5.68/5.97 thf(fact_4987_abs__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.68/5.97 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_numeral
% 5.68/5.97 thf(fact_4988_abs__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.68/5.97 = ( numeral_numeral_real @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_numeral
% 5.68/5.97 thf(fact_4989_abs__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.68/5.97 = ( numeral_numeral_rat @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_numeral
% 5.68/5.97 thf(fact_4990_abs__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.68/5.97 = ( numeral_numeral_int @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_numeral
% 5.68/5.97 thf(fact_4991_abs__mult__self__eq,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.68/5.97 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_mult_self_eq
% 5.68/5.97 thf(fact_4992_abs__mult__self__eq,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.68/5.97 = ( times_times_real @ A @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_mult_self_eq
% 5.68/5.97 thf(fact_4993_abs__mult__self__eq,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.68/5.97 = ( times_times_rat @ A @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_mult_self_eq
% 5.68/5.97 thf(fact_4994_abs__mult__self__eq,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.68/5.97 = ( times_times_int @ A @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_mult_self_eq
% 5.68/5.97 thf(fact_4995_abs__add__abs,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.68/5.97 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_add_abs
% 5.68/5.97 thf(fact_4996_abs__add__abs,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.68/5.97 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_add_abs
% 5.68/5.97 thf(fact_4997_abs__add__abs,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.68/5.97 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_add_abs
% 5.68/5.97 thf(fact_4998_abs__add__abs,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.68/5.97 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_add_abs
% 5.68/5.97 thf(fact_4999_abs__divide,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/5.97 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_divide
% 5.68/5.97 thf(fact_5000_abs__divide,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.97 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_divide
% 5.68/5.97 thf(fact_5001_abs__divide,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.97 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_divide
% 5.68/5.97 thf(fact_5002_abs__minus__cancel,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( abs_abs_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_minus_cancel
% 5.68/5.97 thf(fact_5003_abs__minus__cancel,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( abs_abs_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_minus_cancel
% 5.68/5.97 thf(fact_5004_abs__minus__cancel,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( abs_abs_Code_integer @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_minus_cancel
% 5.68/5.97 thf(fact_5005_abs__minus__cancel,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( abs_abs_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_minus_cancel
% 5.68/5.97 thf(fact_5006_mod__minus__minus,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_minus_minus
% 5.68/5.97 thf(fact_5007_mod__minus__minus,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % mod_minus_minus
% 5.68/5.97 thf(fact_5008_length__replicate,axiom,
% 5.68/5.97 ! [N: nat,X: vEBT_VEBT] :
% 5.68/5.97 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.68/5.97 = N ) ).
% 5.68/5.97
% 5.68/5.97 % length_replicate
% 5.68/5.97 thf(fact_5009_length__replicate,axiom,
% 5.68/5.97 ! [N: nat,X: $o] :
% 5.68/5.97 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 5.68/5.97 = N ) ).
% 5.68/5.97
% 5.68/5.97 % length_replicate
% 5.68/5.97 thf(fact_5010_length__replicate,axiom,
% 5.68/5.97 ! [N: nat,X: nat] :
% 5.68/5.97 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 5.68/5.97 = N ) ).
% 5.68/5.97
% 5.68/5.97 % length_replicate
% 5.68/5.97 thf(fact_5011_length__replicate,axiom,
% 5.68/5.97 ! [N: nat,X: int] :
% 5.68/5.97 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 5.68/5.97 = N ) ).
% 5.68/5.97
% 5.68/5.97 % length_replicate
% 5.68/5.97 thf(fact_5012_tanh__real__le__iff,axiom,
% 5.68/5.97 ! [X: real,Y2: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 5.68/5.97 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % tanh_real_le_iff
% 5.68/5.97 thf(fact_5013_neg__0__le__iff__le,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_le_iff_le
% 5.68/5.97 thf(fact_5014_neg__0__le__iff__le,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_le_iff_le
% 5.68/5.97 thf(fact_5015_neg__0__le__iff__le,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_le_iff_le
% 5.68/5.97 thf(fact_5016_neg__0__le__iff__le,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_le_iff_le
% 5.68/5.97 thf(fact_5017_neg__le__0__iff__le,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.68/5.97 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_0_iff_le
% 5.68/5.97 thf(fact_5018_neg__le__0__iff__le,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_0_iff_le
% 5.68/5.97 thf(fact_5019_neg__le__0__iff__le,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.68/5.97 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_0_iff_le
% 5.68/5.97 thf(fact_5020_neg__le__0__iff__le,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.68/5.97 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_le_0_iff_le
% 5.68/5.97 thf(fact_5021_less__eq__neg__nonpos,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_eq_neg_nonpos
% 5.68/5.97 thf(fact_5022_less__eq__neg__nonpos,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_eq_neg_nonpos
% 5.68/5.97 thf(fact_5023_less__eq__neg__nonpos,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_eq_neg_nonpos
% 5.68/5.97 thf(fact_5024_less__eq__neg__nonpos,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_eq_neg_nonpos
% 5.68/5.97 thf(fact_5025_neg__less__eq__nonneg,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_eq_nonneg
% 5.68/5.97 thf(fact_5026_neg__less__eq__nonneg,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_eq_nonneg
% 5.68/5.97 thf(fact_5027_neg__less__eq__nonneg,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_eq_nonneg
% 5.68/5.97 thf(fact_5028_neg__less__eq__nonneg,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_eq_nonneg
% 5.68/5.97 thf(fact_5029_neg__less__0__iff__less,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.68/5.97 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_0_iff_less
% 5.68/5.97 thf(fact_5030_neg__less__0__iff__less,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.68/5.97 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_0_iff_less
% 5.68/5.97 thf(fact_5031_neg__less__0__iff__less,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.68/5.97 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_0_iff_less
% 5.68/5.97 thf(fact_5032_neg__less__0__iff__less,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.68/5.97 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_0_iff_less
% 5.68/5.97 thf(fact_5033_neg__0__less__iff__less,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_less_iff_less
% 5.68/5.97 thf(fact_5034_neg__0__less__iff__less,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_less_iff_less
% 5.68/5.97 thf(fact_5035_neg__0__less__iff__less,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_less_iff_less
% 5.68/5.97 thf(fact_5036_neg__0__less__iff__less,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_0_less_iff_less
% 5.68/5.97 thf(fact_5037_neg__less__pos,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.68/5.97 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_pos
% 5.68/5.97 thf(fact_5038_neg__less__pos,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.68/5.97 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_pos
% 5.68/5.97 thf(fact_5039_neg__less__pos,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.68/5.97 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_pos
% 5.68/5.97 thf(fact_5040_neg__less__pos,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.68/5.97 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_less_pos
% 5.68/5.97 thf(fact_5041_less__neg__neg,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_neg_neg
% 5.68/5.97 thf(fact_5042_less__neg__neg,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_neg_neg
% 5.68/5.97 thf(fact_5043_less__neg__neg,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_neg_neg
% 5.68/5.97 thf(fact_5044_less__neg__neg,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % less_neg_neg
% 5.68/5.97 thf(fact_5045_ab__left__minus,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % ab_left_minus
% 5.68/5.97 thf(fact_5046_ab__left__minus,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % ab_left_minus
% 5.68/5.97 thf(fact_5047_ab__left__minus,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % ab_left_minus
% 5.68/5.97 thf(fact_5048_ab__left__minus,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % ab_left_minus
% 5.68/5.97 thf(fact_5049_ab__left__minus,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % ab_left_minus
% 5.68/5.97 thf(fact_5050_add_Oright__inverse,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % add.right_inverse
% 5.68/5.97 thf(fact_5051_add_Oright__inverse,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % add.right_inverse
% 5.68/5.97 thf(fact_5052_add_Oright__inverse,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % add.right_inverse
% 5.68/5.97 thf(fact_5053_add_Oright__inverse,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % add.right_inverse
% 5.68/5.97 thf(fact_5054_add_Oright__inverse,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % add.right_inverse
% 5.68/5.97 thf(fact_5055_diff__0,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.68/5.97 = ( uminus_uminus_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_0
% 5.68/5.97 thf(fact_5056_diff__0,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.68/5.97 = ( uminus_uminus_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_0
% 5.68/5.97 thf(fact_5057_diff__0,axiom,
% 5.68/5.97 ! [A: complex] :
% 5.68/5.97 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_0
% 5.68/5.97 thf(fact_5058_diff__0,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_0
% 5.68/5.97 thf(fact_5059_diff__0,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.68/5.97 = ( uminus_uminus_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_0
% 5.68/5.97 thf(fact_5060_add__neg__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_simps(3)
% 5.68/5.97 thf(fact_5061_add__neg__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_simps(3)
% 5.68/5.97 thf(fact_5062_add__neg__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_simps(3)
% 5.68/5.97 thf(fact_5063_add__neg__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_simps(3)
% 5.68/5.97 thf(fact_5064_add__neg__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_simps(3)
% 5.68/5.97 thf(fact_5065_mult__minus1,axiom,
% 5.68/5.97 ! [Z: real] :
% 5.68/5.97 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.68/5.97 = ( uminus_uminus_real @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1
% 5.68/5.97 thf(fact_5066_mult__minus1,axiom,
% 5.68/5.97 ! [Z: int] :
% 5.68/5.97 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.68/5.97 = ( uminus_uminus_int @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1
% 5.68/5.97 thf(fact_5067_mult__minus1,axiom,
% 5.68/5.97 ! [Z: complex] :
% 5.68/5.97 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1
% 5.68/5.97 thf(fact_5068_mult__minus1,axiom,
% 5.68/5.97 ! [Z: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1
% 5.68/5.97 thf(fact_5069_mult__minus1,axiom,
% 5.68/5.97 ! [Z: rat] :
% 5.68/5.97 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.68/5.97 = ( uminus_uminus_rat @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1
% 5.68/5.97 thf(fact_5070_mult__minus1__right,axiom,
% 5.68/5.97 ! [Z: real] :
% 5.68/5.97 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = ( uminus_uminus_real @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1_right
% 5.68/5.97 thf(fact_5071_mult__minus1__right,axiom,
% 5.68/5.97 ! [Z: int] :
% 5.68/5.97 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = ( uminus_uminus_int @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1_right
% 5.68/5.97 thf(fact_5072_mult__minus1__right,axiom,
% 5.68/5.97 ! [Z: complex] :
% 5.68/5.97 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1_right
% 5.68/5.97 thf(fact_5073_mult__minus1__right,axiom,
% 5.68/5.97 ! [Z: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1_right
% 5.68/5.97 thf(fact_5074_mult__minus1__right,axiom,
% 5.68/5.97 ! [Z: rat] :
% 5.68/5.97 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = ( uminus_uminus_rat @ Z ) ) ).
% 5.68/5.97
% 5.68/5.97 % mult_minus1_right
% 5.68/5.97 thf(fact_5075_abs__of__nonneg,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.68/5.97 => ( ( abs_abs_Code_integer @ A )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonneg
% 5.68/5.97 thf(fact_5076_abs__of__nonneg,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/5.97 => ( ( abs_abs_real @ A )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonneg
% 5.68/5.97 thf(fact_5077_abs__of__nonneg,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.68/5.97 => ( ( abs_abs_rat @ A )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonneg
% 5.68/5.97 thf(fact_5078_abs__of__nonneg,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.68/5.97 => ( ( abs_abs_int @ A )
% 5.68/5.97 = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonneg
% 5.68/5.97 thf(fact_5079_abs__le__self__iff,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.68/5.97 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_self_iff
% 5.68/5.97 thf(fact_5080_abs__le__self__iff,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_self_iff
% 5.68/5.97 thf(fact_5081_abs__le__self__iff,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_self_iff
% 5.68/5.97 thf(fact_5082_abs__le__self__iff,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.68/5.97 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_self_iff
% 5.68/5.97 thf(fact_5083_abs__le__zero__iff,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.68/5.97 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_zero_iff
% 5.68/5.97 thf(fact_5084_abs__le__zero__iff,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.68/5.97 = ( A = zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_zero_iff
% 5.68/5.97 thf(fact_5085_abs__le__zero__iff,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.68/5.97 = ( A = zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_zero_iff
% 5.68/5.97 thf(fact_5086_abs__le__zero__iff,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.68/5.97 = ( A = zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_le_zero_iff
% 5.68/5.97 thf(fact_5087_zero__less__abs__iff,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.68/5.97 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_abs_iff
% 5.68/5.97 thf(fact_5088_zero__less__abs__iff,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.68/5.97 = ( A != zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_abs_iff
% 5.68/5.97 thf(fact_5089_zero__less__abs__iff,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.68/5.97 = ( A != zero_zero_rat ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_abs_iff
% 5.68/5.97 thf(fact_5090_zero__less__abs__iff,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.68/5.97 = ( A != zero_zero_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_less_abs_iff
% 5.68/5.97 thf(fact_5091_uminus__add__conv__diff,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.97 = ( minus_minus_real @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % uminus_add_conv_diff
% 5.68/5.97 thf(fact_5092_uminus__add__conv__diff,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.97 = ( minus_minus_int @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % uminus_add_conv_diff
% 5.68/5.97 thf(fact_5093_uminus__add__conv__diff,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.68/5.97 = ( minus_minus_complex @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % uminus_add_conv_diff
% 5.68/5.97 thf(fact_5094_uminus__add__conv__diff,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.97 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % uminus_add_conv_diff
% 5.68/5.97 thf(fact_5095_uminus__add__conv__diff,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.97 = ( minus_minus_rat @ B @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % uminus_add_conv_diff
% 5.68/5.97 thf(fact_5096_diff__minus__eq__add,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.68/5.97 = ( plus_plus_real @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_minus_eq_add
% 5.68/5.97 thf(fact_5097_diff__minus__eq__add,axiom,
% 5.68/5.97 ! [A: int,B: int] :
% 5.68/5.97 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.97 = ( plus_plus_int @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_minus_eq_add
% 5.68/5.97 thf(fact_5098_diff__minus__eq__add,axiom,
% 5.68/5.97 ! [A: complex,B: complex] :
% 5.68/5.97 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.97 = ( plus_plus_complex @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_minus_eq_add
% 5.68/5.97 thf(fact_5099_diff__minus__eq__add,axiom,
% 5.68/5.97 ! [A: code_integer,B: code_integer] :
% 5.68/5.97 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.97 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_minus_eq_add
% 5.68/5.97 thf(fact_5100_diff__minus__eq__add,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.68/5.97 = ( plus_plus_rat @ A @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_minus_eq_add
% 5.68/5.97 thf(fact_5101_div__minus1__right,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = ( uminus_uminus_int @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_minus1_right
% 5.68/5.97 thf(fact_5102_div__minus1__right,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.68/5.97
% 5.68/5.97 % div_minus1_right
% 5.68/5.97 thf(fact_5103_divide__minus1,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = ( uminus_uminus_real @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % divide_minus1
% 5.68/5.97 thf(fact_5104_divide__minus1,axiom,
% 5.68/5.97 ! [X: complex] :
% 5.68/5.97 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % divide_minus1
% 5.68/5.97 thf(fact_5105_divide__minus1,axiom,
% 5.68/5.97 ! [X: rat] :
% 5.68/5.97 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = ( uminus_uminus_rat @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % divide_minus1
% 5.68/5.97 thf(fact_5106_abs__neg__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_real @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_numeral
% 5.68/5.97 thf(fact_5107_abs__neg__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_int @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_numeral
% 5.68/5.97 thf(fact_5108_abs__neg__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.97 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_numeral
% 5.68/5.97 thf(fact_5109_abs__neg__numeral,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_rat @ N ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_numeral
% 5.68/5.97 thf(fact_5110_abs__neg__one,axiom,
% 5.68/5.97 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = one_one_real ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_one
% 5.68/5.97 thf(fact_5111_abs__neg__one,axiom,
% 5.68/5.97 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = one_one_int ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_one
% 5.68/5.97 thf(fact_5112_abs__neg__one,axiom,
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = one_one_Code_integer ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_one
% 5.68/5.97 thf(fact_5113_abs__neg__one,axiom,
% 5.68/5.97 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = one_one_rat ) ).
% 5.68/5.97
% 5.68/5.97 % abs_neg_one
% 5.68/5.97 thf(fact_5114_minus__mod__self1,axiom,
% 5.68/5.97 ! [B: int,A: int] :
% 5.68/5.97 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.68/5.97 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mod_self1
% 5.68/5.97 thf(fact_5115_minus__mod__self1,axiom,
% 5.68/5.97 ! [B: code_integer,A: code_integer] :
% 5.68/5.97 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.68/5.97 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.68/5.97
% 5.68/5.97 % minus_mod_self1
% 5.68/5.97 thf(fact_5116_abs__power__minus,axiom,
% 5.68/5.97 ! [A: real,N: nat] :
% 5.68/5.97 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.68/5.97 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_power_minus
% 5.68/5.97 thf(fact_5117_abs__power__minus,axiom,
% 5.68/5.97 ! [A: int,N: nat] :
% 5.68/5.97 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.68/5.97 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_power_minus
% 5.68/5.97 thf(fact_5118_abs__power__minus,axiom,
% 5.68/5.97 ! [A: code_integer,N: nat] :
% 5.68/5.97 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.68/5.97 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_power_minus
% 5.68/5.97 thf(fact_5119_abs__power__minus,axiom,
% 5.68/5.97 ! [A: rat,N: nat] :
% 5.68/5.97 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.68/5.97 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_power_minus
% 5.68/5.97 thf(fact_5120_signed__take__bit__of__minus__1,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_of_minus_1
% 5.68/5.97 thf(fact_5121_signed__take__bit__of__minus__1,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.97
% 5.68/5.97 % signed_take_bit_of_minus_1
% 5.68/5.97 thf(fact_5122_real__add__minus__iff,axiom,
% 5.68/5.97 ! [X: real,A: real] :
% 5.68/5.97 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.68/5.97 = zero_zero_real )
% 5.68/5.97 = ( X = A ) ) ).
% 5.68/5.97
% 5.68/5.97 % real_add_minus_iff
% 5.68/5.97 thf(fact_5123_Ball__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: int,P: int > $o] :
% 5.68/5.97 ( ( ! [X2: int] :
% 5.68/5.97 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.68/5.97 => ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Ball_set_replicate
% 5.68/5.97 thf(fact_5124_Ball__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: nat,P: nat > $o] :
% 5.68/5.97 ( ( ! [X2: nat] :
% 5.68/5.97 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.68/5.97 => ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Ball_set_replicate
% 5.68/5.97 thf(fact_5125_Ball__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.68/5.97 ( ( ! [X2: vEBT_VEBT] :
% 5.68/5.97 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.68/5.97 => ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Ball_set_replicate
% 5.68/5.97 thf(fact_5126_Bex__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: int,P: int > $o] :
% 5.68/5.97 ( ( ? [X2: int] :
% 5.68/5.97 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.68/5.97 & ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Bex_set_replicate
% 5.68/5.97 thf(fact_5127_Bex__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: nat,P: nat > $o] :
% 5.68/5.97 ( ( ? [X2: nat] :
% 5.68/5.97 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.68/5.97 & ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Bex_set_replicate
% 5.68/5.97 thf(fact_5128_Bex__set__replicate,axiom,
% 5.68/5.97 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.68/5.97 ( ( ? [X2: vEBT_VEBT] :
% 5.68/5.97 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.68/5.97 & ( P @ X2 ) ) )
% 5.68/5.97 = ( ( P @ A )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % Bex_set_replicate
% 5.68/5.97 thf(fact_5129_in__set__replicate,axiom,
% 5.68/5.97 ! [X: real,N: nat,Y2: real] :
% 5.68/5.97 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5130_in__set__replicate,axiom,
% 5.68/5.97 ! [X: complex,N: nat,Y2: complex] :
% 5.68/5.97 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5131_in__set__replicate,axiom,
% 5.68/5.97 ! [X: product_prod_nat_nat,N: nat,Y2: product_prod_nat_nat] :
% 5.68/5.97 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5132_in__set__replicate,axiom,
% 5.68/5.97 ! [X: int,N: nat,Y2: int] :
% 5.68/5.97 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5133_in__set__replicate,axiom,
% 5.68/5.97 ! [X: nat,N: nat,Y2: nat] :
% 5.68/5.97 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5134_in__set__replicate,axiom,
% 5.68/5.97 ! [X: vEBT_VEBT,N: nat,Y2: vEBT_VEBT] :
% 5.68/5.97 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y2 ) ) )
% 5.68/5.97 = ( ( X = Y2 )
% 5.68/5.97 & ( N != zero_zero_nat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % in_set_replicate
% 5.68/5.97 thf(fact_5135_nth__replicate,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,X: int] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( nth_int @ ( replicate_int @ N @ X ) @ I2 )
% 5.68/5.97 = X ) ) ).
% 5.68/5.97
% 5.68/5.97 % nth_replicate
% 5.68/5.97 thf(fact_5136_nth__replicate,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,X: nat] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 )
% 5.68/5.97 = X ) ) ).
% 5.68/5.97
% 5.68/5.97 % nth_replicate
% 5.68/5.97 thf(fact_5137_nth__replicate,axiom,
% 5.68/5.97 ! [I2: nat,N: nat,X: vEBT_VEBT] :
% 5.68/5.97 ( ( ord_less_nat @ I2 @ N )
% 5.68/5.97 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 )
% 5.68/5.97 = X ) ) ).
% 5.68/5.97
% 5.68/5.97 % nth_replicate
% 5.68/5.97 thf(fact_5138_tanh__real__nonneg__iff,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.68/5.97 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/5.97
% 5.68/5.97 % tanh_real_nonneg_iff
% 5.68/5.97 thf(fact_5139_tanh__real__nonpos__iff,axiom,
% 5.68/5.97 ! [X: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.68/5.97 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/5.97
% 5.68/5.97 % tanh_real_nonpos_iff
% 5.68/5.97 thf(fact_5140_dbl__simps_I1_J,axiom,
% 5.68/5.97 ! [K: num] :
% 5.68/5.97 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dbl_simps(1)
% 5.68/5.97 thf(fact_5141_dbl__simps_I1_J,axiom,
% 5.68/5.97 ! [K: num] :
% 5.68/5.97 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dbl_simps(1)
% 5.68/5.97 thf(fact_5142_dbl__simps_I1_J,axiom,
% 5.68/5.97 ! [K: num] :
% 5.68/5.97 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dbl_simps(1)
% 5.68/5.97 thf(fact_5143_dbl__simps_I1_J,axiom,
% 5.68/5.97 ! [K: num] :
% 5.68/5.97 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dbl_simps(1)
% 5.68/5.97 thf(fact_5144_dbl__simps_I1_J,axiom,
% 5.68/5.97 ! [K: num] :
% 5.68/5.97 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % dbl_simps(1)
% 5.68/5.97 thf(fact_5145_triangle__Suc,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( nat_triangle @ ( suc @ N ) )
% 5.68/5.97 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % triangle_Suc
% 5.68/5.97 thf(fact_5146_add__neg__numeral__special_I7_J,axiom,
% 5.68/5.97 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(7)
% 5.68/5.97 thf(fact_5147_add__neg__numeral__special_I7_J,axiom,
% 5.68/5.97 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(7)
% 5.68/5.97 thf(fact_5148_add__neg__numeral__special_I7_J,axiom,
% 5.68/5.97 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(7)
% 5.68/5.97 thf(fact_5149_add__neg__numeral__special_I7_J,axiom,
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(7)
% 5.68/5.97 thf(fact_5150_add__neg__numeral__special_I7_J,axiom,
% 5.68/5.97 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(7)
% 5.68/5.97 thf(fact_5151_add__neg__numeral__special_I8_J,axiom,
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(8)
% 5.68/5.97 thf(fact_5152_add__neg__numeral__special_I8_J,axiom,
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(8)
% 5.68/5.97 thf(fact_5153_add__neg__numeral__special_I8_J,axiom,
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(8)
% 5.68/5.97 thf(fact_5154_add__neg__numeral__special_I8_J,axiom,
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(8)
% 5.68/5.97 thf(fact_5155_add__neg__numeral__special_I8_J,axiom,
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % add_neg_numeral_special(8)
% 5.68/5.97 thf(fact_5156_diff__numeral__special_I12_J,axiom,
% 5.68/5.97 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = zero_zero_real ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_special(12)
% 5.68/5.97 thf(fact_5157_diff__numeral__special_I12_J,axiom,
% 5.68/5.97 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_special(12)
% 5.68/5.97 thf(fact_5158_diff__numeral__special_I12_J,axiom,
% 5.68/5.97 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.97 = zero_zero_complex ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_special(12)
% 5.68/5.97 thf(fact_5159_diff__numeral__special_I12_J,axiom,
% 5.68/5.97 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_special(12)
% 5.68/5.97 thf(fact_5160_diff__numeral__special_I12_J,axiom,
% 5.68/5.97 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = zero_zero_rat ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_special(12)
% 5.68/5.97 thf(fact_5161_neg__one__eq__numeral__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ one_one_real )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_one_eq_numeral_iff
% 5.68/5.97 thf(fact_5162_neg__one__eq__numeral__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ one_one_int )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_one_eq_numeral_iff
% 5.68/5.97 thf(fact_5163_neg__one__eq__numeral__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_one_eq_numeral_iff
% 5.68/5.97 thf(fact_5164_neg__one__eq__numeral__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_one_eq_numeral_iff
% 5.68/5.97 thf(fact_5165_neg__one__eq__numeral__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % neg_one_eq_numeral_iff
% 5.68/5.97 thf(fact_5166_numeral__eq__neg__one__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.68/5.97 = ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % numeral_eq_neg_one_iff
% 5.68/5.97 thf(fact_5167_numeral__eq__neg__one__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.68/5.97 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % numeral_eq_neg_one_iff
% 5.68/5.97 thf(fact_5168_numeral__eq__neg__one__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % numeral_eq_neg_one_iff
% 5.68/5.97 thf(fact_5169_numeral__eq__neg__one__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % numeral_eq_neg_one_iff
% 5.68/5.97 thf(fact_5170_numeral__eq__neg__one__iff,axiom,
% 5.68/5.97 ! [N: num] :
% 5.68/5.97 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.68/5.97 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.97 = ( N = one ) ) ).
% 5.68/5.97
% 5.68/5.97 % numeral_eq_neg_one_iff
% 5.68/5.97 thf(fact_5171_zero__le__divide__abs__iff,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.68/5.97 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/5.97 | ( B = zero_zero_real ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_divide_abs_iff
% 5.68/5.97 thf(fact_5172_zero__le__divide__abs__iff,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.68/5.97 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.68/5.97 | ( B = zero_zero_rat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % zero_le_divide_abs_iff
% 5.68/5.97 thf(fact_5173_divide__le__0__abs__iff,axiom,
% 5.68/5.97 ! [A: real,B: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.68/5.97 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/5.97 | ( B = zero_zero_real ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % divide_le_0_abs_iff
% 5.68/5.97 thf(fact_5174_divide__le__0__abs__iff,axiom,
% 5.68/5.97 ! [A: rat,B: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.68/5.97 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.68/5.97 | ( B = zero_zero_rat ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % divide_le_0_abs_iff
% 5.68/5.97 thf(fact_5175_abs__of__nonpos,axiom,
% 5.68/5.97 ! [A: real] :
% 5.68/5.97 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/5.97 => ( ( abs_abs_real @ A )
% 5.68/5.97 = ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonpos
% 5.68/5.97 thf(fact_5176_abs__of__nonpos,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.68/5.97 => ( ( abs_abs_Code_integer @ A )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonpos
% 5.68/5.97 thf(fact_5177_abs__of__nonpos,axiom,
% 5.68/5.97 ! [A: rat] :
% 5.68/5.97 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.68/5.97 => ( ( abs_abs_rat @ A )
% 5.68/5.97 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonpos
% 5.68/5.97 thf(fact_5178_abs__of__nonpos,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.68/5.97 => ( ( abs_abs_int @ A )
% 5.68/5.97 = ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % abs_of_nonpos
% 5.68/5.97 thf(fact_5179_left__minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat,A: real] :
% 5.68/5.97 ( ( 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 ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % left_minus_one_mult_self
% 5.68/5.97 thf(fact_5180_left__minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat,A: int] :
% 5.68/5.97 ( ( 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 ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % left_minus_one_mult_self
% 5.68/5.97 thf(fact_5181_left__minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat,A: complex] :
% 5.68/5.97 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % left_minus_one_mult_self
% 5.68/5.97 thf(fact_5182_left__minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat,A: code_integer] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % left_minus_one_mult_self
% 5.68/5.97 thf(fact_5183_left__minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat,A: rat] :
% 5.68/5.97 ( ( 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 ) )
% 5.68/5.97 = A ) ).
% 5.68/5.97
% 5.68/5.97 % left_minus_one_mult_self
% 5.68/5.97 thf(fact_5184_minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.68/5.97 = one_one_real ) ).
% 5.68/5.97
% 5.68/5.97 % minus_one_mult_self
% 5.68/5.97 thf(fact_5185_minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.68/5.97 = one_one_int ) ).
% 5.68/5.97
% 5.68/5.97 % minus_one_mult_self
% 5.68/5.97 thf(fact_5186_minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.68/5.97 = one_one_complex ) ).
% 5.68/5.97
% 5.68/5.97 % minus_one_mult_self
% 5.68/5.97 thf(fact_5187_minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.68/5.97 = one_one_Code_integer ) ).
% 5.68/5.97
% 5.68/5.97 % minus_one_mult_self
% 5.68/5.97 thf(fact_5188_minus__one__mult__self,axiom,
% 5.68/5.97 ! [N: nat] :
% 5.68/5.97 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.68/5.97 = one_one_rat ) ).
% 5.68/5.97
% 5.68/5.97 % minus_one_mult_self
% 5.68/5.97 thf(fact_5189_mod__minus1__right,axiom,
% 5.68/5.97 ! [A: int] :
% 5.68/5.97 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.97 = zero_zero_int ) ).
% 5.68/5.97
% 5.68/5.97 % mod_minus1_right
% 5.68/5.97 thf(fact_5190_mod__minus1__right,axiom,
% 5.68/5.97 ! [A: code_integer] :
% 5.68/5.97 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.97 = zero_z3403309356797280102nteger ) ).
% 5.68/5.97
% 5.68/5.97 % mod_minus1_right
% 5.68/5.97 thf(fact_5191_max__number__of_I2_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(2)
% 5.68/5.97 thf(fact_5192_max__number__of_I2_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(2)
% 5.68/5.97 thf(fact_5193_max__number__of_I2_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(2)
% 5.68/5.97 thf(fact_5194_max__number__of_I2_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(2)
% 5.68/5.97 thf(fact_5195_max__number__of_I3_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.68/5.97 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.68/5.97 = ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.68/5.97 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(3)
% 5.68/5.97 thf(fact_5196_max__number__of_I3_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.68/5.97 = ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(3)
% 5.68/5.97 thf(fact_5197_max__number__of_I3_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.68/5.97 = ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(3)
% 5.68/5.97 thf(fact_5198_max__number__of_I3_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.68/5.97 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.68/5.97 = ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.68/5.97 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(3)
% 5.68/5.97 thf(fact_5199_max__number__of_I4_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(4)
% 5.68/5.97 thf(fact_5200_max__number__of_I4_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(4)
% 5.68/5.97 thf(fact_5201_max__number__of_I4_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(4)
% 5.68/5.97 thf(fact_5202_max__number__of_I4_J,axiom,
% 5.68/5.97 ! [U: num,V: num] :
% 5.68/5.97 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.68/5.97 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % max_number_of(4)
% 5.68/5.97 thf(fact_5203_semiring__norm_I168_J,axiom,
% 5.68/5.97 ! [V: num,W: num,Y2: real] :
% 5.68/5.97 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.68/5.97 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % semiring_norm(168)
% 5.68/5.97 thf(fact_5204_semiring__norm_I168_J,axiom,
% 5.68/5.97 ! [V: num,W: num,Y2: int] :
% 5.68/5.97 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.68/5.97 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % semiring_norm(168)
% 5.68/5.97 thf(fact_5205_semiring__norm_I168_J,axiom,
% 5.68/5.97 ! [V: num,W: num,Y2: complex] :
% 5.68/5.97 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.68/5.97 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % semiring_norm(168)
% 5.68/5.97 thf(fact_5206_semiring__norm_I168_J,axiom,
% 5.68/5.97 ! [V: num,W: num,Y2: code_integer] :
% 5.68/5.97 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.68/5.97 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % semiring_norm(168)
% 5.68/5.97 thf(fact_5207_semiring__norm_I168_J,axiom,
% 5.68/5.97 ! [V: num,W: num,Y2: rat] :
% 5.68/5.97 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.68/5.97 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.97
% 5.68/5.97 % semiring_norm(168)
% 5.68/5.97 thf(fact_5208_diff__numeral__simps_I2_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(2)
% 5.68/5.97 thf(fact_5209_diff__numeral__simps_I2_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(2)
% 5.68/5.97 thf(fact_5210_diff__numeral__simps_I2_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.97 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(2)
% 5.68/5.97 thf(fact_5211_diff__numeral__simps_I2_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.97 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(2)
% 5.68/5.97 thf(fact_5212_diff__numeral__simps_I2_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.97 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(2)
% 5.68/5.97 thf(fact_5213_diff__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.68/5.97 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(3)
% 5.68/5.97 thf(fact_5214_diff__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(3)
% 5.68/5.97 thf(fact_5215_diff__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.68/5.97 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(3)
% 5.68/5.97 thf(fact_5216_diff__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.97 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.68/5.97 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.68/5.97
% 5.68/5.97 % diff_numeral_simps(3)
% 5.68/5.97 thf(fact_5217_diff__numeral__simps_I3_J,axiom,
% 5.68/5.97 ! [M: num,N: num] :
% 5.68/5.98 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_simps(3)
% 5.68/5.98 thf(fact_5218_mult__neg__numeral__simps_I1_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(1)
% 5.68/5.98 thf(fact_5219_mult__neg__numeral__simps_I1_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(1)
% 5.68/5.98 thf(fact_5220_mult__neg__numeral__simps_I1_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.98 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(1)
% 5.68/5.98 thf(fact_5221_mult__neg__numeral__simps_I1_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.98 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(1)
% 5.68/5.98 thf(fact_5222_mult__neg__numeral__simps_I1_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(1)
% 5.68/5.98 thf(fact_5223_mult__neg__numeral__simps_I2_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(2)
% 5.68/5.98 thf(fact_5224_mult__neg__numeral__simps_I2_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(2)
% 5.68/5.98 thf(fact_5225_mult__neg__numeral__simps_I2_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(2)
% 5.68/5.98 thf(fact_5226_mult__neg__numeral__simps_I2_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(2)
% 5.68/5.98 thf(fact_5227_mult__neg__numeral__simps_I2_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(2)
% 5.68/5.98 thf(fact_5228_mult__neg__numeral__simps_I3_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(3)
% 5.68/5.98 thf(fact_5229_mult__neg__numeral__simps_I3_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(3)
% 5.68/5.98 thf(fact_5230_mult__neg__numeral__simps_I3_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(3)
% 5.68/5.98 thf(fact_5231_mult__neg__numeral__simps_I3_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(3)
% 5.68/5.98 thf(fact_5232_mult__neg__numeral__simps_I3_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_neg_numeral_simps(3)
% 5.68/5.98 thf(fact_5233_semiring__norm_I170_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: real] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y2 ) )
% 5.68/5.98 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(170)
% 5.68/5.98 thf(fact_5234_semiring__norm_I170_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: int] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y2 ) )
% 5.68/5.98 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(170)
% 5.68/5.98 thf(fact_5235_semiring__norm_I170_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y2 ) )
% 5.68/5.98 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(170)
% 5.68/5.98 thf(fact_5236_semiring__norm_I170_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y2 ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(170)
% 5.68/5.98 thf(fact_5237_semiring__norm_I170_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y2 ) )
% 5.68/5.98 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(170)
% 5.68/5.98 thf(fact_5238_semiring__norm_I171_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: real] :
% 5.68/5.98 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(171)
% 5.68/5.98 thf(fact_5239_semiring__norm_I171_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: int] :
% 5.68/5.98 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(171)
% 5.68/5.98 thf(fact_5240_semiring__norm_I171_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(171)
% 5.68/5.98 thf(fact_5241_semiring__norm_I171_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(171)
% 5.68/5.98 thf(fact_5242_semiring__norm_I171_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(171)
% 5.68/5.98 thf(fact_5243_semiring__norm_I172_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: real] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(172)
% 5.68/5.98 thf(fact_5244_semiring__norm_I172_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: int] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(172)
% 5.68/5.98 thf(fact_5245_semiring__norm_I172_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(172)
% 5.68/5.98 thf(fact_5246_semiring__norm_I172_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(172)
% 5.68/5.98 thf(fact_5247_semiring__norm_I172_J,axiom,
% 5.68/5.98 ! [V: num,W: num,Y2: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y2 ) )
% 5.68/5.98 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(172)
% 5.68/5.98 thf(fact_5248_neg__numeral__le__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_iff
% 5.68/5.98 thf(fact_5249_neg__numeral__le__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_iff
% 5.68/5.98 thf(fact_5250_neg__numeral__le__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_iff
% 5.68/5.98 thf(fact_5251_neg__numeral__le__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.98 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_iff
% 5.68/5.98 thf(fact_5252_neg__numeral__less__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_iff
% 5.68/5.98 thf(fact_5253_neg__numeral__less__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_iff
% 5.68/5.98 thf(fact_5254_neg__numeral__less__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_iff
% 5.68/5.98 thf(fact_5255_neg__numeral__less__iff,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.98 = ( ord_less_num @ N @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_iff
% 5.68/5.98 thf(fact_5256_not__neg__one__le__neg__numeral__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_le_neg_numeral_iff
% 5.68/5.98 thf(fact_5257_not__neg__one__le__neg__numeral__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_le_neg_numeral_iff
% 5.68/5.98 thf(fact_5258_not__neg__one__le__neg__numeral__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_le_neg_numeral_iff
% 5.68/5.98 thf(fact_5259_not__neg__one__le__neg__numeral__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_le_neg_numeral_iff
% 5.68/5.98 thf(fact_5260_divide__le__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: real,W: num,A: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_le_eq_numeral1(2)
% 5.68/5.98 thf(fact_5261_divide__le__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: rat,W: num,A: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_le_eq_numeral1(2)
% 5.68/5.98 thf(fact_5262_le__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: real,B: real,W: num] :
% 5.68/5.98 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.68/5.98 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5263_le__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: rat,B: rat,W: num] :
% 5.68/5.98 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.68/5.98 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5264_divide__eq__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: real,W: num,A: real] :
% 5.68/5.98 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 != zero_zero_real )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.68/5.98 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 = zero_zero_real )
% 5.68/5.98 => ( A = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral1(2)
% 5.68/5.98 thf(fact_5265_divide__eq__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: complex,W: num,A: complex] :
% 5.68/5.98 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 != zero_zero_complex )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.68/5.98 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 = zero_zero_complex )
% 5.68/5.98 => ( A = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral1(2)
% 5.68/5.98 thf(fact_5266_divide__eq__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: rat,W: num,A: rat] :
% 5.68/5.98 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 != zero_zero_rat )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.68/5.98 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 = zero_zero_rat )
% 5.68/5.98 => ( A = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral1(2)
% 5.68/5.98 thf(fact_5267_eq__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: real,B: real,W: num] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.68/5.98 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 != zero_zero_real )
% 5.68/5.98 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 = zero_zero_real )
% 5.68/5.98 => ( A = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5268_eq__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: complex,B: complex,W: num] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.68/5.98 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 != zero_zero_complex )
% 5.68/5.98 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 = zero_zero_complex )
% 5.68/5.98 => ( A = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5269_eq__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: rat,B: rat,W: num] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.68/5.98 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 != zero_zero_rat )
% 5.68/5.98 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 = zero_zero_rat )
% 5.68/5.98 => ( A = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5270_neg__numeral__less__neg__one__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_neg_one_iff
% 5.68/5.98 thf(fact_5271_neg__numeral__less__neg__one__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_neg_one_iff
% 5.68/5.98 thf(fact_5272_neg__numeral__less__neg__one__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_neg_one_iff
% 5.68/5.98 thf(fact_5273_neg__numeral__less__neg__one__iff,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.98 = ( M != one ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_neg_one_iff
% 5.68/5.98 thf(fact_5274_divide__less__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: real,W: num,A: real] :
% 5.68/5.98 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.68/5.98 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_less_eq_numeral1(2)
% 5.68/5.98 thf(fact_5275_divide__less__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [B: rat,W: num,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.68/5.98 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_less_eq_numeral1(2)
% 5.68/5.98 thf(fact_5276_less__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: real,B: real,W: num] :
% 5.68/5.98 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.68/5.98 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5277_less__divide__eq__numeral1_I2_J,axiom,
% 5.68/5.98 ! [A: rat,B: rat,W: num] :
% 5.68/5.98 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.68/5.98 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_divide_eq_numeral1(2)
% 5.68/5.98 thf(fact_5278_power2__minus,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_minus
% 5.68/5.98 thf(fact_5279_power2__minus,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_minus
% 5.68/5.98 thf(fact_5280_power2__minus,axiom,
% 5.68/5.98 ! [A: complex] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_minus
% 5.68/5.98 thf(fact_5281_power2__minus,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_minus
% 5.68/5.98 thf(fact_5282_power2__minus,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_minus
% 5.68/5.98 thf(fact_5283_zero__less__power__abs__iff,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.68/5.98 = ( ( A != zero_z3403309356797280102nteger )
% 5.68/5.98 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_power_abs_iff
% 5.68/5.98 thf(fact_5284_zero__less__power__abs__iff,axiom,
% 5.68/5.98 ! [A: real,N: nat] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.68/5.98 = ( ( A != zero_zero_real )
% 5.68/5.98 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_power_abs_iff
% 5.68/5.98 thf(fact_5285_zero__less__power__abs__iff,axiom,
% 5.68/5.98 ! [A: rat,N: nat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.68/5.98 = ( ( A != zero_zero_rat )
% 5.68/5.98 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_power_abs_iff
% 5.68/5.98 thf(fact_5286_zero__less__power__abs__iff,axiom,
% 5.68/5.98 ! [A: int,N: nat] :
% 5.68/5.98 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.68/5.98 = ( ( A != zero_zero_int )
% 5.68/5.98 | ( N = zero_zero_nat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_power_abs_iff
% 5.68/5.98 thf(fact_5287_abs__power2,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_power2
% 5.68/5.98 thf(fact_5288_abs__power2,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_power2
% 5.68/5.98 thf(fact_5289_abs__power2,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_power2
% 5.68/5.98 thf(fact_5290_abs__power2,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_power2
% 5.68/5.98 thf(fact_5291_power2__abs,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_abs
% 5.68/5.98 thf(fact_5292_power2__abs,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_abs
% 5.68/5.98 thf(fact_5293_power2__abs,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_abs
% 5.68/5.98 thf(fact_5294_power2__abs,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_abs
% 5.68/5.98 thf(fact_5295_add__neg__numeral__special_I9_J,axiom,
% 5.68/5.98 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_neg_numeral_special(9)
% 5.68/5.98 thf(fact_5296_add__neg__numeral__special_I9_J,axiom,
% 5.68/5.98 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_neg_numeral_special(9)
% 5.68/5.98 thf(fact_5297_add__neg__numeral__special_I9_J,axiom,
% 5.68/5.98 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_neg_numeral_special(9)
% 5.68/5.98 thf(fact_5298_add__neg__numeral__special_I9_J,axiom,
% 5.68/5.98 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_neg_numeral_special(9)
% 5.68/5.98 thf(fact_5299_add__neg__numeral__special_I9_J,axiom,
% 5.68/5.98 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_neg_numeral_special(9)
% 5.68/5.98 thf(fact_5300_diff__numeral__special_I11_J,axiom,
% 5.68/5.98 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.98 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(11)
% 5.68/5.98 thf(fact_5301_diff__numeral__special_I11_J,axiom,
% 5.68/5.98 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(11)
% 5.68/5.98 thf(fact_5302_diff__numeral__special_I11_J,axiom,
% 5.68/5.98 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.98 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(11)
% 5.68/5.98 thf(fact_5303_diff__numeral__special_I11_J,axiom,
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.98 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(11)
% 5.68/5.98 thf(fact_5304_diff__numeral__special_I11_J,axiom,
% 5.68/5.98 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.98 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(11)
% 5.68/5.98 thf(fact_5305_diff__numeral__special_I10_J,axiom,
% 5.68/5.98 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(10)
% 5.68/5.98 thf(fact_5306_diff__numeral__special_I10_J,axiom,
% 5.68/5.98 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(10)
% 5.68/5.98 thf(fact_5307_diff__numeral__special_I10_J,axiom,
% 5.68/5.98 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(10)
% 5.68/5.98 thf(fact_5308_diff__numeral__special_I10_J,axiom,
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(10)
% 5.68/5.98 thf(fact_5309_diff__numeral__special_I10_J,axiom,
% 5.68/5.98 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(10)
% 5.68/5.98 thf(fact_5310_minus__1__div__2__eq,axiom,
% 5.68/5.98 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_1_div_2_eq
% 5.68/5.98 thf(fact_5311_minus__1__div__2__eq,axiom,
% 5.68/5.98 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_1_div_2_eq
% 5.68/5.98 thf(fact_5312_minus__1__mod__2__eq,axiom,
% 5.68/5.98 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_int ) ).
% 5.68/5.98
% 5.68/5.98 % minus_1_mod_2_eq
% 5.68/5.98 thf(fact_5313_minus__1__mod__2__eq,axiom,
% 5.68/5.98 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_Code_integer ) ).
% 5.68/5.98
% 5.68/5.98 % minus_1_mod_2_eq
% 5.68/5.98 thf(fact_5314_bits__minus__1__mod__2__eq,axiom,
% 5.68/5.98 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_int ) ).
% 5.68/5.98
% 5.68/5.98 % bits_minus_1_mod_2_eq
% 5.68/5.98 thf(fact_5315_bits__minus__1__mod__2__eq,axiom,
% 5.68/5.98 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_Code_integer ) ).
% 5.68/5.98
% 5.68/5.98 % bits_minus_1_mod_2_eq
% 5.68/5.98 thf(fact_5316_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [A: real,N: nat] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Power.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5317_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [A: int,N: nat] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Power.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5318_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [A: complex,N: nat] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Power.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5319_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Power.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5320_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [A: rat,N: nat] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Power.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5321_power__minus__odd,axiom,
% 5.68/5.98 ! [N: nat,A: real] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_odd
% 5.68/5.98 thf(fact_5322_power__minus__odd,axiom,
% 5.68/5.98 ! [N: nat,A: int] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_odd
% 5.68/5.98 thf(fact_5323_power__minus__odd,axiom,
% 5.68/5.98 ! [N: nat,A: complex] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_odd
% 5.68/5.98 thf(fact_5324_power__minus__odd,axiom,
% 5.68/5.98 ! [N: nat,A: code_integer] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_odd
% 5.68/5.98 thf(fact_5325_power__minus__odd,axiom,
% 5.68/5.98 ! [N: nat,A: rat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_odd
% 5.68/5.98 thf(fact_5326_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [N: nat,A: real] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.68/5.98 = ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Parity.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5327_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [N: nat,A: int] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.68/5.98 = ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Parity.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5328_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [N: nat,A: complex] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.68/5.98 = ( power_power_complex @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Parity.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5329_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [N: nat,A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Parity.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5330_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.68/5.98 ! [N: nat,A: rat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.68/5.98 = ( power_power_rat @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Parity.ring_1_class.power_minus_even
% 5.68/5.98 thf(fact_5331_power__even__abs__numeral,axiom,
% 5.68/5.98 ! [W: num,A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs_numeral
% 5.68/5.98 thf(fact_5332_power__even__abs__numeral,axiom,
% 5.68/5.98 ! [W: num,A: rat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs_numeral
% 5.68/5.98 thf(fact_5333_power__even__abs__numeral,axiom,
% 5.68/5.98 ! [W: num,A: real] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs_numeral
% 5.68/5.98 thf(fact_5334_power__even__abs__numeral,axiom,
% 5.68/5.98 ! [W: num,A: int] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.68/5.98 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs_numeral
% 5.68/5.98 thf(fact_5335_diff__numeral__special_I3_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(3)
% 5.68/5.98 thf(fact_5336_diff__numeral__special_I3_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(3)
% 5.68/5.98 thf(fact_5337_diff__numeral__special_I3_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.68/5.98 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(3)
% 5.68/5.98 thf(fact_5338_diff__numeral__special_I3_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.68/5.98 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(3)
% 5.68/5.98 thf(fact_5339_diff__numeral__special_I3_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/5.98 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(3)
% 5.68/5.98 thf(fact_5340_diff__numeral__special_I4_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(4)
% 5.68/5.98 thf(fact_5341_diff__numeral__special_I4_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(4)
% 5.68/5.98 thf(fact_5342_diff__numeral__special_I4_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(4)
% 5.68/5.98 thf(fact_5343_diff__numeral__special_I4_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(4)
% 5.68/5.98 thf(fact_5344_diff__numeral__special_I4_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_numeral_special(4)
% 5.68/5.98 thf(fact_5345_signed__take__bit__Suc__minus__bit0,axiom,
% 5.68/5.98 ! [N: nat,K: num] :
% 5.68/5.98 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/5.98 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_Suc_minus_bit0
% 5.68/5.98 thf(fact_5346_dbl__simps_I4_J,axiom,
% 5.68/5.98 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dbl_simps(4)
% 5.68/5.98 thf(fact_5347_dbl__simps_I4_J,axiom,
% 5.68/5.98 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dbl_simps(4)
% 5.68/5.98 thf(fact_5348_dbl__simps_I4_J,axiom,
% 5.68/5.98 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dbl_simps(4)
% 5.68/5.98 thf(fact_5349_dbl__simps_I4_J,axiom,
% 5.68/5.98 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dbl_simps(4)
% 5.68/5.98 thf(fact_5350_dbl__simps_I4_J,axiom,
% 5.68/5.98 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dbl_simps(4)
% 5.68/5.98 thf(fact_5351_power__minus1__even,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = one_one_real ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_even
% 5.68/5.98 thf(fact_5352_power__minus1__even,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = one_one_int ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_even
% 5.68/5.98 thf(fact_5353_power__minus1__even,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = one_one_complex ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_even
% 5.68/5.98 thf(fact_5354_power__minus1__even,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = one_one_Code_integer ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_even
% 5.68/5.98 thf(fact_5355_power__minus1__even,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = one_one_rat ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_even
% 5.68/5.98 thf(fact_5356_neg__one__odd__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_odd_power
% 5.68/5.98 thf(fact_5357_neg__one__odd__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_odd_power
% 5.68/5.98 thf(fact_5358_neg__one__odd__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_odd_power
% 5.68/5.98 thf(fact_5359_neg__one__odd__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_odd_power
% 5.68/5.98 thf(fact_5360_neg__one__odd__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_odd_power
% 5.68/5.98 thf(fact_5361_neg__one__even__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.68/5.98 = one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_even_power
% 5.68/5.98 thf(fact_5362_neg__one__even__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.68/5.98 = one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_even_power
% 5.68/5.98 thf(fact_5363_neg__one__even__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.68/5.98 = one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_even_power
% 5.68/5.98 thf(fact_5364_neg__one__even__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.68/5.98 = one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_even_power
% 5.68/5.98 thf(fact_5365_neg__one__even__power,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.68/5.98 = one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_even_power
% 5.68/5.98 thf(fact_5366_signed__take__bit__0,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_0
% 5.68/5.98 thf(fact_5367_signed__take__bit__0,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.68/5.98 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_0
% 5.68/5.98 thf(fact_5368_abs__leI,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ A @ B )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_leI
% 5.68/5.98 thf(fact_5369_abs__leI,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.68/5.98 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_leI
% 5.68/5.98 thf(fact_5370_abs__leI,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.98 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_leI
% 5.68/5.98 thf(fact_5371_abs__leI,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.98 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_leI
% 5.68/5.98 thf(fact_5372_abs__le__D2,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D2
% 5.68/5.98 thf(fact_5373_abs__le__D2,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D2
% 5.68/5.98 thf(fact_5374_abs__le__D2,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D2
% 5.68/5.98 thf(fact_5375_abs__le__D2,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D2
% 5.68/5.98 thf(fact_5376_abs__le__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_eq_real @ A @ B )
% 5.68/5.98 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_iff
% 5.68/5.98 thf(fact_5377_abs__le__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.68/5.98 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.68/5.98 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_iff
% 5.68/5.98 thf(fact_5378_abs__le__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.98 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_iff
% 5.68/5.98 thf(fact_5379_abs__le__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_eq_int @ A @ B )
% 5.68/5.98 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_iff
% 5.68/5.98 thf(fact_5380_abs__ge__minus__self,axiom,
% 5.68/5.98 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_minus_self
% 5.68/5.98 thf(fact_5381_abs__ge__minus__self,axiom,
% 5.68/5.98 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_minus_self
% 5.68/5.98 thf(fact_5382_abs__ge__minus__self,axiom,
% 5.68/5.98 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_minus_self
% 5.68/5.98 thf(fact_5383_abs__ge__minus__self,axiom,
% 5.68/5.98 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_minus_self
% 5.68/5.98 thf(fact_5384_dvd__antisym,axiom,
% 5.68/5.98 ! [M: nat,N: nat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ M @ N )
% 5.68/5.98 => ( ( dvd_dvd_nat @ N @ M )
% 5.68/5.98 => ( M = N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_antisym
% 5.68/5.98 thf(fact_5385_signed__take__bit__minus,axiom,
% 5.68/5.98 ! [N: nat,K: int] :
% 5.68/5.98 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.68/5.98 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_minus
% 5.68/5.98 thf(fact_5386_abs__less__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_real @ A @ B )
% 5.68/5.98 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_less_iff
% 5.68/5.98 thf(fact_5387_abs__less__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_int @ A @ B )
% 5.68/5.98 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_less_iff
% 5.68/5.98 thf(fact_5388_abs__less__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.68/5.98 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.68/5.98 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_less_iff
% 5.68/5.98 thf(fact_5389_abs__less__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.68/5.98 = ( ( ord_less_rat @ A @ B )
% 5.68/5.98 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_less_iff
% 5.68/5.98 thf(fact_5390_equation__minus__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % equation_minus_iff
% 5.68/5.98 thf(fact_5391_equation__minus__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % equation_minus_iff
% 5.68/5.98 thf(fact_5392_equation__minus__iff,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % equation_minus_iff
% 5.68/5.98 thf(fact_5393_equation__minus__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % equation_minus_iff
% 5.68/5.98 thf(fact_5394_equation__minus__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % equation_minus_iff
% 5.68/5.98 thf(fact_5395_minus__equation__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( uminus_uminus_real @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( uminus_uminus_real @ B )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_equation_iff
% 5.68/5.98 thf(fact_5396_minus__equation__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( uminus_uminus_int @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( uminus_uminus_int @ B )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_equation_iff
% 5.68/5.98 thf(fact_5397_minus__equation__iff,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( uminus1482373934393186551omplex @ B )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_equation_iff
% 5.68/5.98 thf(fact_5398_minus__equation__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( uminus1351360451143612070nteger @ B )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_equation_iff
% 5.68/5.98 thf(fact_5399_minus__equation__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( uminus_uminus_rat @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( uminus_uminus_rat @ B )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_equation_iff
% 5.68/5.98 thf(fact_5400_abs__eq__iff_H,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( abs_abs_real @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.68/5.98 & ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_iff'
% 5.68/5.98 thf(fact_5401_abs__eq__iff_H,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( abs_abs_Code_integer @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.68/5.98 & ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_iff'
% 5.68/5.98 thf(fact_5402_abs__eq__iff_H,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( abs_abs_rat @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.68/5.98 & ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_iff'
% 5.68/5.98 thf(fact_5403_abs__eq__iff_H,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( abs_abs_int @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.68/5.98 & ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_iff'
% 5.68/5.98 thf(fact_5404_eq__abs__iff_H,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( abs_abs_real @ B ) )
% 5.68/5.98 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/5.98 & ( ( B = A )
% 5.68/5.98 | ( B
% 5.68/5.98 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_abs_iff'
% 5.68/5.98 thf(fact_5405_eq__abs__iff_H,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( abs_abs_Code_integer @ B ) )
% 5.68/5.98 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.68/5.98 & ( ( B = A )
% 5.68/5.98 | ( B
% 5.68/5.98 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_abs_iff'
% 5.68/5.98 thf(fact_5406_eq__abs__iff_H,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( abs_abs_rat @ B ) )
% 5.68/5.98 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.68/5.98 & ( ( B = A )
% 5.68/5.98 | ( B
% 5.68/5.98 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_abs_iff'
% 5.68/5.98 thf(fact_5407_eq__abs__iff_H,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( abs_abs_int @ B ) )
% 5.68/5.98 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.68/5.98 & ( ( B = A )
% 5.68/5.98 | ( B
% 5.68/5.98 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_abs_iff'
% 5.68/5.98 thf(fact_5408_abs__minus__le__zero,axiom,
% 5.68/5.98 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_le_zero
% 5.68/5.98 thf(fact_5409_abs__minus__le__zero,axiom,
% 5.68/5.98 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_le_zero
% 5.68/5.98 thf(fact_5410_abs__minus__le__zero,axiom,
% 5.68/5.98 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_le_zero
% 5.68/5.98 thf(fact_5411_abs__minus__le__zero,axiom,
% 5.68/5.98 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_le_zero
% 5.68/5.98 thf(fact_5412_abs__if__raw,axiom,
% 5.68/5.98 ( abs_abs_real
% 5.68/5.98 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if_raw
% 5.68/5.98 thf(fact_5413_abs__if__raw,axiom,
% 5.68/5.98 ( abs_abs_int
% 5.68/5.98 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if_raw
% 5.68/5.98 thf(fact_5414_abs__if__raw,axiom,
% 5.68/5.98 ( abs_abs_Code_integer
% 5.68/5.98 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if_raw
% 5.68/5.98 thf(fact_5415_abs__if__raw,axiom,
% 5.68/5.98 ( abs_abs_rat
% 5.68/5.98 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if_raw
% 5.68/5.98 thf(fact_5416_abs__if,axiom,
% 5.68/5.98 ( abs_abs_real
% 5.68/5.98 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if
% 5.68/5.98 thf(fact_5417_abs__if,axiom,
% 5.68/5.98 ( abs_abs_int
% 5.68/5.98 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if
% 5.68/5.98 thf(fact_5418_abs__if,axiom,
% 5.68/5.98 ( abs_abs_Code_integer
% 5.68/5.98 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if
% 5.68/5.98 thf(fact_5419_abs__if,axiom,
% 5.68/5.98 ( abs_abs_rat
% 5.68/5.98 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_if
% 5.68/5.98 thf(fact_5420_abs__of__neg,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( ord_less_real @ A @ zero_zero_real )
% 5.68/5.98 => ( ( abs_abs_real @ A )
% 5.68/5.98 = ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_neg
% 5.68/5.98 thf(fact_5421_abs__of__neg,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( ord_less_int @ A @ zero_zero_int )
% 5.68/5.98 => ( ( abs_abs_int @ A )
% 5.68/5.98 = ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_neg
% 5.68/5.98 thf(fact_5422_abs__of__neg,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.68/5.98 => ( ( abs_abs_Code_integer @ A )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_neg
% 5.68/5.98 thf(fact_5423_abs__of__neg,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.68/5.98 => ( ( abs_abs_rat @ A )
% 5.68/5.98 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_neg
% 5.68/5.98 thf(fact_5424_abs__real__def,axiom,
% 5.68/5.98 ( abs_abs_real
% 5.68/5.98 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_real_def
% 5.68/5.98 thf(fact_5425_abs__ge__self,axiom,
% 5.68/5.98 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_self
% 5.68/5.98 thf(fact_5426_abs__ge__self,axiom,
% 5.68/5.98 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_self
% 5.68/5.98 thf(fact_5427_abs__ge__self,axiom,
% 5.68/5.98 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_self
% 5.68/5.98 thf(fact_5428_abs__ge__self,axiom,
% 5.68/5.98 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_self
% 5.68/5.98 thf(fact_5429_abs__le__D1,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D1
% 5.68/5.98 thf(fact_5430_abs__le__D1,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D1
% 5.68/5.98 thf(fact_5431_abs__le__D1,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D1
% 5.68/5.98 thf(fact_5432_abs__le__D1,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.68/5.98 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_D1
% 5.68/5.98 thf(fact_5433_abs__mult,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult
% 5.68/5.98 thf(fact_5434_abs__mult,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.68/5.98 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult
% 5.68/5.98 thf(fact_5435_abs__mult,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.68/5.98 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult
% 5.68/5.98 thf(fact_5436_abs__mult,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.68/5.98 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult
% 5.68/5.98 thf(fact_5437_abs__minus__commute,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.68/5.98 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_commute
% 5.68/5.98 thf(fact_5438_abs__minus__commute,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.68/5.98 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_commute
% 5.68/5.98 thf(fact_5439_abs__minus__commute,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.68/5.98 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_commute
% 5.68/5.98 thf(fact_5440_abs__minus__commute,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.68/5.98 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_minus_commute
% 5.68/5.98 thf(fact_5441_power__abs,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] :
% 5.68/5.98 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_abs
% 5.68/5.98 thf(fact_5442_power__abs,axiom,
% 5.68/5.98 ! [A: rat,N: nat] :
% 5.68/5.98 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.68/5.98 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_abs
% 5.68/5.98 thf(fact_5443_power__abs,axiom,
% 5.68/5.98 ! [A: real,N: nat] :
% 5.68/5.98 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.68/5.98 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_abs
% 5.68/5.98 thf(fact_5444_power__abs,axiom,
% 5.68/5.98 ! [A: int,N: nat] :
% 5.68/5.98 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.68/5.98 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_abs
% 5.68/5.98 thf(fact_5445_le__imp__neg__le,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ A @ B )
% 5.68/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_imp_neg_le
% 5.68/5.98 thf(fact_5446_le__imp__neg__le,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_imp_neg_le
% 5.68/5.98 thf(fact_5447_le__imp__neg__le,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ A @ B )
% 5.68/5.98 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_imp_neg_le
% 5.68/5.98 thf(fact_5448_le__imp__neg__le,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ A @ B )
% 5.68/5.98 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_imp_neg_le
% 5.68/5.98 thf(fact_5449_minus__le__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.98 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_le_iff
% 5.68/5.98 thf(fact_5450_minus__le__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_le_iff
% 5.68/5.98 thf(fact_5451_minus__le__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.98 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_le_iff
% 5.68/5.98 thf(fact_5452_minus__le__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_le_iff
% 5.68/5.98 thf(fact_5453_le__minus__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_iff
% 5.68/5.98 thf(fact_5454_le__minus__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_iff
% 5.68/5.98 thf(fact_5455_le__minus__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_iff
% 5.68/5.98 thf(fact_5456_le__minus__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_iff
% 5.68/5.98 thf(fact_5457_compl__mono,axiom,
% 5.68/5.98 ! [X: set_int,Y2: set_int] :
% 5.68/5.98 ( ( ord_less_eq_set_int @ X @ Y2 )
% 5.68/5.98 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y2 ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % compl_mono
% 5.68/5.98 thf(fact_5458_compl__le__swap1,axiom,
% 5.68/5.98 ! [Y2: set_int,X: set_int] :
% 5.68/5.98 ( ( ord_less_eq_set_int @ Y2 @ ( uminus1532241313380277803et_int @ X ) )
% 5.68/5.98 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y2 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % compl_le_swap1
% 5.68/5.98 thf(fact_5459_compl__le__swap2,axiom,
% 5.68/5.98 ! [Y2: set_int,X: set_int] :
% 5.68/5.98 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y2 ) @ X )
% 5.68/5.98 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % compl_le_swap2
% 5.68/5.98 thf(fact_5460_verit__negate__coefficient_I2_J,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ A @ B )
% 5.68/5.98 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % verit_negate_coefficient(2)
% 5.68/5.98 thf(fact_5461_verit__negate__coefficient_I2_J,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_int @ A @ B )
% 5.68/5.98 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % verit_negate_coefficient(2)
% 5.68/5.98 thf(fact_5462_verit__negate__coefficient_I2_J,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.68/5.98 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % verit_negate_coefficient(2)
% 5.68/5.98 thf(fact_5463_verit__negate__coefficient_I2_J,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ A @ B )
% 5.68/5.98 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % verit_negate_coefficient(2)
% 5.68/5.98 thf(fact_5464_less__minus__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_iff
% 5.68/5.98 thf(fact_5465_less__minus__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_iff
% 5.68/5.98 thf(fact_5466_less__minus__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_iff
% 5.68/5.98 thf(fact_5467_less__minus__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_iff
% 5.68/5.98 thf(fact_5468_minus__less__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.98 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_less_iff
% 5.68/5.98 thf(fact_5469_minus__less__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_less_iff
% 5.68/5.98 thf(fact_5470_minus__less__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_less_iff
% 5.68/5.98 thf(fact_5471_minus__less__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.98 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_less_iff
% 5.68/5.98 thf(fact_5472_neg__numeral__neq__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.68/5.98 != ( numeral_numeral_real @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_neq_numeral
% 5.68/5.98 thf(fact_5473_neg__numeral__neq__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.68/5.98 != ( numeral_numeral_int @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_neq_numeral
% 5.68/5.98 thf(fact_5474_neg__numeral__neq__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.68/5.98 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_neq_numeral
% 5.68/5.98 thf(fact_5475_neg__numeral__neq__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.68/5.98 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_neq_numeral
% 5.68/5.98 thf(fact_5476_neg__numeral__neq__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.68/5.98 != ( numeral_numeral_rat @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_neq_numeral
% 5.68/5.98 thf(fact_5477_numeral__neq__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( numeral_numeral_real @ M )
% 5.68/5.98 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_numeral
% 5.68/5.98 thf(fact_5478_numeral__neq__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( numeral_numeral_int @ M )
% 5.68/5.98 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_numeral
% 5.68/5.98 thf(fact_5479_numeral__neq__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( numera6690914467698888265omplex @ M )
% 5.68/5.98 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_numeral
% 5.68/5.98 thf(fact_5480_numeral__neq__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( numera6620942414471956472nteger @ M )
% 5.68/5.98 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_numeral
% 5.68/5.98 thf(fact_5481_numeral__neq__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( numeral_numeral_rat @ M )
% 5.68/5.98 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_numeral
% 5.68/5.98 thf(fact_5482_minus__mult__commute,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.98 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mult_commute
% 5.68/5.98 thf(fact_5483_minus__mult__commute,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mult_commute
% 5.68/5.98 thf(fact_5484_minus__mult__commute,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.68/5.98 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mult_commute
% 5.68/5.98 thf(fact_5485_minus__mult__commute,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mult_commute
% 5.68/5.98 thf(fact_5486_minus__mult__commute,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.98 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mult_commute
% 5.68/5.98 thf(fact_5487_square__eq__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( times_times_real @ A @ A )
% 5.68/5.98 = ( times_times_real @ B @ B ) )
% 5.68/5.98 = ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_iff
% 5.68/5.98 thf(fact_5488_square__eq__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( times_times_int @ A @ A )
% 5.68/5.98 = ( times_times_int @ B @ B ) )
% 5.68/5.98 = ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_iff
% 5.68/5.98 thf(fact_5489_square__eq__iff,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( times_times_complex @ A @ A )
% 5.68/5.98 = ( times_times_complex @ B @ B ) )
% 5.68/5.98 = ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_iff
% 5.68/5.98 thf(fact_5490_square__eq__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.68/5.98 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.68/5.98 = ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_iff
% 5.68/5.98 thf(fact_5491_square__eq__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( times_times_rat @ A @ A )
% 5.68/5.98 = ( times_times_rat @ B @ B ) )
% 5.68/5.98 = ( ( A = B )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_iff
% 5.68/5.98 thf(fact_5492_one__neq__neg__one,axiom,
% 5.68/5.98 ( one_one_real
% 5.68/5.98 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_one
% 5.68/5.98 thf(fact_5493_one__neq__neg__one,axiom,
% 5.68/5.98 ( one_one_int
% 5.68/5.98 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_one
% 5.68/5.98 thf(fact_5494_one__neq__neg__one,axiom,
% 5.68/5.98 ( one_one_complex
% 5.68/5.98 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_one
% 5.68/5.98 thf(fact_5495_one__neq__neg__one,axiom,
% 5.68/5.98 ( one_one_Code_integer
% 5.68/5.98 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_one
% 5.68/5.98 thf(fact_5496_one__neq__neg__one,axiom,
% 5.68/5.98 ( one_one_rat
% 5.68/5.98 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_one
% 5.68/5.98 thf(fact_5497_is__num__normalize_I8_J,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.68/5.98 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % is_num_normalize(8)
% 5.68/5.98 thf(fact_5498_is__num__normalize_I8_J,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.68/5.98 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % is_num_normalize(8)
% 5.68/5.98 thf(fact_5499_is__num__normalize_I8_J,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.68/5.98 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % is_num_normalize(8)
% 5.68/5.98 thf(fact_5500_is__num__normalize_I8_J,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % is_num_normalize(8)
% 5.68/5.98 thf(fact_5501_is__num__normalize_I8_J,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.68/5.98 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % is_num_normalize(8)
% 5.68/5.98 thf(fact_5502_add_Oinverse__distrib__swap,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.68/5.98 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_distrib_swap
% 5.68/5.98 thf(fact_5503_add_Oinverse__distrib__swap,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.68/5.98 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_distrib_swap
% 5.68/5.98 thf(fact_5504_add_Oinverse__distrib__swap,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.68/5.98 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_distrib_swap
% 5.68/5.98 thf(fact_5505_add_Oinverse__distrib__swap,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_distrib_swap
% 5.68/5.98 thf(fact_5506_add_Oinverse__distrib__swap,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.68/5.98 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_distrib_swap
% 5.68/5.98 thf(fact_5507_group__cancel_Oneg1,axiom,
% 5.68/5.98 ! [A2: real,K: real,A: real] :
% 5.68/5.98 ( ( A2
% 5.68/5.98 = ( plus_plus_real @ K @ A ) )
% 5.68/5.98 => ( ( uminus_uminus_real @ A2 )
% 5.68/5.98 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.neg1
% 5.68/5.98 thf(fact_5508_group__cancel_Oneg1,axiom,
% 5.68/5.98 ! [A2: int,K: int,A: int] :
% 5.68/5.98 ( ( A2
% 5.68/5.98 = ( plus_plus_int @ K @ A ) )
% 5.68/5.98 => ( ( uminus_uminus_int @ A2 )
% 5.68/5.98 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.neg1
% 5.68/5.98 thf(fact_5509_group__cancel_Oneg1,axiom,
% 5.68/5.98 ! [A2: complex,K: complex,A: complex] :
% 5.68/5.98 ( ( A2
% 5.68/5.98 = ( plus_plus_complex @ K @ A ) )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.68/5.98 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.neg1
% 5.68/5.98 thf(fact_5510_group__cancel_Oneg1,axiom,
% 5.68/5.98 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.68/5.98 ( ( A2
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.68/5.98 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.neg1
% 5.68/5.98 thf(fact_5511_group__cancel_Oneg1,axiom,
% 5.68/5.98 ! [A2: rat,K: rat,A: rat] :
% 5.68/5.98 ( ( A2
% 5.68/5.98 = ( plus_plus_rat @ K @ A ) )
% 5.68/5.98 => ( ( uminus_uminus_rat @ A2 )
% 5.68/5.98 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.neg1
% 5.68/5.98 thf(fact_5512_minus__diff__commute,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.68/5.98 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_commute
% 5.68/5.98 thf(fact_5513_minus__diff__commute,axiom,
% 5.68/5.98 ! [B: int,A: int] :
% 5.68/5.98 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.68/5.98 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_commute
% 5.68/5.98 thf(fact_5514_minus__diff__commute,axiom,
% 5.68/5.98 ! [B: complex,A: complex] :
% 5.68/5.98 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.68/5.98 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_commute
% 5.68/5.98 thf(fact_5515_minus__diff__commute,axiom,
% 5.68/5.98 ! [B: code_integer,A: code_integer] :
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.68/5.98 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_commute
% 5.68/5.98 thf(fact_5516_minus__diff__commute,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.68/5.98 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_commute
% 5.68/5.98 thf(fact_5517_minus__diff__minus,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_minus
% 5.68/5.98 thf(fact_5518_minus__diff__minus,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_minus
% 5.68/5.98 thf(fact_5519_minus__diff__minus,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_minus
% 5.68/5.98 thf(fact_5520_minus__diff__minus,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_minus
% 5.68/5.98 thf(fact_5521_minus__diff__minus,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_diff_minus
% 5.68/5.98 thf(fact_5522_div__minus__right,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % div_minus_right
% 5.68/5.98 thf(fact_5523_div__minus__right,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % div_minus_right
% 5.68/5.98 thf(fact_5524_minus__divide__right,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.98 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_right
% 5.68/5.98 thf(fact_5525_minus__divide__right,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_right
% 5.68/5.98 thf(fact_5526_minus__divide__right,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_right
% 5.68/5.98 thf(fact_5527_minus__divide__divide,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( divide_divide_real @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_divide
% 5.68/5.98 thf(fact_5528_minus__divide__divide,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_divide
% 5.68/5.98 thf(fact_5529_minus__divide__divide,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ A @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_divide
% 5.68/5.98 thf(fact_5530_minus__divide__left,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.98 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_left
% 5.68/5.98 thf(fact_5531_minus__divide__left,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_left
% 5.68/5.98 thf(fact_5532_minus__divide__left,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_left
% 5.68/5.98 thf(fact_5533_mod__minus__eq,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.68/5.98 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_eq
% 5.68/5.98 thf(fact_5534_mod__minus__eq,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.68/5.98 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_eq
% 5.68/5.98 thf(fact_5535_mod__minus__cong,axiom,
% 5.68/5.98 ! [A: int,B: int,A5: int] :
% 5.68/5.98 ( ( ( modulo_modulo_int @ A @ B )
% 5.68/5.98 = ( modulo_modulo_int @ A5 @ B ) )
% 5.68/5.98 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_cong
% 5.68/5.98 thf(fact_5536_mod__minus__cong,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer,A5: code_integer] :
% 5.68/5.98 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.68/5.98 = ( modulo364778990260209775nteger @ A5 @ B ) )
% 5.68/5.98 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_cong
% 5.68/5.98 thf(fact_5537_mod__minus__right,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_right
% 5.68/5.98 thf(fact_5538_mod__minus__right,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % mod_minus_right
% 5.68/5.98 thf(fact_5539_abs__ge__zero,axiom,
% 5.68/5.98 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_zero
% 5.68/5.98 thf(fact_5540_abs__ge__zero,axiom,
% 5.68/5.98 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_zero
% 5.68/5.98 thf(fact_5541_abs__ge__zero,axiom,
% 5.68/5.98 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_zero
% 5.68/5.98 thf(fact_5542_abs__ge__zero,axiom,
% 5.68/5.98 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ge_zero
% 5.68/5.98 thf(fact_5543_abs__of__pos,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.68/5.98 => ( ( abs_abs_Code_integer @ A )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_pos
% 5.68/5.98 thf(fact_5544_abs__of__pos,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/5.98 => ( ( abs_abs_real @ A )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_pos
% 5.68/5.98 thf(fact_5545_abs__of__pos,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.68/5.98 => ( ( abs_abs_rat @ A )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_pos
% 5.68/5.98 thf(fact_5546_abs__of__pos,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( ord_less_int @ zero_zero_int @ A )
% 5.68/5.98 => ( ( abs_abs_int @ A )
% 5.68/5.98 = A ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_of_pos
% 5.68/5.98 thf(fact_5547_abs__not__less__zero,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.68/5.98
% 5.68/5.98 % abs_not_less_zero
% 5.68/5.98 thf(fact_5548_abs__not__less__zero,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.68/5.98
% 5.68/5.98 % abs_not_less_zero
% 5.68/5.98 thf(fact_5549_abs__not__less__zero,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.68/5.98
% 5.68/5.98 % abs_not_less_zero
% 5.68/5.98 thf(fact_5550_abs__not__less__zero,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.68/5.98
% 5.68/5.98 % abs_not_less_zero
% 5.68/5.98 thf(fact_5551_abs__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq
% 5.68/5.98 thf(fact_5552_abs__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq
% 5.68/5.98 thf(fact_5553_abs__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq
% 5.68/5.98 thf(fact_5554_abs__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq
% 5.68/5.98 thf(fact_5555_abs__mult__less,axiom,
% 5.68/5.98 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.68/5.98 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.68/5.98 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_less
% 5.68/5.98 thf(fact_5556_abs__mult__less,axiom,
% 5.68/5.98 ! [A: real,C: real,B: real,D: real] :
% 5.68/5.98 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.68/5.98 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.68/5.98 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_less
% 5.68/5.98 thf(fact_5557_abs__mult__less,axiom,
% 5.68/5.98 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.68/5.98 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.68/5.98 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_less
% 5.68/5.98 thf(fact_5558_abs__mult__less,axiom,
% 5.68/5.98 ! [A: int,C: int,B: int,D: int] :
% 5.68/5.98 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.68/5.98 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.68/5.98 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_less
% 5.68/5.98 thf(fact_5559_abs__triangle__ineq2,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2
% 5.68/5.98 thf(fact_5560_abs__triangle__ineq2,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2
% 5.68/5.98 thf(fact_5561_abs__triangle__ineq2,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2
% 5.68/5.98 thf(fact_5562_abs__triangle__ineq2,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2
% 5.68/5.98 thf(fact_5563_abs__triangle__ineq3,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq3
% 5.68/5.98 thf(fact_5564_abs__triangle__ineq3,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq3
% 5.68/5.98 thf(fact_5565_abs__triangle__ineq3,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq3
% 5.68/5.98 thf(fact_5566_abs__triangle__ineq3,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq3
% 5.68/5.98 thf(fact_5567_abs__triangle__ineq2__sym,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2_sym
% 5.68/5.98 thf(fact_5568_abs__triangle__ineq2__sym,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2_sym
% 5.68/5.98 thf(fact_5569_abs__triangle__ineq2__sym,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2_sym
% 5.68/5.98 thf(fact_5570_abs__triangle__ineq2__sym,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq2_sym
% 5.68/5.98 thf(fact_5571_nonzero__abs__divide,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( B != zero_zero_real )
% 5.68/5.98 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.98 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_abs_divide
% 5.68/5.98 thf(fact_5572_nonzero__abs__divide,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( B != zero_zero_rat )
% 5.68/5.98 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_abs_divide
% 5.68/5.98 thf(fact_5573_neg__numeral__le__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_numeral
% 5.68/5.98 thf(fact_5574_neg__numeral__le__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_numeral
% 5.68/5.98 thf(fact_5575_neg__numeral__le__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_numeral
% 5.68/5.98 thf(fact_5576_neg__numeral__le__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_numeral
% 5.68/5.98 thf(fact_5577_not__numeral__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_numeral
% 5.68/5.98 thf(fact_5578_not__numeral__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_numeral
% 5.68/5.98 thf(fact_5579_not__numeral__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_numeral
% 5.68/5.98 thf(fact_5580_not__numeral__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_numeral
% 5.68/5.98 thf(fact_5581_zero__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( zero_zero_real
% 5.68/5.98 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_numeral
% 5.68/5.98 thf(fact_5582_zero__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( zero_zero_int
% 5.68/5.98 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_numeral
% 5.68/5.98 thf(fact_5583_zero__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( zero_zero_complex
% 5.68/5.98 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_numeral
% 5.68/5.98 thf(fact_5584_zero__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( zero_z3403309356797280102nteger
% 5.68/5.98 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_numeral
% 5.68/5.98 thf(fact_5585_zero__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( zero_zero_rat
% 5.68/5.98 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_numeral
% 5.68/5.98 thf(fact_5586_neg__numeral__less__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_numeral
% 5.68/5.98 thf(fact_5587_neg__numeral__less__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_numeral
% 5.68/5.98 thf(fact_5588_neg__numeral__less__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_numeral
% 5.68/5.98 thf(fact_5589_neg__numeral__less__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_numeral
% 5.68/5.98 thf(fact_5590_not__numeral__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_numeral
% 5.68/5.98 thf(fact_5591_not__numeral__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_numeral
% 5.68/5.98 thf(fact_5592_not__numeral__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_numeral
% 5.68/5.98 thf(fact_5593_not__numeral__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_numeral
% 5.68/5.98 thf(fact_5594_le__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(2)
% 5.68/5.98 thf(fact_5595_le__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(2)
% 5.68/5.98 thf(fact_5596_le__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(2)
% 5.68/5.98 thf(fact_5597_le__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(2)
% 5.68/5.98 thf(fact_5598_le__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(4)
% 5.68/5.98 thf(fact_5599_le__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(4)
% 5.68/5.98 thf(fact_5600_le__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(4)
% 5.68/5.98 thf(fact_5601_le__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(4)
% 5.68/5.98 thf(fact_5602_zero__neq__neg__one,axiom,
% 5.68/5.98 ( zero_zero_real
% 5.68/5.98 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_one
% 5.68/5.98 thf(fact_5603_zero__neq__neg__one,axiom,
% 5.68/5.98 ( zero_zero_int
% 5.68/5.98 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_one
% 5.68/5.98 thf(fact_5604_zero__neq__neg__one,axiom,
% 5.68/5.98 ( zero_zero_complex
% 5.68/5.98 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_one
% 5.68/5.98 thf(fact_5605_zero__neq__neg__one,axiom,
% 5.68/5.98 ( zero_z3403309356797280102nteger
% 5.68/5.98 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_one
% 5.68/5.98 thf(fact_5606_zero__neq__neg__one,axiom,
% 5.68/5.98 ( zero_zero_rat
% 5.68/5.98 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_neq_neg_one
% 5.68/5.98 thf(fact_5607_neg__eq__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( uminus_uminus_real @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( plus_plus_real @ A @ B )
% 5.68/5.98 = zero_zero_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_eq_iff_add_eq_0
% 5.68/5.98 thf(fact_5608_neg__eq__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( uminus_uminus_int @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( plus_plus_int @ A @ B )
% 5.68/5.98 = zero_zero_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_eq_iff_add_eq_0
% 5.68/5.98 thf(fact_5609_neg__eq__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( plus_plus_complex @ A @ B )
% 5.68/5.98 = zero_zero_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_eq_iff_add_eq_0
% 5.68/5.98 thf(fact_5610_neg__eq__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.68/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_eq_iff_add_eq_0
% 5.68/5.98 thf(fact_5611_neg__eq__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( uminus_uminus_rat @ A )
% 5.68/5.98 = B )
% 5.68/5.98 = ( ( plus_plus_rat @ A @ B )
% 5.68/5.98 = zero_zero_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_eq_iff_add_eq_0
% 5.68/5.98 thf(fact_5612_eq__neg__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( ( plus_plus_real @ A @ B )
% 5.68/5.98 = zero_zero_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_neg_iff_add_eq_0
% 5.68/5.98 thf(fact_5613_eq__neg__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( ( plus_plus_int @ A @ B )
% 5.68/5.98 = zero_zero_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_neg_iff_add_eq_0
% 5.68/5.98 thf(fact_5614_eq__neg__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( ( plus_plus_complex @ A @ B )
% 5.68/5.98 = zero_zero_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_neg_iff_add_eq_0
% 5.68/5.98 thf(fact_5615_eq__neg__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.68/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_neg_iff_add_eq_0
% 5.68/5.98 thf(fact_5616_eq__neg__iff__add__eq__0,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( ( plus_plus_rat @ A @ B )
% 5.68/5.98 = zero_zero_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_neg_iff_add_eq_0
% 5.68/5.98 thf(fact_5617_add_Oinverse__unique,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( plus_plus_real @ A @ B )
% 5.68/5.98 = zero_zero_real )
% 5.68/5.98 => ( ( uminus_uminus_real @ A )
% 5.68/5.98 = B ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_unique
% 5.68/5.98 thf(fact_5618_add_Oinverse__unique,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( plus_plus_int @ A @ B )
% 5.68/5.98 = zero_zero_int )
% 5.68/5.98 => ( ( uminus_uminus_int @ A )
% 5.68/5.98 = B ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_unique
% 5.68/5.98 thf(fact_5619_add_Oinverse__unique,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( plus_plus_complex @ A @ B )
% 5.68/5.98 = zero_zero_complex )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.98 = B ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_unique
% 5.68/5.98 thf(fact_5620_add_Oinverse__unique,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.68/5.98 = zero_z3403309356797280102nteger )
% 5.68/5.98 => ( ( uminus1351360451143612070nteger @ A )
% 5.68/5.98 = B ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_unique
% 5.68/5.98 thf(fact_5621_add_Oinverse__unique,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( plus_plus_rat @ A @ B )
% 5.68/5.98 = zero_zero_rat )
% 5.68/5.98 => ( ( uminus_uminus_rat @ A )
% 5.68/5.98 = B ) ) ).
% 5.68/5.98
% 5.68/5.98 % add.inverse_unique
% 5.68/5.98 thf(fact_5622_ab__group__add__class_Oab__left__minus,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.68/5.98 = zero_zero_real ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_left_minus
% 5.68/5.98 thf(fact_5623_ab__group__add__class_Oab__left__minus,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.68/5.98 = zero_zero_int ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_left_minus
% 5.68/5.98 thf(fact_5624_ab__group__add__class_Oab__left__minus,axiom,
% 5.68/5.98 ! [A: complex] :
% 5.68/5.98 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.68/5.98 = zero_zero_complex ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_left_minus
% 5.68/5.98 thf(fact_5625_ab__group__add__class_Oab__left__minus,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.68/5.98 = zero_z3403309356797280102nteger ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_left_minus
% 5.68/5.98 thf(fact_5626_ab__group__add__class_Oab__left__minus,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.68/5.98 = zero_zero_rat ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_left_minus
% 5.68/5.98 thf(fact_5627_add__eq__0__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( plus_plus_real @ A @ B )
% 5.68/5.98 = zero_zero_real )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_real @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_eq_0_iff
% 5.68/5.98 thf(fact_5628_add__eq__0__iff,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( plus_plus_int @ A @ B )
% 5.68/5.98 = zero_zero_int )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_int @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_eq_0_iff
% 5.68/5.98 thf(fact_5629_add__eq__0__iff,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( plus_plus_complex @ A @ B )
% 5.68/5.98 = zero_zero_complex )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_eq_0_iff
% 5.68/5.98 thf(fact_5630_add__eq__0__iff,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.68/5.98 = zero_z3403309356797280102nteger )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_eq_0_iff
% 5.68/5.98 thf(fact_5631_add__eq__0__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( plus_plus_rat @ A @ B )
% 5.68/5.98 = zero_zero_rat )
% 5.68/5.98 = ( B
% 5.68/5.98 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_eq_0_iff
% 5.68/5.98 thf(fact_5632_less__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(2)
% 5.68/5.98 thf(fact_5633_less__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(2)
% 5.68/5.98 thf(fact_5634_less__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(2)
% 5.68/5.98 thf(fact_5635_less__minus__one__simps_I2_J,axiom,
% 5.68/5.98 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(2)
% 5.68/5.98 thf(fact_5636_less__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(4)
% 5.68/5.98 thf(fact_5637_less__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(4)
% 5.68/5.98 thf(fact_5638_less__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(4)
% 5.68/5.98 thf(fact_5639_less__minus__one__simps_I4_J,axiom,
% 5.68/5.98 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(4)
% 5.68/5.98 thf(fact_5640_numeral__times__minus__swap,axiom,
% 5.68/5.98 ! [W: num,X: real] :
% 5.68/5.98 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.68/5.98 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_times_minus_swap
% 5.68/5.98 thf(fact_5641_numeral__times__minus__swap,axiom,
% 5.68/5.98 ! [W: num,X: int] :
% 5.68/5.98 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.68/5.98 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_times_minus_swap
% 5.68/5.98 thf(fact_5642_numeral__times__minus__swap,axiom,
% 5.68/5.98 ! [W: num,X: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.68/5.98 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_times_minus_swap
% 5.68/5.98 thf(fact_5643_numeral__times__minus__swap,axiom,
% 5.68/5.98 ! [W: num,X: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_times_minus_swap
% 5.68/5.98 thf(fact_5644_numeral__times__minus__swap,axiom,
% 5.68/5.98 ! [W: num,X: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.68/5.98 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_times_minus_swap
% 5.68/5.98 thf(fact_5645_nonzero__minus__divide__right,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( B != zero_zero_real )
% 5.68/5.98 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.98 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_right
% 5.68/5.98 thf(fact_5646_nonzero__minus__divide__right,axiom,
% 5.68/5.98 ! [B: complex,A: complex] :
% 5.68/5.98 ( ( B != zero_zero_complex )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_right
% 5.68/5.98 thf(fact_5647_nonzero__minus__divide__right,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( B != zero_zero_rat )
% 5.68/5.98 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_right
% 5.68/5.98 thf(fact_5648_nonzero__minus__divide__divide,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( B != zero_zero_real )
% 5.68/5.98 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_divide
% 5.68/5.98 thf(fact_5649_nonzero__minus__divide__divide,axiom,
% 5.68/5.98 ! [B: complex,A: complex] :
% 5.68/5.98 ( ( B != zero_zero_complex )
% 5.68/5.98 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_divide
% 5.68/5.98 thf(fact_5650_nonzero__minus__divide__divide,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( B != zero_zero_rat )
% 5.68/5.98 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_minus_divide_divide
% 5.68/5.98 thf(fact_5651_one__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one_one_real
% 5.68/5.98 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_numeral
% 5.68/5.98 thf(fact_5652_one__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one_one_int
% 5.68/5.98 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_numeral
% 5.68/5.98 thf(fact_5653_one__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one_one_complex
% 5.68/5.98 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_numeral
% 5.68/5.98 thf(fact_5654_one__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one_one_Code_integer
% 5.68/5.98 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_numeral
% 5.68/5.98 thf(fact_5655_one__neq__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one_one_rat
% 5.68/5.98 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % one_neq_neg_numeral
% 5.68/5.98 thf(fact_5656_numeral__neq__neg__one,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( numeral_numeral_real @ N )
% 5.68/5.98 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_one
% 5.68/5.98 thf(fact_5657_numeral__neq__neg__one,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( numeral_numeral_int @ N )
% 5.68/5.98 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_one
% 5.68/5.98 thf(fact_5658_numeral__neq__neg__one,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( numera6690914467698888265omplex @ N )
% 5.68/5.98 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_one
% 5.68/5.98 thf(fact_5659_numeral__neq__neg__one,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( numera6620942414471956472nteger @ N )
% 5.68/5.98 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_one
% 5.68/5.98 thf(fact_5660_numeral__neq__neg__one,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( ( numeral_numeral_rat @ N )
% 5.68/5.98 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % numeral_neq_neg_one
% 5.68/5.98 thf(fact_5661_square__eq__1__iff,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ( times_times_real @ X @ X )
% 5.68/5.98 = one_one_real )
% 5.68/5.98 = ( ( X = one_one_real )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_1_iff
% 5.68/5.98 thf(fact_5662_square__eq__1__iff,axiom,
% 5.68/5.98 ! [X: int] :
% 5.68/5.98 ( ( ( times_times_int @ X @ X )
% 5.68/5.98 = one_one_int )
% 5.68/5.98 = ( ( X = one_one_int )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_1_iff
% 5.68/5.98 thf(fact_5663_square__eq__1__iff,axiom,
% 5.68/5.98 ! [X: complex] :
% 5.68/5.98 ( ( ( times_times_complex @ X @ X )
% 5.68/5.98 = one_one_complex )
% 5.68/5.98 = ( ( X = one_one_complex )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_1_iff
% 5.68/5.98 thf(fact_5664_square__eq__1__iff,axiom,
% 5.68/5.98 ! [X: code_integer] :
% 5.68/5.98 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.68/5.98 = one_one_Code_integer )
% 5.68/5.98 = ( ( X = one_one_Code_integer )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_1_iff
% 5.68/5.98 thf(fact_5665_square__eq__1__iff,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ( ( times_times_rat @ X @ X )
% 5.68/5.98 = one_one_rat )
% 5.68/5.98 = ( ( X = one_one_rat )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_eq_1_iff
% 5.68/5.98 thf(fact_5666_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_real
% 5.68/5.98 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.68/5.98 thf(fact_5667_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_int
% 5.68/5.98 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.68/5.98 thf(fact_5668_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_complex
% 5.68/5.98 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.68/5.98 thf(fact_5669_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_8373710615458151222nteger
% 5.68/5.98 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.68/5.98 thf(fact_5670_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_rat
% 5.68/5.98 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.68/5.98 thf(fact_5671_diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_real
% 5.68/5.98 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_conv_add_uminus
% 5.68/5.98 thf(fact_5672_diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_int
% 5.68/5.98 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_conv_add_uminus
% 5.68/5.98 thf(fact_5673_diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_complex
% 5.68/5.98 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_conv_add_uminus
% 5.68/5.98 thf(fact_5674_diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_8373710615458151222nteger
% 5.68/5.98 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_conv_add_uminus
% 5.68/5.98 thf(fact_5675_diff__conv__add__uminus,axiom,
% 5.68/5.98 ( minus_minus_rat
% 5.68/5.98 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % diff_conv_add_uminus
% 5.68/5.98 thf(fact_5676_group__cancel_Osub2,axiom,
% 5.68/5.98 ! [B4: real,K: real,B: real,A: real] :
% 5.68/5.98 ( ( B4
% 5.68/5.98 = ( plus_plus_real @ K @ B ) )
% 5.68/5.98 => ( ( minus_minus_real @ A @ B4 )
% 5.68/5.98 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.sub2
% 5.68/5.98 thf(fact_5677_group__cancel_Osub2,axiom,
% 5.68/5.98 ! [B4: int,K: int,B: int,A: int] :
% 5.68/5.98 ( ( B4
% 5.68/5.98 = ( plus_plus_int @ K @ B ) )
% 5.68/5.98 => ( ( minus_minus_int @ A @ B4 )
% 5.68/5.98 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.sub2
% 5.68/5.98 thf(fact_5678_group__cancel_Osub2,axiom,
% 5.68/5.98 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.68/5.98 ( ( B4
% 5.68/5.98 = ( plus_plus_complex @ K @ B ) )
% 5.68/5.98 => ( ( minus_minus_complex @ A @ B4 )
% 5.68/5.98 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.sub2
% 5.68/5.98 thf(fact_5679_group__cancel_Osub2,axiom,
% 5.68/5.98 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.68/5.98 ( ( B4
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.68/5.98 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.sub2
% 5.68/5.98 thf(fact_5680_group__cancel_Osub2,axiom,
% 5.68/5.98 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.68/5.98 ( ( B4
% 5.68/5.98 = ( plus_plus_rat @ K @ B ) )
% 5.68/5.98 => ( ( minus_minus_rat @ A @ B4 )
% 5.68/5.98 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % group_cancel.sub2
% 5.68/5.98 thf(fact_5681_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_real,N: nat,X: real] :
% 5.68/5.98 ( ( ( size_size_list_real @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: real] :
% 5.68/5.98 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_real @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5682_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_complex,N: nat,X: complex] :
% 5.68/5.98 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: complex] :
% 5.68/5.98 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_complex @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5683_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 5.68/5.98 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: product_prod_nat_nat] :
% 5.68/5.98 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replic4235873036481779905at_nat @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5684_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.68/5.98 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: vEBT_VEBT] :
% 5.68/5.98 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5685_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_o,N: nat,X: $o] :
% 5.68/5.98 ( ( ( size_size_list_o @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: $o] :
% 5.68/5.98 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_o @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5686_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_nat,N: nat,X: nat] :
% 5.68/5.98 ( ( ( size_size_list_nat @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: nat] :
% 5.68/5.98 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_nat @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5687_replicate__eqI,axiom,
% 5.68/5.98 ! [Xs2: list_int,N: nat,X: int] :
% 5.68/5.98 ( ( ( size_size_list_int @ Xs2 )
% 5.68/5.98 = N )
% 5.68/5.98 => ( ! [Y3: int] :
% 5.68/5.98 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.68/5.98 => ( Y3 = X ) )
% 5.68/5.98 => ( Xs2
% 5.68/5.98 = ( replicate_int @ N @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_eqI
% 5.68/5.98 thf(fact_5688_replicate__length__same,axiom,
% 5.68/5.98 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.68/5.98 ( ! [X3: vEBT_VEBT] :
% 5.68/5.98 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.68/5.98 => ( X3 = X ) )
% 5.68/5.98 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.68/5.98 = Xs2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_length_same
% 5.68/5.98 thf(fact_5689_replicate__length__same,axiom,
% 5.68/5.98 ! [Xs2: list_o,X: $o] :
% 5.68/5.98 ( ! [X3: $o] :
% 5.68/5.98 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.68/5.98 => ( X3 = X ) )
% 5.68/5.98 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.68/5.98 = Xs2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_length_same
% 5.68/5.98 thf(fact_5690_replicate__length__same,axiom,
% 5.68/5.98 ! [Xs2: list_nat,X: nat] :
% 5.68/5.98 ( ! [X3: nat] :
% 5.68/5.98 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.68/5.98 => ( X3 = X ) )
% 5.68/5.98 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 5.68/5.98 = Xs2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_length_same
% 5.68/5.98 thf(fact_5691_replicate__length__same,axiom,
% 5.68/5.98 ! [Xs2: list_int,X: int] :
% 5.68/5.98 ( ! [X3: int] :
% 5.68/5.98 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.68/5.98 => ( X3 = X ) )
% 5.68/5.98 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.68/5.98 = Xs2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % replicate_length_same
% 5.68/5.98 thf(fact_5692_dvd__neg__div,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( dvd_dvd_real @ B @ A )
% 5.68/5.98 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.68/5.98 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_neg_div
% 5.68/5.98 thf(fact_5693_dvd__neg__div,axiom,
% 5.68/5.98 ! [B: int,A: int] :
% 5.68/5.98 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.98 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.68/5.98 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_neg_div
% 5.68/5.98 thf(fact_5694_dvd__neg__div,axiom,
% 5.68/5.98 ! [B: complex,A: complex] :
% 5.68/5.98 ( ( dvd_dvd_complex @ B @ A )
% 5.68/5.98 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_neg_div
% 5.68/5.98 thf(fact_5695_dvd__neg__div,axiom,
% 5.68/5.98 ! [B: code_integer,A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.98 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_neg_div
% 5.68/5.98 thf(fact_5696_dvd__neg__div,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( dvd_dvd_rat @ B @ A )
% 5.68/5.98 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_neg_div
% 5.68/5.98 thf(fact_5697_dvd__div__neg,axiom,
% 5.68/5.98 ! [B: real,A: real] :
% 5.68/5.98 ( ( dvd_dvd_real @ B @ A )
% 5.68/5.98 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.68/5.98 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_div_neg
% 5.68/5.98 thf(fact_5698_dvd__div__neg,axiom,
% 5.68/5.98 ! [B: int,A: int] :
% 5.68/5.98 ( ( dvd_dvd_int @ B @ A )
% 5.68/5.98 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.68/5.98 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_div_neg
% 5.68/5.98 thf(fact_5699_dvd__div__neg,axiom,
% 5.68/5.98 ! [B: complex,A: complex] :
% 5.68/5.98 ( ( dvd_dvd_complex @ B @ A )
% 5.68/5.98 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_div_neg
% 5.68/5.98 thf(fact_5700_dvd__div__neg,axiom,
% 5.68/5.98 ! [B: code_integer,A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.68/5.98 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_div_neg
% 5.68/5.98 thf(fact_5701_dvd__div__neg,axiom,
% 5.68/5.98 ! [B: rat,A: rat] :
% 5.68/5.98 ( ( dvd_dvd_rat @ B @ A )
% 5.68/5.98 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.68/5.98 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % dvd_div_neg
% 5.68/5.98 thf(fact_5702_subset__Compl__self__eq,axiom,
% 5.68/5.98 ! [A2: set_nat] :
% 5.68/5.98 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.68/5.98 = ( A2 = bot_bot_set_nat ) ) ).
% 5.68/5.98
% 5.68/5.98 % subset_Compl_self_eq
% 5.68/5.98 thf(fact_5703_subset__Compl__self__eq,axiom,
% 5.68/5.98 ! [A2: set_real] :
% 5.68/5.98 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.68/5.98 = ( A2 = bot_bot_set_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % subset_Compl_self_eq
% 5.68/5.98 thf(fact_5704_subset__Compl__self__eq,axiom,
% 5.68/5.98 ! [A2: set_int] :
% 5.68/5.98 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.68/5.98 = ( A2 = bot_bot_set_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % subset_Compl_self_eq
% 5.68/5.98 thf(fact_5705_sin__bound__lemma,axiom,
% 5.68/5.98 ! [X: real,Y2: real,U: real,V: real] :
% 5.68/5.98 ( ( X = Y2 )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.68/5.98 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y2 ) ) @ V ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % sin_bound_lemma
% 5.68/5.98 thf(fact_5706_real__minus__mult__self__le,axiom,
% 5.68/5.98 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.68/5.98
% 5.68/5.98 % real_minus_mult_self_le
% 5.68/5.98 thf(fact_5707_pos__zmult__eq__1__iff__lemma,axiom,
% 5.68/5.98 ! [M: int,N: int] :
% 5.68/5.98 ( ( ( times_times_int @ M @ N )
% 5.68/5.98 = one_one_int )
% 5.68/5.98 => ( ( M = one_one_int )
% 5.68/5.98 | ( M
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_zmult_eq_1_iff_lemma
% 5.68/5.98 thf(fact_5708_zmult__eq__1__iff,axiom,
% 5.68/5.98 ! [M: int,N: int] :
% 5.68/5.98 ( ( ( times_times_int @ M @ N )
% 5.68/5.98 = one_one_int )
% 5.68/5.98 = ( ( ( M = one_one_int )
% 5.68/5.98 & ( N = one_one_int ) )
% 5.68/5.98 | ( ( M
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 & ( N
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zmult_eq_1_iff
% 5.68/5.98 thf(fact_5709_minus__real__def,axiom,
% 5.68/5.98 ( minus_minus_real
% 5.68/5.98 = ( ^ [X2: real,Y: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_real_def
% 5.68/5.98 thf(fact_5710_dense__eq0__I,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ! [E2: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.68/5.98 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.68/5.98 => ( X = zero_zero_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % dense_eq0_I
% 5.68/5.98 thf(fact_5711_dense__eq0__I,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ! [E2: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.68/5.98 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.68/5.98 => ( X = zero_zero_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % dense_eq0_I
% 5.68/5.98 thf(fact_5712_abs__eq__mult,axiom,
% 5.68/5.98 ! [A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.68/5.98 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.68/5.98 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.68/5.98 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.68/5.98 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_mult
% 5.68/5.98 thf(fact_5713_abs__eq__mult,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/5.98 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.68/5.98 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.68/5.98 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.68/5.98 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.68/5.98 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_mult
% 5.68/5.98 thf(fact_5714_abs__eq__mult,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.68/5.98 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.68/5.98 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.68/5.98 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.68/5.98 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.68/5.98 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_mult
% 5.68/5.98 thf(fact_5715_abs__eq__mult,axiom,
% 5.68/5.98 ! [A: int,B: int] :
% 5.68/5.98 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.68/5.98 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.68/5.98 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.68/5.98 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.68/5.98 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.68/5.98 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_eq_mult
% 5.68/5.98 thf(fact_5716_abs__mult__pos,axiom,
% 5.68/5.98 ! [X: code_integer,Y2: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.68/5.98 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y2 ) @ X )
% 5.68/5.98 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y2 @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_pos
% 5.68/5.98 thf(fact_5717_abs__mult__pos,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.98 => ( ( times_times_real @ ( abs_abs_real @ Y2 ) @ X )
% 5.68/5.98 = ( abs_abs_real @ ( times_times_real @ Y2 @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_pos
% 5.68/5.98 thf(fact_5718_abs__mult__pos,axiom,
% 5.68/5.98 ! [X: rat,Y2: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.68/5.98 => ( ( times_times_rat @ ( abs_abs_rat @ Y2 ) @ X )
% 5.68/5.98 = ( abs_abs_rat @ ( times_times_rat @ Y2 @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_pos
% 5.68/5.98 thf(fact_5719_abs__mult__pos,axiom,
% 5.68/5.98 ! [X: int,Y2: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/5.98 => ( ( times_times_int @ ( abs_abs_int @ Y2 ) @ X )
% 5.68/5.98 = ( abs_abs_int @ ( times_times_int @ Y2 @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_mult_pos
% 5.68/5.98 thf(fact_5720_abs__div__pos,axiom,
% 5.68/5.98 ! [Y2: real,X: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/5.98 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y2 )
% 5.68/5.98 = ( abs_abs_real @ ( divide_divide_real @ X @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_div_pos
% 5.68/5.98 thf(fact_5721_abs__div__pos,axiom,
% 5.68/5.98 ! [Y2: rat,X: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ Y2 )
% 5.68/5.98 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y2 )
% 5.68/5.98 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_div_pos
% 5.68/5.98 thf(fact_5722_zero__le__power__abs,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_le_power_abs
% 5.68/5.98 thf(fact_5723_zero__le__power__abs,axiom,
% 5.68/5.98 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_le_power_abs
% 5.68/5.98 thf(fact_5724_zero__le__power__abs,axiom,
% 5.68/5.98 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_le_power_abs
% 5.68/5.98 thf(fact_5725_zero__le__power__abs,axiom,
% 5.68/5.98 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % zero_le_power_abs
% 5.68/5.98 thf(fact_5726_abs__triangle__ineq4,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq4
% 5.68/5.98 thf(fact_5727_abs__triangle__ineq4,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq4
% 5.68/5.98 thf(fact_5728_abs__triangle__ineq4,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq4
% 5.68/5.98 thf(fact_5729_abs__triangle__ineq4,axiom,
% 5.68/5.98 ! [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 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_triangle_ineq4
% 5.68/5.98 thf(fact_5730_abs__diff__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_triangle_ineq
% 5.68/5.98 thf(fact_5731_abs__diff__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_triangle_ineq
% 5.68/5.98 thf(fact_5732_abs__diff__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_triangle_ineq
% 5.68/5.98 thf(fact_5733_abs__diff__triangle__ineq,axiom,
% 5.68/5.98 ! [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 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_triangle_ineq
% 5.68/5.98 thf(fact_5734_abs__diff__le__iff,axiom,
% 5.68/5.98 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_le_iff
% 5.68/5.98 thf(fact_5735_abs__diff__le__iff,axiom,
% 5.68/5.98 ! [X: real,A: real,R2: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_le_iff
% 5.68/5.98 thf(fact_5736_abs__diff__le__iff,axiom,
% 5.68/5.98 ! [X: rat,A: rat,R2: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_le_iff
% 5.68/5.98 thf(fact_5737_abs__diff__le__iff,axiom,
% 5.68/5.98 ! [X: int,A: int,R2: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_le_iff
% 5.68/5.98 thf(fact_5738_abs__diff__less__iff,axiom,
% 5.68/5.98 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_less_iff
% 5.68/5.98 thf(fact_5739_abs__diff__less__iff,axiom,
% 5.68/5.98 ! [X: real,A: real,R2: real] :
% 5.68/5.98 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_less_iff
% 5.68/5.98 thf(fact_5740_abs__diff__less__iff,axiom,
% 5.68/5.98 ! [X: rat,A: rat,R2: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_less_iff
% 5.68/5.98 thf(fact_5741_abs__diff__less__iff,axiom,
% 5.68/5.98 ! [X: int,A: int,R2: int] :
% 5.68/5.98 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.68/5.98 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.68/5.98 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_diff_less_iff
% 5.68/5.98 thf(fact_5742_not__zero__le__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_le_neg_numeral
% 5.68/5.98 thf(fact_5743_not__zero__le__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_le_neg_numeral
% 5.68/5.98 thf(fact_5744_not__zero__le__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_le_neg_numeral
% 5.68/5.98 thf(fact_5745_not__zero__le__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_le_neg_numeral
% 5.68/5.98 thf(fact_5746_neg__numeral__le__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_zero
% 5.68/5.98 thf(fact_5747_neg__numeral__le__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_zero
% 5.68/5.98 thf(fact_5748_neg__numeral__le__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_zero
% 5.68/5.98 thf(fact_5749_neg__numeral__le__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_zero
% 5.68/5.98 thf(fact_5750_neg__numeral__less__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_zero
% 5.68/5.98 thf(fact_5751_neg__numeral__less__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_zero
% 5.68/5.98 thf(fact_5752_neg__numeral__less__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_zero
% 5.68/5.98 thf(fact_5753_neg__numeral__less__zero,axiom,
% 5.68/5.98 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_zero
% 5.68/5.98 thf(fact_5754_not__zero__less__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_less_neg_numeral
% 5.68/5.98 thf(fact_5755_not__zero__less__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_less_neg_numeral
% 5.68/5.98 thf(fact_5756_not__zero__less__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_less_neg_numeral
% 5.68/5.98 thf(fact_5757_not__zero__less__neg__numeral,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_zero_less_neg_numeral
% 5.68/5.98 thf(fact_5758_le__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(1)
% 5.68/5.98 thf(fact_5759_le__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(1)
% 5.68/5.98 thf(fact_5760_le__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(1)
% 5.68/5.98 thf(fact_5761_le__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(1)
% 5.68/5.98 thf(fact_5762_le__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(3)
% 5.68/5.98 thf(fact_5763_le__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(3)
% 5.68/5.98 thf(fact_5764_le__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(3)
% 5.68/5.98 thf(fact_5765_le__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_one_simps(3)
% 5.68/5.98 thf(fact_5766_less__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(1)
% 5.68/5.98 thf(fact_5767_less__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(1)
% 5.68/5.98 thf(fact_5768_less__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(1)
% 5.68/5.98 thf(fact_5769_less__minus__one__simps_I1_J,axiom,
% 5.68/5.98 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(1)
% 5.68/5.98 thf(fact_5770_less__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(3)
% 5.68/5.98 thf(fact_5771_less__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(3)
% 5.68/5.98 thf(fact_5772_less__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(3)
% 5.68/5.98 thf(fact_5773_less__minus__one__simps_I3_J,axiom,
% 5.68/5.98 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_one_simps(3)
% 5.68/5.98 thf(fact_5774_not__one__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_le_neg_numeral
% 5.68/5.98 thf(fact_5775_not__one__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_le_neg_numeral
% 5.68/5.98 thf(fact_5776_not__one__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_le_neg_numeral
% 5.68/5.98 thf(fact_5777_not__one__le__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_le_neg_numeral
% 5.68/5.98 thf(fact_5778_not__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_one
% 5.68/5.98 thf(fact_5779_not__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_one
% 5.68/5.98 thf(fact_5780_not__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_one
% 5.68/5.98 thf(fact_5781_not__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_le_neg_one
% 5.68/5.98 thf(fact_5782_neg__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_neg_one
% 5.68/5.98 thf(fact_5783_neg__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_neg_one
% 5.68/5.98 thf(fact_5784_neg__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_neg_one
% 5.68/5.98 thf(fact_5785_neg__numeral__le__neg__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_neg_one
% 5.68/5.98 thf(fact_5786_neg__one__le__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_le_numeral
% 5.68/5.98 thf(fact_5787_neg__one__le__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_le_numeral
% 5.68/5.98 thf(fact_5788_neg__one__le__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_le_numeral
% 5.68/5.98 thf(fact_5789_neg__one__le__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_le_numeral
% 5.68/5.98 thf(fact_5790_neg__numeral__le__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_one
% 5.68/5.98 thf(fact_5791_neg__numeral__le__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_one
% 5.68/5.98 thf(fact_5792_neg__numeral__le__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_one
% 5.68/5.98 thf(fact_5793_neg__numeral__le__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_le_one
% 5.68/5.98 thf(fact_5794_neg__numeral__less__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_one
% 5.68/5.98 thf(fact_5795_neg__numeral__less__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_one
% 5.68/5.98 thf(fact_5796_neg__numeral__less__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_one
% 5.68/5.98 thf(fact_5797_neg__numeral__less__one,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.68/5.98
% 5.68/5.98 % neg_numeral_less_one
% 5.68/5.98 thf(fact_5798_neg__one__less__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_less_numeral
% 5.68/5.98 thf(fact_5799_neg__one__less__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_less_numeral
% 5.68/5.98 thf(fact_5800_neg__one__less__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_less_numeral
% 5.68/5.98 thf(fact_5801_neg__one__less__numeral,axiom,
% 5.68/5.98 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_less_numeral
% 5.68/5.98 thf(fact_5802_not__numeral__less__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_one
% 5.68/5.98 thf(fact_5803_not__numeral__less__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_one
% 5.68/5.98 thf(fact_5804_not__numeral__less__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_one
% 5.68/5.98 thf(fact_5805_not__numeral__less__neg__one,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_numeral_less_neg_one
% 5.68/5.98 thf(fact_5806_not__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_less_neg_numeral
% 5.68/5.98 thf(fact_5807_not__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_less_neg_numeral
% 5.68/5.98 thf(fact_5808_not__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_less_neg_numeral
% 5.68/5.98 thf(fact_5809_not__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_one_less_neg_numeral
% 5.68/5.98 thf(fact_5810_not__neg__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_less_neg_numeral
% 5.68/5.98 thf(fact_5811_not__neg__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_less_neg_numeral
% 5.68/5.98 thf(fact_5812_not__neg__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_less_neg_numeral
% 5.68/5.98 thf(fact_5813_not__neg__one__less__neg__numeral,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % not_neg_one_less_neg_numeral
% 5.68/5.98 thf(fact_5814_eq__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: real,B: real,C: real] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_real )
% 5.68/5.98 => ( ( times_times_real @ A @ C )
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ( C = zero_zero_real )
% 5.68/5.98 => ( A = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_minus_divide_eq
% 5.68/5.98 thf(fact_5815_eq__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: complex,B: complex,C: complex] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_complex )
% 5.68/5.98 => ( ( times_times_complex @ A @ C )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.68/5.98 & ( ( C = zero_zero_complex )
% 5.68/5.98 => ( A = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_minus_divide_eq
% 5.68/5.98 thf(fact_5816_eq__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: rat,B: rat,C: rat] :
% 5.68/5.98 ( ( A
% 5.68/5.98 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_rat )
% 5.68/5.98 => ( ( times_times_rat @ A @ C )
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ( C = zero_zero_rat )
% 5.68/5.98 => ( A = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_minus_divide_eq
% 5.68/5.98 thf(fact_5817_minus__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: real,C: real,A: real] :
% 5.68/5.98 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( C != zero_zero_real )
% 5.68/5.98 => ( ( uminus_uminus_real @ B )
% 5.68/5.98 = ( times_times_real @ A @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_real )
% 5.68/5.98 => ( A = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_eq_eq
% 5.68/5.98 thf(fact_5818_minus__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: complex,C: complex,A: complex] :
% 5.68/5.98 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( C != zero_zero_complex )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ B )
% 5.68/5.98 = ( times_times_complex @ A @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_complex )
% 5.68/5.98 => ( A = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_eq_eq
% 5.68/5.98 thf(fact_5819_minus__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: rat,C: rat,A: rat] :
% 5.68/5.98 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.68/5.98 = A )
% 5.68/5.98 = ( ( ( C != zero_zero_rat )
% 5.68/5.98 => ( ( uminus_uminus_rat @ B )
% 5.68/5.98 = ( times_times_rat @ A @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_rat )
% 5.68/5.98 => ( A = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_eq_eq
% 5.68/5.98 thf(fact_5820_nonzero__neg__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: real,A: real,C: real] :
% 5.68/5.98 ( ( B != zero_zero_real )
% 5.68/5.98 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.68/5.98 = C )
% 5.68/5.98 = ( ( uminus_uminus_real @ A )
% 5.68/5.98 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq
% 5.68/5.98 thf(fact_5821_nonzero__neg__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: complex,A: complex,C: complex] :
% 5.68/5.98 ( ( B != zero_zero_complex )
% 5.68/5.98 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/5.98 = C )
% 5.68/5.98 = ( ( uminus1482373934393186551omplex @ A )
% 5.68/5.98 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq
% 5.68/5.98 thf(fact_5822_nonzero__neg__divide__eq__eq,axiom,
% 5.68/5.98 ! [B: rat,A: rat,C: rat] :
% 5.68/5.98 ( ( B != zero_zero_rat )
% 5.68/5.98 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.68/5.98 = C )
% 5.68/5.98 = ( ( uminus_uminus_rat @ A )
% 5.68/5.98 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq
% 5.68/5.98 thf(fact_5823_nonzero__neg__divide__eq__eq2,axiom,
% 5.68/5.98 ! [B: real,C: real,A: real] :
% 5.68/5.98 ( ( B != zero_zero_real )
% 5.68/5.98 => ( ( C
% 5.68/5.98 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.68/5.98 = ( ( times_times_real @ C @ B )
% 5.68/5.98 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq2
% 5.68/5.98 thf(fact_5824_nonzero__neg__divide__eq__eq2,axiom,
% 5.68/5.98 ! [B: complex,C: complex,A: complex] :
% 5.68/5.98 ( ( B != zero_zero_complex )
% 5.68/5.98 => ( ( C
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/5.98 = ( ( times_times_complex @ C @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq2
% 5.68/5.98 thf(fact_5825_nonzero__neg__divide__eq__eq2,axiom,
% 5.68/5.98 ! [B: rat,C: rat,A: rat] :
% 5.68/5.98 ( ( B != zero_zero_rat )
% 5.68/5.98 => ( ( C
% 5.68/5.98 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.68/5.98 = ( ( times_times_rat @ C @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % nonzero_neg_divide_eq_eq2
% 5.68/5.98 thf(fact_5826_mult__1s__ring__1_I2_J,axiom,
% 5.68/5.98 ! [B: real] :
% 5.68/5.98 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(2)
% 5.68/5.98 thf(fact_5827_mult__1s__ring__1_I2_J,axiom,
% 5.68/5.98 ! [B: int] :
% 5.68/5.98 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.68/5.98 = ( uminus_uminus_int @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(2)
% 5.68/5.98 thf(fact_5828_mult__1s__ring__1_I2_J,axiom,
% 5.68/5.98 ! [B: complex] :
% 5.68/5.98 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(2)
% 5.68/5.98 thf(fact_5829_mult__1s__ring__1_I2_J,axiom,
% 5.68/5.98 ! [B: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(2)
% 5.68/5.98 thf(fact_5830_mult__1s__ring__1_I2_J,axiom,
% 5.68/5.98 ! [B: rat] :
% 5.68/5.98 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(2)
% 5.68/5.98 thf(fact_5831_mult__1s__ring__1_I1_J,axiom,
% 5.68/5.98 ! [B: real] :
% 5.68/5.98 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(1)
% 5.68/5.98 thf(fact_5832_mult__1s__ring__1_I1_J,axiom,
% 5.68/5.98 ! [B: int] :
% 5.68/5.98 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.68/5.98 = ( uminus_uminus_int @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(1)
% 5.68/5.98 thf(fact_5833_mult__1s__ring__1_I1_J,axiom,
% 5.68/5.98 ! [B: complex] :
% 5.68/5.98 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(1)
% 5.68/5.98 thf(fact_5834_mult__1s__ring__1_I1_J,axiom,
% 5.68/5.98 ! [B: code_integer] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(1)
% 5.68/5.98 thf(fact_5835_mult__1s__ring__1_I1_J,axiom,
% 5.68/5.98 ! [B: rat] :
% 5.68/5.98 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) ).
% 5.68/5.98
% 5.68/5.98 % mult_1s_ring_1(1)
% 5.68/5.98 thf(fact_5836_divide__eq__minus__1__iff,axiom,
% 5.68/5.98 ! [A: real,B: real] :
% 5.68/5.98 ( ( ( divide_divide_real @ A @ B )
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.98 = ( ( B != zero_zero_real )
% 5.68/5.98 & ( A
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_minus_1_iff
% 5.68/5.98 thf(fact_5837_divide__eq__minus__1__iff,axiom,
% 5.68/5.98 ! [A: complex,B: complex] :
% 5.68/5.98 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.98 = ( ( B != zero_zero_complex )
% 5.68/5.98 & ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_minus_1_iff
% 5.68/5.98 thf(fact_5838_divide__eq__minus__1__iff,axiom,
% 5.68/5.98 ! [A: rat,B: rat] :
% 5.68/5.98 ( ( ( divide_divide_rat @ A @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.98 = ( ( B != zero_zero_rat )
% 5.68/5.98 & ( A
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_minus_1_iff
% 5.68/5.98 thf(fact_5839_uminus__numeral__One,axiom,
% 5.68/5.98 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_numeral_One
% 5.68/5.98 thf(fact_5840_uminus__numeral__One,axiom,
% 5.68/5.98 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_numeral_One
% 5.68/5.98 thf(fact_5841_uminus__numeral__One,axiom,
% 5.68/5.98 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_numeral_One
% 5.68/5.98 thf(fact_5842_uminus__numeral__One,axiom,
% 5.68/5.98 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_numeral_One
% 5.68/5.98 thf(fact_5843_uminus__numeral__One,axiom,
% 5.68/5.98 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_numeral_One
% 5.68/5.98 thf(fact_5844_power__minus,axiom,
% 5.68/5.98 ! [A: real,N: nat] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.68/5.98 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus
% 5.68/5.98 thf(fact_5845_power__minus,axiom,
% 5.68/5.98 ! [A: int,N: nat] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.68/5.98 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus
% 5.68/5.98 thf(fact_5846_power__minus,axiom,
% 5.68/5.98 ! [A: complex,N: nat] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.68/5.98 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus
% 5.68/5.98 thf(fact_5847_power__minus,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.68/5.98 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus
% 5.68/5.98 thf(fact_5848_power__minus,axiom,
% 5.68/5.98 ! [A: rat,N: nat] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.68/5.98 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus
% 5.68/5.98 thf(fact_5849_power__minus__Bit0,axiom,
% 5.68/5.98 ! [X: real,K: num] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.68/5.98 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_Bit0
% 5.68/5.98 thf(fact_5850_power__minus__Bit0,axiom,
% 5.68/5.98 ! [X: int,K: num] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.68/5.98 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_Bit0
% 5.68/5.98 thf(fact_5851_power__minus__Bit0,axiom,
% 5.68/5.98 ! [X: complex,K: num] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.68/5.98 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_Bit0
% 5.68/5.98 thf(fact_5852_power__minus__Bit0,axiom,
% 5.68/5.98 ! [X: code_integer,K: num] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_Bit0
% 5.68/5.98 thf(fact_5853_power__minus__Bit0,axiom,
% 5.68/5.98 ! [X: rat,K: num] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.68/5.98 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus_Bit0
% 5.68/5.98 thf(fact_5854_real__0__less__add__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/5.98 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % real_0_less_add_iff
% 5.68/5.98 thf(fact_5855_real__add__less__0__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 5.68/5.98 = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % real_add_less_0_iff
% 5.68/5.98 thf(fact_5856_real__0__le__add__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/5.98 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 5.68/5.98
% 5.68/5.98 % real_0_le_add_iff
% 5.68/5.98 thf(fact_5857_real__add__le__0__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 5.68/5.98 = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % real_add_le_0_iff
% 5.68/5.98 thf(fact_5858_abs__add__one__gt__zero,axiom,
% 5.68/5.98 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_add_one_gt_zero
% 5.68/5.98 thf(fact_5859_abs__add__one__gt__zero,axiom,
% 5.68/5.98 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_add_one_gt_zero
% 5.68/5.98 thf(fact_5860_abs__add__one__gt__zero,axiom,
% 5.68/5.98 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_add_one_gt_zero
% 5.68/5.98 thf(fact_5861_abs__add__one__gt__zero,axiom,
% 5.68/5.98 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_add_one_gt_zero
% 5.68/5.98 thf(fact_5862_power__even__abs,axiom,
% 5.68/5.98 ! [N: nat,A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs
% 5.68/5.98 thf(fact_5863_power__even__abs,axiom,
% 5.68/5.98 ! [N: nat,A: rat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.68/5.98 = ( power_power_rat @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs
% 5.68/5.98 thf(fact_5864_power__even__abs,axiom,
% 5.68/5.98 ! [N: nat,A: real] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.68/5.98 = ( power_power_real @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs
% 5.68/5.98 thf(fact_5865_power__even__abs,axiom,
% 5.68/5.98 ! [N: nat,A: int] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.68/5.98 = ( power_power_int @ A @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_even_abs
% 5.68/5.98 thf(fact_5866_less__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: real,B: real,C: real] :
% 5.68/5.98 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_divide_eq
% 5.68/5.98 thf(fact_5867_less__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: rat,B: rat,C: rat] :
% 5.68/5.98 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_minus_divide_eq
% 5.68/5.98 thf(fact_5868_minus__divide__less__eq,axiom,
% 5.68/5.98 ! [B: real,C: real,A: real] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_less_eq
% 5.68/5.98 thf(fact_5869_minus__divide__less__eq,axiom,
% 5.68/5.98 ! [B: rat,C: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_less_eq
% 5.68/5.98 thf(fact_5870_neg__less__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: real,A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_less_minus_divide_eq
% 5.68/5.98 thf(fact_5871_neg__less__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_less_minus_divide_eq
% 5.68/5.98 thf(fact_5872_neg__minus__divide__less__eq,axiom,
% 5.68/5.98 ! [C: real,B: real,A: real] :
% 5.68/5.98 ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_minus_divide_less_eq
% 5.68/5.98 thf(fact_5873_neg__minus__divide__less__eq,axiom,
% 5.68/5.98 ! [C: rat,B: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_minus_divide_less_eq
% 5.68/5.98 thf(fact_5874_pos__less__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: real,A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_less_minus_divide_eq
% 5.68/5.98 thf(fact_5875_pos__less__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_less_minus_divide_eq
% 5.68/5.98 thf(fact_5876_pos__minus__divide__less__eq,axiom,
% 5.68/5.98 ! [C: real,B: real,A: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_minus_divide_less_eq
% 5.68/5.98 thf(fact_5877_pos__minus__divide__less__eq,axiom,
% 5.68/5.98 ! [C: rat,B: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_minus_divide_less_eq
% 5.68/5.98 thf(fact_5878_divide__eq__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: real,C: real,W: num] :
% 5.68/5.98 ( ( ( divide_divide_real @ B @ C )
% 5.68/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_real )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_real )
% 5.68/5.98 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral(2)
% 5.68/5.98 thf(fact_5879_divide__eq__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: complex,C: complex,W: num] :
% 5.68/5.98 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_complex )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_complex )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral(2)
% 5.68/5.98 thf(fact_5880_divide__eq__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: rat,C: rat,W: num] :
% 5.68/5.98 ( ( ( divide_divide_rat @ B @ C )
% 5.68/5.98 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.68/5.98 = ( ( ( C != zero_zero_rat )
% 5.68/5.98 => ( B
% 5.68/5.98 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ( C = zero_zero_rat )
% 5.68/5.98 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_eq_eq_numeral(2)
% 5.68/5.98 thf(fact_5881_eq__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: real,C: real] :
% 5.68/5.98 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 = ( divide_divide_real @ B @ C ) )
% 5.68/5.98 = ( ( ( C != zero_zero_real )
% 5.68/5.98 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( C = zero_zero_real )
% 5.68/5.98 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.68/5.98 = zero_zero_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5882_eq__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: complex,C: complex] :
% 5.68/5.98 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.68/5.98 = ( ( ( C != zero_zero_complex )
% 5.68/5.98 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( C = zero_zero_complex )
% 5.68/5.98 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/5.98 = zero_zero_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5883_eq__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: rat,C: rat] :
% 5.68/5.98 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 = ( divide_divide_rat @ B @ C ) )
% 5.68/5.98 = ( ( ( C != zero_zero_rat )
% 5.68/5.98 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( C = zero_zero_rat )
% 5.68/5.98 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.68/5.98 = zero_zero_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5884_add__divide__eq__if__simps_I3_J,axiom,
% 5.68/5.98 ! [Z: real,A: real,B: real] :
% 5.68/5.98 ( ( ( Z = zero_zero_real )
% 5.68/5.98 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( Z != zero_zero_real )
% 5.68/5.98 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(3)
% 5.68/5.98 thf(fact_5885_add__divide__eq__if__simps_I3_J,axiom,
% 5.68/5.98 ! [Z: complex,A: complex,B: complex] :
% 5.68/5.98 ( ( ( Z = zero_zero_complex )
% 5.68/5.98 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( Z != zero_zero_complex )
% 5.68/5.98 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(3)
% 5.68/5.98 thf(fact_5886_add__divide__eq__if__simps_I3_J,axiom,
% 5.68/5.98 ! [Z: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ( Z = zero_zero_rat )
% 5.68/5.98 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.68/5.98 = B ) )
% 5.68/5.98 & ( ( Z != zero_zero_rat )
% 5.68/5.98 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(3)
% 5.68/5.98 thf(fact_5887_minus__divide__add__eq__iff,axiom,
% 5.68/5.98 ! [Z: real,X: real,Y2: real] :
% 5.68/5.98 ( ( Z != zero_zero_real )
% 5.68/5.98 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_add_eq_iff
% 5.68/5.98 thf(fact_5888_minus__divide__add__eq__iff,axiom,
% 5.68/5.98 ! [Z: complex,X: complex,Y2: complex] :
% 5.68/5.98 ( ( Z != zero_zero_complex )
% 5.68/5.98 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_add_eq_iff
% 5.68/5.98 thf(fact_5889_minus__divide__add__eq__iff,axiom,
% 5.68/5.98 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.98 ( ( Z != zero_zero_rat )
% 5.68/5.98 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_add_eq_iff
% 5.68/5.98 thf(fact_5890_add__divide__eq__if__simps_I6_J,axiom,
% 5.68/5.98 ! [Z: real,A: real,B: real] :
% 5.68/5.98 ( ( ( Z = zero_zero_real )
% 5.68/5.98 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_real )
% 5.68/5.98 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(6)
% 5.68/5.98 thf(fact_5891_add__divide__eq__if__simps_I6_J,axiom,
% 5.68/5.98 ! [Z: complex,A: complex,B: complex] :
% 5.68/5.98 ( ( ( Z = zero_zero_complex )
% 5.68/5.98 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_complex )
% 5.68/5.98 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(6)
% 5.68/5.98 thf(fact_5892_add__divide__eq__if__simps_I6_J,axiom,
% 5.68/5.98 ! [Z: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ( Z = zero_zero_rat )
% 5.68/5.98 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_rat )
% 5.68/5.98 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.68/5.98 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(6)
% 5.68/5.98 thf(fact_5893_add__divide__eq__if__simps_I5_J,axiom,
% 5.68/5.98 ! [Z: real,A: real,B: real] :
% 5.68/5.98 ( ( ( Z = zero_zero_real )
% 5.68/5.98 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.68/5.98 = ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_real )
% 5.68/5.98 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.68/5.98 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(5)
% 5.68/5.98 thf(fact_5894_add__divide__eq__if__simps_I5_J,axiom,
% 5.68/5.98 ! [Z: complex,A: complex,B: complex] :
% 5.68/5.98 ( ( ( Z = zero_zero_complex )
% 5.68/5.98 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_complex )
% 5.68/5.98 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(5)
% 5.68/5.98 thf(fact_5895_add__divide__eq__if__simps_I5_J,axiom,
% 5.68/5.98 ! [Z: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ( Z = zero_zero_rat )
% 5.68/5.98 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.68/5.98 = ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ( Z != zero_zero_rat )
% 5.68/5.98 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.68/5.98 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % add_divide_eq_if_simps(5)
% 5.68/5.98 thf(fact_5896_minus__divide__diff__eq__iff,axiom,
% 5.68/5.98 ! [Z: real,X: real,Y2: real] :
% 5.68/5.98 ( ( Z != zero_zero_real )
% 5.68/5.98 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_diff_eq_iff
% 5.68/5.98 thf(fact_5897_minus__divide__diff__eq__iff,axiom,
% 5.68/5.98 ! [Z: complex,X: complex,Y2: complex] :
% 5.68/5.98 ( ( Z != zero_zero_complex )
% 5.68/5.98 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_diff_eq_iff
% 5.68/5.98 thf(fact_5898_minus__divide__diff__eq__iff,axiom,
% 5.68/5.98 ! [Z: rat,X: rat,Y2: rat] :
% 5.68/5.98 ( ( Z != zero_zero_rat )
% 5.68/5.98 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y2 )
% 5.68/5.98 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y2 @ Z ) ) @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_diff_eq_iff
% 5.68/5.98 thf(fact_5899_even__minus,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.68/5.98 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % even_minus
% 5.68/5.98 thf(fact_5900_even__minus,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.68/5.98 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.68/5.98
% 5.68/5.98 % even_minus
% 5.68/5.98 thf(fact_5901_lemma__interval,axiom,
% 5.68/5.98 ! [A: real,X: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ A @ X )
% 5.68/5.98 => ( ( ord_less_real @ X @ B )
% 5.68/5.98 => ? [D3: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.68/5.98 & ! [Y4: real] :
% 5.68/5.98 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 5.68/5.98 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.68/5.98 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % lemma_interval
% 5.68/5.98 thf(fact_5902_power2__eq__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ( X = Y2 )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_iff
% 5.68/5.98 thf(fact_5903_power2__eq__iff,axiom,
% 5.68/5.98 ! [X: int,Y2: int] :
% 5.68/5.98 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ( X = Y2 )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_int @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_iff
% 5.68/5.98 thf(fact_5904_power2__eq__iff,axiom,
% 5.68/5.98 ! [X: complex,Y2: complex] :
% 5.68/5.98 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_complex @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ( X = Y2 )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus1482373934393186551omplex @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_iff
% 5.68/5.98 thf(fact_5905_power2__eq__iff,axiom,
% 5.68/5.98 ! [X: code_integer,Y2: code_integer] :
% 5.68/5.98 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ( X = Y2 )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus1351360451143612070nteger @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_iff
% 5.68/5.98 thf(fact_5906_power2__eq__iff,axiom,
% 5.68/5.98 ! [X: rat,Y2: rat] :
% 5.68/5.98 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ( X = Y2 )
% 5.68/5.98 | ( X
% 5.68/5.98 = ( uminus_uminus_rat @ Y2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_iff
% 5.68/5.98 thf(fact_5907_uminus__power__if,axiom,
% 5.68/5.98 ! [N: nat,A: real] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.68/5.98 = ( power_power_real @ A @ N ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_power_if
% 5.68/5.98 thf(fact_5908_uminus__power__if,axiom,
% 5.68/5.98 ! [N: nat,A: int] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.68/5.98 = ( power_power_int @ A @ N ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_power_if
% 5.68/5.98 thf(fact_5909_uminus__power__if,axiom,
% 5.68/5.98 ! [N: nat,A: complex] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.68/5.98 = ( power_power_complex @ A @ N ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_power_if
% 5.68/5.98 thf(fact_5910_uminus__power__if,axiom,
% 5.68/5.98 ! [N: nat,A: code_integer] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_power_if
% 5.68/5.98 thf(fact_5911_uminus__power__if,axiom,
% 5.68/5.98 ! [N: nat,A: rat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.68/5.98 = ( power_power_rat @ A @ N ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.68/5.98 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % uminus_power_if
% 5.68/5.98 thf(fact_5912_ln__add__one__self__le__self2,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/5.98 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.68/5.98
% 5.68/5.98 % ln_add_one_self_le_self2
% 5.68/5.98 thf(fact_5913_verit__less__mono__div__int2,axiom,
% 5.68/5.98 ! [A2: int,B4: int,N: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ A2 @ B4 )
% 5.68/5.98 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.68/5.98 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % verit_less_mono_div_int2
% 5.68/5.98 thf(fact_5914_abs__le__square__iff,axiom,
% 5.68/5.98 ! [X: code_integer,Y2: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y2 ) )
% 5.68/5.98 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_square_iff
% 5.68/5.98 thf(fact_5915_abs__le__square__iff,axiom,
% 5.68/5.98 ! [X: real,Y2: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) )
% 5.68/5.98 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_square_iff
% 5.68/5.98 thf(fact_5916_abs__le__square__iff,axiom,
% 5.68/5.98 ! [X: rat,Y2: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y2 ) )
% 5.68/5.98 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_square_iff
% 5.68/5.98 thf(fact_5917_abs__le__square__iff,axiom,
% 5.68/5.98 ! [X: int,Y2: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y2 ) )
% 5.68/5.98 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_le_square_iff
% 5.68/5.98 thf(fact_5918_power__mono__even,axiom,
% 5.68/5.98 ! [N: nat,A: code_integer,B: code_integer] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_mono_even
% 5.68/5.98 thf(fact_5919_power__mono__even,axiom,
% 5.68/5.98 ! [N: nat,A: real,B: real] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.68/5.98 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_mono_even
% 5.68/5.98 thf(fact_5920_power__mono__even,axiom,
% 5.68/5.98 ! [N: nat,A: rat,B: rat] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.68/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_mono_even
% 5.68/5.98 thf(fact_5921_power__mono__even,axiom,
% 5.68/5.98 ! [N: nat,A: int,B: int] :
% 5.68/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.68/5.98 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_mono_even
% 5.68/5.98 thf(fact_5922_abs__square__eq__1,axiom,
% 5.68/5.98 ! [X: code_integer] :
% 5.68/5.98 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_Code_integer )
% 5.68/5.98 = ( ( abs_abs_Code_integer @ X )
% 5.68/5.98 = one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_eq_1
% 5.68/5.98 thf(fact_5923_abs__square__eq__1,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_rat )
% 5.68/5.98 = ( ( abs_abs_rat @ X )
% 5.68/5.98 = one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_eq_1
% 5.68/5.98 thf(fact_5924_abs__square__eq__1,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_real )
% 5.68/5.98 = ( ( abs_abs_real @ X )
% 5.68/5.98 = one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_eq_1
% 5.68/5.98 thf(fact_5925_abs__square__eq__1,axiom,
% 5.68/5.98 ! [X: int] :
% 5.68/5.98 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_int )
% 5.68/5.98 = ( ( abs_abs_int @ X )
% 5.68/5.98 = one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_eq_1
% 5.68/5.98 thf(fact_5926_pos__minus__divide__le__eq,axiom,
% 5.68/5.98 ! [C: real,B: real,A: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_minus_divide_le_eq
% 5.68/5.98 thf(fact_5927_pos__minus__divide__le__eq,axiom,
% 5.68/5.98 ! [C: rat,B: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_minus_divide_le_eq
% 5.68/5.98 thf(fact_5928_pos__le__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: real,A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_le_minus_divide_eq
% 5.68/5.98 thf(fact_5929_pos__le__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % pos_le_minus_divide_eq
% 5.68/5.98 thf(fact_5930_neg__minus__divide__le__eq,axiom,
% 5.68/5.98 ! [C: real,B: real,A: real] :
% 5.68/5.98 ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_minus_divide_le_eq
% 5.68/5.98 thf(fact_5931_neg__minus__divide__le__eq,axiom,
% 5.68/5.98 ! [C: rat,B: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_minus_divide_le_eq
% 5.68/5.98 thf(fact_5932_neg__le__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: real,A: real,B: real] :
% 5.68/5.98 ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_le_minus_divide_eq
% 5.68/5.98 thf(fact_5933_neg__le__minus__divide__eq,axiom,
% 5.68/5.98 ! [C: rat,A: rat,B: rat] :
% 5.68/5.98 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_le_minus_divide_eq
% 5.68/5.98 thf(fact_5934_minus__divide__le__eq,axiom,
% 5.68/5.98 ! [B: real,C: real,A: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_le_eq
% 5.68/5.98 thf(fact_5935_minus__divide__le__eq,axiom,
% 5.68/5.98 ! [B: rat,C: rat,A: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_divide_le_eq
% 5.68/5.98 thf(fact_5936_le__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: real,B: real,C: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_divide_eq
% 5.68/5.98 thf(fact_5937_le__minus__divide__eq,axiom,
% 5.68/5.98 ! [A: rat,B: rat,C: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_minus_divide_eq
% 5.68/5.98 thf(fact_5938_divide__less__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: real,C: real,W: num] :
% 5.68/5.98 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_less_eq_numeral(2)
% 5.68/5.98 thf(fact_5939_divide__less__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: rat,C: rat,W: num] :
% 5.68/5.98 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_less_eq_numeral(2)
% 5.68/5.98 thf(fact_5940_less__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: real,C: real] :
% 5.68/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5941_less__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: rat,C: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % less_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5942_power2__eq__1__iff,axiom,
% 5.68/5.98 ! [A: real] :
% 5.68/5.98 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_real )
% 5.68/5.98 = ( ( A = one_one_real )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_1_iff
% 5.68/5.98 thf(fact_5943_power2__eq__1__iff,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_int )
% 5.68/5.98 = ( ( A = one_one_int )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_1_iff
% 5.68/5.98 thf(fact_5944_power2__eq__1__iff,axiom,
% 5.68/5.98 ! [A: complex] :
% 5.68/5.98 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_complex )
% 5.68/5.98 = ( ( A = one_one_complex )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_1_iff
% 5.68/5.98 thf(fact_5945_power2__eq__1__iff,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_Code_integer )
% 5.68/5.98 = ( ( A = one_one_Code_integer )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_1_iff
% 5.68/5.98 thf(fact_5946_power2__eq__1__iff,axiom,
% 5.68/5.98 ! [A: rat] :
% 5.68/5.98 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.98 = one_one_rat )
% 5.68/5.98 = ( ( A = one_one_rat )
% 5.68/5.98 | ( A
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_eq_1_iff
% 5.68/5.98 thf(fact_5947_minus__one__power__iff,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.68/5.98 = one_one_real ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_one_power_iff
% 5.68/5.98 thf(fact_5948_minus__one__power__iff,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.68/5.98 = one_one_int ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_one_power_iff
% 5.68/5.98 thf(fact_5949_minus__one__power__iff,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.68/5.98 = one_one_complex ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_one_power_iff
% 5.68/5.98 thf(fact_5950_minus__one__power__iff,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.68/5.98 = one_one_Code_integer ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_one_power_iff
% 5.68/5.98 thf(fact_5951_minus__one__power__iff,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.68/5.98 = one_one_rat ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_one_power_iff
% 5.68/5.98 thf(fact_5952_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.68/5.98 ! [K: nat,N: nat] :
% 5.68/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.68/5.98 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.68/5.98 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_power_add_eq_neg_one_power_diff
% 5.68/5.98 thf(fact_5953_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.68/5.98 ! [K: nat,N: nat] :
% 5.68/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.68/5.98 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.68/5.98 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_power_add_eq_neg_one_power_diff
% 5.68/5.98 thf(fact_5954_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.68/5.98 ! [K: nat,N: nat] :
% 5.68/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.68/5.98 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.68/5.98 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_power_add_eq_neg_one_power_diff
% 5.68/5.98 thf(fact_5955_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.68/5.98 ! [K: nat,N: nat] :
% 5.68/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.68/5.98 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_power_add_eq_neg_one_power_diff
% 5.68/5.98 thf(fact_5956_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.68/5.98 ! [K: nat,N: nat] :
% 5.68/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.68/5.98 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.68/5.98 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % neg_one_power_add_eq_neg_one_power_diff
% 5.68/5.98 thf(fact_5957_realpow__square__minus__le,axiom,
% 5.68/5.98 ! [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 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % realpow_square_minus_le
% 5.68/5.98 thf(fact_5958_ln__one__minus__pos__upper__bound,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.98 => ( ( ord_less_real @ X @ one_one_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % ln_one_minus_pos_upper_bound
% 5.68/5.98 thf(fact_5959_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.68/5.98 ! [N: nat,K: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.68/5.98 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_less_eq_self_iff
% 5.68/5.98 thf(fact_5960_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.68/5.98 ! [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 ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_greater_eq_minus_exp
% 5.68/5.98 thf(fact_5961_signed__take__bit__int__greater__self__iff,axiom,
% 5.68/5.98 ! [K: int,N: nat] :
% 5.68/5.98 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.68/5.98 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_greater_self_iff
% 5.68/5.98 thf(fact_5962_minus__mod__int__eq,axiom,
% 5.68/5.98 ! [L2: int,K: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.68/5.98 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.68/5.98 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_mod_int_eq
% 5.68/5.98 thf(fact_5963_power2__le__iff__abs__le,axiom,
% 5.68/5.98 ! [Y2: code_integer,X: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y2 )
% 5.68/5.98 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y2 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_le_iff_abs_le
% 5.68/5.98 thf(fact_5964_power2__le__iff__abs__le,axiom,
% 5.68/5.98 ! [Y2: real,X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/5.98 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y2 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_le_iff_abs_le
% 5.68/5.98 thf(fact_5965_power2__le__iff__abs__le,axiom,
% 5.68/5.98 ! [Y2: rat,X: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ Y2 )
% 5.68/5.98 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y2 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_le_iff_abs_le
% 5.68/5.98 thf(fact_5966_power2__le__iff__abs__le,axiom,
% 5.68/5.98 ! [Y2: int,X: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/5.98 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/5.98 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y2 ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % power2_le_iff_abs_le
% 5.68/5.98 thf(fact_5967_abs__sqrt__wlog,axiom,
% 5.68/5.98 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.68/5.98 ( ! [X3: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.68/5.98 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/5.98 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_sqrt_wlog
% 5.68/5.98 thf(fact_5968_abs__sqrt__wlog,axiom,
% 5.68/5.98 ! [P: real > real > $o,X: real] :
% 5.68/5.98 ( ! [X3: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.68/5.98 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/5.98 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_sqrt_wlog
% 5.68/5.98 thf(fact_5969_abs__sqrt__wlog,axiom,
% 5.68/5.98 ! [P: rat > rat > $o,X: rat] :
% 5.68/5.98 ( ! [X3: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.68/5.98 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/5.98 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_sqrt_wlog
% 5.68/5.98 thf(fact_5970_abs__sqrt__wlog,axiom,
% 5.68/5.98 ! [P: int > int > $o,X: int] :
% 5.68/5.98 ( ! [X3: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.68/5.98 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/5.98 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_sqrt_wlog
% 5.68/5.98 thf(fact_5971_abs__square__le__1,axiom,
% 5.68/5.98 ! [X: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.68/5.98 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_le_1
% 5.68/5.98 thf(fact_5972_abs__square__le__1,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.68/5.98 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_le_1
% 5.68/5.98 thf(fact_5973_abs__square__le__1,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.68/5.98 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_le_1
% 5.68/5.98 thf(fact_5974_abs__square__le__1,axiom,
% 5.68/5.98 ! [X: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.68/5.98 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_le_1
% 5.68/5.98 thf(fact_5975_abs__square__less__1,axiom,
% 5.68/5.98 ! [X: code_integer] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.68/5.98 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_less_1
% 5.68/5.98 thf(fact_5976_abs__square__less__1,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.68/5.98 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_less_1
% 5.68/5.98 thf(fact_5977_abs__square__less__1,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.68/5.98 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_less_1
% 5.68/5.98 thf(fact_5978_abs__square__less__1,axiom,
% 5.68/5.98 ! [X: int] :
% 5.68/5.98 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.68/5.98 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_square_less_1
% 5.68/5.98 thf(fact_5979_zminus1__lemma,axiom,
% 5.68/5.98 ! [A: int,B: int,Q2: int,R2: int] :
% 5.68/5.98 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/5.98 => ( ( B != zero_zero_int )
% 5.68/5.98 => ( 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 ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % zminus1_lemma
% 5.68/5.98 thf(fact_5980_divide__le__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: real,C: real,W: num] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_le_eq_numeral(2)
% 5.68/5.98 thf(fact_5981_divide__le__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [B: rat,C: rat,W: num] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % divide_le_eq_numeral(2)
% 5.68/5.98 thf(fact_5982_le__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: real,C: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.68/5.98 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.68/5.98 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5983_le__divide__eq__numeral_I2_J,axiom,
% 5.68/5.98 ! [W: num,B: rat,C: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.68/5.98 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.68/5.98 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.68/5.98 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % le_divide_eq_numeral(2)
% 5.68/5.98 thf(fact_5984_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/5.98 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/5.98 => ( 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 ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.68/5.98 thf(fact_5985_square__le__1,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/5.98 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/5.98 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_le_1
% 5.68/5.98 thf(fact_5986_square__le__1,axiom,
% 5.68/5.98 ! [X: code_integer] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.68/5.98 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.68/5.98 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_le_1
% 5.68/5.98 thf(fact_5987_square__le__1,axiom,
% 5.68/5.98 ! [X: rat] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.68/5.98 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.68/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_le_1
% 5.68/5.98 thf(fact_5988_square__le__1,axiom,
% 5.68/5.98 ! [X: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.68/5.98 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.68/5.98 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % square_le_1
% 5.68/5.98 thf(fact_5989_minus__power__mult__self,axiom,
% 5.68/5.98 ! [A: real,N: nat] :
% 5.68/5.98 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.68/5.98 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_power_mult_self
% 5.68/5.98 thf(fact_5990_minus__power__mult__self,axiom,
% 5.68/5.98 ! [A: int,N: nat] :
% 5.68/5.98 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.68/5.98 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_power_mult_self
% 5.68/5.98 thf(fact_5991_minus__power__mult__self,axiom,
% 5.68/5.98 ! [A: complex,N: nat] :
% 5.68/5.98 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.68/5.98 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_power_mult_self
% 5.68/5.98 thf(fact_5992_minus__power__mult__self,axiom,
% 5.68/5.98 ! [A: code_integer,N: nat] :
% 5.68/5.98 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.68/5.98 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_power_mult_self
% 5.68/5.98 thf(fact_5993_minus__power__mult__self,axiom,
% 5.68/5.98 ! [A: rat,N: nat] :
% 5.68/5.98 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.68/5.98 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_power_mult_self
% 5.68/5.98 thf(fact_5994_signed__take__bit__int__eq__self,axiom,
% 5.68/5.98 ! [N: nat,K: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.68/5.98 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.68/5.98 = K ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_eq_self
% 5.68/5.98 thf(fact_5995_signed__take__bit__int__eq__self__iff,axiom,
% 5.68/5.98 ! [N: nat,K: int] :
% 5.68/5.98 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.68/5.98 = K )
% 5.68/5.98 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.68/5.98 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_eq_self_iff
% 5.68/5.98 thf(fact_5996_minus__1__div__exp__eq__int,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % minus_1_div_exp_eq_int
% 5.68/5.98 thf(fact_5997_div__pos__neg__trivial,axiom,
% 5.68/5.98 ! [K: int,L2: int] :
% 5.68/5.98 ( ( ord_less_int @ zero_zero_int @ K )
% 5.68/5.98 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.68/5.98 => ( ( divide_divide_int @ K @ L2 )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % div_pos_neg_trivial
% 5.68/5.98 thf(fact_5998_power__minus1__odd,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_odd
% 5.68/5.98 thf(fact_5999_power__minus1__odd,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_odd
% 5.68/5.98 thf(fact_6000_power__minus1__odd,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_odd
% 5.68/5.98 thf(fact_6001_power__minus1__odd,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_odd
% 5.68/5.98 thf(fact_6002_power__minus1__odd,axiom,
% 5.68/5.98 ! [N: nat] :
% 5.68/5.98 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.98
% 5.68/5.98 % power_minus1_odd
% 5.68/5.98 thf(fact_6003_int__bit__induct,axiom,
% 5.68/5.98 ! [P: int > $o,K: int] :
% 5.68/5.98 ( ( P @ zero_zero_int )
% 5.68/5.98 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 => ( ! [K2: int] :
% 5.68/5.98 ( ( P @ K2 )
% 5.68/5.98 => ( ( K2 != zero_zero_int )
% 5.68/5.98 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.68/5.98 => ( ! [K2: int] :
% 5.68/5.98 ( ( P @ K2 )
% 5.68/5.98 => ( ( K2
% 5.68/5.98 != ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.98 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.68/5.98 => ( P @ K ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % int_bit_induct
% 5.68/5.98 thf(fact_6004_eq__diff__eq_H,axiom,
% 5.68/5.98 ! [X: real,Y2: real,Z: real] :
% 5.68/5.98 ( ( X
% 5.68/5.98 = ( minus_minus_real @ Y2 @ Z ) )
% 5.68/5.98 = ( Y2
% 5.68/5.98 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % eq_diff_eq'
% 5.68/5.98 thf(fact_6005_signed__take__bit__int__greater__eq,axiom,
% 5.68/5.98 ! [K: int,N: nat] :
% 5.68/5.98 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/5.98 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_int_greater_eq
% 5.68/5.98 thf(fact_6006_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/5.98 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/5.98 => ( 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 ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.68/5.98 thf(fact_6007_vebt__buildup_Osimps_I3_J,axiom,
% 5.68/5.98 ! [Va: nat] :
% 5.68/5.98 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.68/5.98 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.68/5.98 = ( 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 ) ) ) ) ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.68/5.98 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.68/5.98 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % vebt_buildup.simps(3)
% 5.68/5.98 thf(fact_6008_arctan__double,axiom,
% 5.68/5.98 ! [X: real] :
% 5.68/5.98 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/5.98 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.68/5.98 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % arctan_double
% 5.68/5.98 thf(fact_6009_signed__take__bit__Suc__minus__bit1,axiom,
% 5.68/5.98 ! [N: nat,K: num] :
% 5.68/5.98 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/5.98 = ( 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 ) ) ).
% 5.68/5.98
% 5.68/5.98 % signed_take_bit_Suc_minus_bit1
% 5.68/5.98 thf(fact_6010_vebt__buildup_Opelims,axiom,
% 5.68/5.98 ! [X: nat,Y2: vEBT_VEBT] :
% 5.68/5.98 ( ( ( vEBT_vebt_buildup @ X )
% 5.68/5.98 = Y2 )
% 5.68/5.98 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.68/5.98 => ( ( ( X = zero_zero_nat )
% 5.68/5.98 => ( ( Y2
% 5.68/5.98 = ( vEBT_Leaf @ $false @ $false ) )
% 5.68/5.98 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.68/5.98 => ( ( ( X
% 5.68/5.98 = ( suc @ zero_zero_nat ) )
% 5.68/5.98 => ( ( Y2
% 5.68/5.98 = ( vEBT_Leaf @ $false @ $false ) )
% 5.68/5.98 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.68/5.98 => ~ ! [Va3: nat] :
% 5.68/5.98 ( ( X
% 5.68/5.98 = ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.98 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.98 => ( Y2
% 5.68/5.98 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.68/5.98 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.68/5.98 => ( Y2
% 5.68/5.98 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.68/5.98 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % vebt_buildup.pelims
% 5.68/5.98 thf(fact_6011_flip__bit__0,axiom,
% 5.68/5.98 ! [A: code_integer] :
% 5.68/5.98 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.68/5.98 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % flip_bit_0
% 5.68/5.98 thf(fact_6012_flip__bit__0,axiom,
% 5.68/5.98 ! [A: int] :
% 5.68/5.98 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.68/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % flip_bit_0
% 5.68/5.98 thf(fact_6013_flip__bit__0,axiom,
% 5.68/5.98 ! [A: nat] :
% 5.68/5.98 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.68/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % flip_bit_0
% 5.68/5.98 thf(fact_6014_set__decode__0,axiom,
% 5.68/5.98 ! [X: nat] :
% 5.68/5.98 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.68/5.98 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % set_decode_0
% 5.68/5.98 thf(fact_6015_set__decode__Suc,axiom,
% 5.68/5.98 ! [N: nat,X: nat] :
% 5.68/5.98 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.68/5.98 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % set_decode_Suc
% 5.68/5.98 thf(fact_6016_Sum__Icc__int,axiom,
% 5.68/5.98 ! [M: int,N: int] :
% 5.68/5.98 ( ( ord_less_eq_int @ M @ N )
% 5.68/5.98 => ( ( groups4538972089207619220nt_int
% 5.68/5.98 @ ^ [X2: int] : X2
% 5.68/5.98 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.68/5.98 = ( 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 ) ) ) ) ) ).
% 5.68/5.98
% 5.68/5.98 % Sum_Icc_int
% 5.68/5.98 thf(fact_6017_semiring__norm_I90_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ( bit1 @ M )
% 5.68/5.98 = ( bit1 @ N ) )
% 5.68/5.98 = ( M = N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(90)
% 5.68/5.98 thf(fact_6018_semiring__norm_I88_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( bit0 @ M )
% 5.68/5.98 != ( bit1 @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(88)
% 5.68/5.98 thf(fact_6019_semiring__norm_I89_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( bit1 @ M )
% 5.68/5.98 != ( bit0 @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(89)
% 5.68/5.98 thf(fact_6020_semiring__norm_I84_J,axiom,
% 5.68/5.98 ! [N: num] :
% 5.68/5.98 ( one
% 5.68/5.98 != ( bit1 @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(84)
% 5.68/5.98 thf(fact_6021_semiring__norm_I86_J,axiom,
% 5.68/5.98 ! [M: num] :
% 5.68/5.98 ( ( bit1 @ M )
% 5.68/5.98 != one ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(86)
% 5.68/5.98 thf(fact_6022_of__bool__less__eq__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.68/5.98 = ( P
% 5.68/5.98 => Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_eq_iff
% 5.68/5.98 thf(fact_6023_of__bool__less__eq__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.68/5.98 = ( P
% 5.68/5.98 => Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_eq_iff
% 5.68/5.98 thf(fact_6024_of__bool__less__eq__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.68/5.98 = ( P
% 5.68/5.98 => Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_eq_iff
% 5.68/5.98 thf(fact_6025_of__bool__less__eq__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.68/5.98 = ( P
% 5.68/5.98 => Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_eq_iff
% 5.68/5.98 thf(fact_6026_of__bool__less__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.68/5.98 = ( ~ P
% 5.68/5.98 & Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_iff
% 5.68/5.98 thf(fact_6027_of__bool__less__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.68/5.98 = ( ~ P
% 5.68/5.98 & Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_iff
% 5.68/5.98 thf(fact_6028_of__bool__less__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.68/5.98 = ( ~ P
% 5.68/5.98 & Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_iff
% 5.68/5.98 thf(fact_6029_of__bool__less__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.68/5.98 = ( ~ P
% 5.68/5.98 & Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_iff
% 5.68/5.98 thf(fact_6030_of__bool__less__iff,axiom,
% 5.68/5.98 ! [P: $o,Q: $o] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.68/5.98 = ( ~ P
% 5.68/5.98 & Q ) ) ).
% 5.68/5.98
% 5.68/5.98 % of_bool_less_iff
% 5.68/5.98 thf(fact_6031_semiring__norm_I80_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.98 = ( ord_less_num @ M @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(80)
% 5.68/5.98 thf(fact_6032_semiring__norm_I73_J,axiom,
% 5.68/5.98 ! [M: num,N: num] :
% 5.68/5.98 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.98 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.68/5.98
% 5.68/5.98 % semiring_norm(73)
% 5.68/5.98 thf(fact_6033_zero__less__of__bool__iff,axiom,
% 5.68/5.98 ! [P: $o] :
% 5.68/5.98 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.68/5.98 = P ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_of_bool_iff
% 5.68/5.98 thf(fact_6034_zero__less__of__bool__iff,axiom,
% 5.68/5.98 ! [P: $o] :
% 5.68/5.98 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.68/5.98 = P ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_of_bool_iff
% 5.68/5.98 thf(fact_6035_zero__less__of__bool__iff,axiom,
% 5.68/5.98 ! [P: $o] :
% 5.68/5.98 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/5.98 = P ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_of_bool_iff
% 5.68/5.98 thf(fact_6036_zero__less__of__bool__iff,axiom,
% 5.68/5.98 ! [P: $o] :
% 5.68/5.98 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.68/5.98 = P ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_of_bool_iff
% 5.68/5.98 thf(fact_6037_zero__less__of__bool__iff,axiom,
% 5.68/5.98 ! [P: $o] :
% 5.68/5.98 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.68/5.98 = P ) ).
% 5.68/5.98
% 5.68/5.98 % zero_less_of_bool_iff
% 5.68/5.99 thf(fact_6038_of__bool__less__one__iff,axiom,
% 5.68/5.99 ! [P: $o] :
% 5.68/5.99 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.68/5.99 = ~ P ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_one_iff
% 5.68/5.99 thf(fact_6039_of__bool__less__one__iff,axiom,
% 5.68/5.99 ! [P: $o] :
% 5.68/5.99 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.68/5.99 = ~ P ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_one_iff
% 5.68/5.99 thf(fact_6040_of__bool__less__one__iff,axiom,
% 5.68/5.99 ! [P: $o] :
% 5.68/5.99 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.68/5.99 = ~ P ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_one_iff
% 5.68/5.99 thf(fact_6041_of__bool__less__one__iff,axiom,
% 5.68/5.99 ! [P: $o] :
% 5.68/5.99 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.68/5.99 = ~ P ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_one_iff
% 5.68/5.99 thf(fact_6042_of__bool__less__one__iff,axiom,
% 5.68/5.99 ! [P: $o] :
% 5.68/5.99 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.68/5.99 = ~ P ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_one_iff
% 5.68/5.99 thf(fact_6043_Suc__0__mod__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/5.99 = ( zero_n2687167440665602831ol_nat
% 5.68/5.99 @ ( N
% 5.68/5.99 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_0_mod_eq
% 5.68/5.99 thf(fact_6044_semiring__norm_I9_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/5.99 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(9)
% 5.68/5.99 thf(fact_6045_semiring__norm_I7_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(7)
% 5.68/5.99 thf(fact_6046_zero__le__arctan__iff,axiom,
% 5.68/5.99 ! [X: real] :
% 5.68/5.99 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.68/5.99 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_le_arctan_iff
% 5.68/5.99 thf(fact_6047_arctan__le__zero__iff,axiom,
% 5.68/5.99 ! [X: real] :
% 5.68/5.99 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.68/5.99 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % arctan_le_zero_iff
% 5.68/5.99 thf(fact_6048_semiring__norm_I15_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/5.99 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(15)
% 5.68/5.99 thf(fact_6049_semiring__norm_I14_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(14)
% 5.68/5.99 thf(fact_6050_semiring__norm_I81_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/5.99 = ( ord_less_num @ M @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(81)
% 5.68/5.99 thf(fact_6051_semiring__norm_I72_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(72)
% 5.68/5.99 thf(fact_6052_semiring__norm_I77_J,axiom,
% 5.68/5.99 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(77)
% 5.68/5.99 thf(fact_6053_semiring__norm_I70_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(70)
% 5.68/5.99 thf(fact_6054_sum__abs,axiom,
% 5.68/5.99 ! [F: int > int,A2: set_int] :
% 5.68/5.99 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.68/5.99 @ ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_abs
% 5.68/5.99 thf(fact_6055_sum__abs,axiom,
% 5.68/5.99 ! [F: nat > real,A2: set_nat] :
% 5.68/5.99 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.68/5.99 @ ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_abs
% 5.68/5.99 thf(fact_6056_zdiv__numeral__Bit1,axiom,
% 5.68/5.99 ! [V: num,W: num] :
% 5.68/5.99 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.68/5.99 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % zdiv_numeral_Bit1
% 5.68/5.99 thf(fact_6057_semiring__norm_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.68/5.99 = ( bit1 @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(3)
% 5.68/5.99 thf(fact_6058_semiring__norm_I4_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.68/5.99 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(4)
% 5.68/5.99 thf(fact_6059_semiring__norm_I5_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.68/5.99 = ( bit1 @ M ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(5)
% 5.68/5.99 thf(fact_6060_semiring__norm_I8_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.68/5.99 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(8)
% 5.68/5.99 thf(fact_6061_semiring__norm_I10_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(10)
% 5.68/5.99 thf(fact_6062_sum__abs__ge__zero,axiom,
% 5.68/5.99 ! [F: int > int,A2: set_int] :
% 5.68/5.99 ( ord_less_eq_int @ zero_zero_int
% 5.68/5.99 @ ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_abs_ge_zero
% 5.68/5.99 thf(fact_6063_sum__abs__ge__zero,axiom,
% 5.68/5.99 ! [F: nat > real,A2: set_nat] :
% 5.68/5.99 ( ord_less_eq_real @ zero_zero_real
% 5.68/5.99 @ ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_abs_ge_zero
% 5.68/5.99 thf(fact_6064_semiring__norm_I16_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(16)
% 5.68/5.99 thf(fact_6065_semiring__norm_I79_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(79)
% 5.68/5.99 thf(fact_6066_semiring__norm_I74_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/5.99 = ( ord_less_num @ M @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % semiring_norm(74)
% 5.68/5.99 thf(fact_6067_odd__of__bool__self,axiom,
% 5.68/5.99 ! [P4: $o] :
% 5.68/5.99 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P4 ) ) )
% 5.68/5.99 = P4 ) ).
% 5.68/5.99
% 5.68/5.99 % odd_of_bool_self
% 5.68/5.99 thf(fact_6068_odd__of__bool__self,axiom,
% 5.68/5.99 ! [P4: $o] :
% 5.68/5.99 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P4 ) ) )
% 5.68/5.99 = P4 ) ).
% 5.68/5.99
% 5.68/5.99 % odd_of_bool_self
% 5.68/5.99 thf(fact_6069_odd__of__bool__self,axiom,
% 5.68/5.99 ! [P4: $o] :
% 5.68/5.99 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P4 ) ) )
% 5.68/5.99 = P4 ) ).
% 5.68/5.99
% 5.68/5.99 % odd_of_bool_self
% 5.68/5.99 thf(fact_6070_of__bool__half__eq__0,axiom,
% 5.68/5.99 ! [B: $o] :
% 5.68/5.99 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.99 = zero_zero_nat ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_half_eq_0
% 5.68/5.99 thf(fact_6071_of__bool__half__eq__0,axiom,
% 5.68/5.99 ! [B: $o] :
% 5.68/5.99 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.99 = zero_zero_int ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_half_eq_0
% 5.68/5.99 thf(fact_6072_of__bool__half__eq__0,axiom,
% 5.68/5.99 ! [B: $o] :
% 5.68/5.99 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.99 = zero_z3403309356797280102nteger ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_half_eq_0
% 5.68/5.99 thf(fact_6073_Suc__div__eq__add3__div__numeral,axiom,
% 5.68/5.99 ! [M: nat,V: num] :
% 5.68/5.99 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.68/5.99 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_div_eq_add3_div_numeral
% 5.68/5.99 thf(fact_6074_div__Suc__eq__div__add3,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.68/5.99 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % div_Suc_eq_div_add3
% 5.68/5.99 thf(fact_6075_mod__Suc__eq__mod__add3,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.68/5.99 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % mod_Suc_eq_mod_add3
% 5.68/5.99 thf(fact_6076_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.68/5.99 ! [M: nat,V: num] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.68/5.99 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_mod_eq_add3_mod_numeral
% 5.68/5.99 thf(fact_6077_bits__1__div__exp,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_1_div_exp
% 5.68/5.99 thf(fact_6078_bits__1__div__exp,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_1_div_exp
% 5.68/5.99 thf(fact_6079_bits__1__div__exp,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_1_div_exp
% 5.68/5.99 thf(fact_6080_one__div__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_div_2_pow_eq
% 5.68/5.99 thf(fact_6081_one__div__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_div_2_pow_eq
% 5.68/5.99 thf(fact_6082_one__div__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_div_2_pow_eq
% 5.68/5.99 thf(fact_6083_zmod__numeral__Bit1,axiom,
% 5.68/5.99 ! [V: num,W: num] :
% 5.68/5.99 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.68/5.99 = ( 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 ) ) ).
% 5.68/5.99
% 5.68/5.99 % zmod_numeral_Bit1
% 5.68/5.99 thf(fact_6084_one__mod__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_mod_2_pow_eq
% 5.68/5.99 thf(fact_6085_one__mod__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_mod_2_pow_eq
% 5.68/5.99 thf(fact_6086_one__mod__2__pow__eq,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % one_mod_2_pow_eq
% 5.68/5.99 thf(fact_6087_signed__take__bit__Suc__bit1,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % signed_take_bit_Suc_bit1
% 5.68/5.99 thf(fact_6088_of__bool__conj,axiom,
% 5.68/5.99 ! [P: $o,Q: $o] :
% 5.68/5.99 ( ( zero_n3304061248610475627l_real
% 5.68/5.99 @ ( P
% 5.68/5.99 & Q ) )
% 5.68/5.99 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_conj
% 5.68/5.99 thf(fact_6089_of__bool__conj,axiom,
% 5.68/5.99 ! [P: $o,Q: $o] :
% 5.68/5.99 ( ( zero_n2052037380579107095ol_rat
% 5.68/5.99 @ ( P
% 5.68/5.99 & Q ) )
% 5.68/5.99 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_conj
% 5.68/5.99 thf(fact_6090_of__bool__conj,axiom,
% 5.68/5.99 ! [P: $o,Q: $o] :
% 5.68/5.99 ( ( zero_n2687167440665602831ol_nat
% 5.68/5.99 @ ( P
% 5.68/5.99 & Q ) )
% 5.68/5.99 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_conj
% 5.68/5.99 thf(fact_6091_of__bool__conj,axiom,
% 5.68/5.99 ! [P: $o,Q: $o] :
% 5.68/5.99 ( ( zero_n2684676970156552555ol_int
% 5.68/5.99 @ ( P
% 5.68/5.99 & Q ) )
% 5.68/5.99 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_conj
% 5.68/5.99 thf(fact_6092_of__bool__conj,axiom,
% 5.68/5.99 ! [P: $o,Q: $o] :
% 5.68/5.99 ( ( zero_n356916108424825756nteger
% 5.68/5.99 @ ( P
% 5.68/5.99 & Q ) )
% 5.68/5.99 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_conj
% 5.68/5.99 thf(fact_6093_verit__eq__simplify_I14_J,axiom,
% 5.68/5.99 ! [X22: num,X32: num] :
% 5.68/5.99 ( ( bit0 @ X22 )
% 5.68/5.99 != ( bit1 @ X32 ) ) ).
% 5.68/5.99
% 5.68/5.99 % verit_eq_simplify(14)
% 5.68/5.99 thf(fact_6094_verit__eq__simplify_I12_J,axiom,
% 5.68/5.99 ! [X32: num] :
% 5.68/5.99 ( one
% 5.68/5.99 != ( bit1 @ X32 ) ) ).
% 5.68/5.99
% 5.68/5.99 % verit_eq_simplify(12)
% 5.68/5.99 thf(fact_6095_arctan__monotone_H,axiom,
% 5.68/5.99 ! [X: real,Y2: real] :
% 5.68/5.99 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % arctan_monotone'
% 5.68/5.99 thf(fact_6096_arctan__le__iff,axiom,
% 5.68/5.99 ! [X: real,Y2: real] :
% 5.68/5.99 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 5.68/5.99 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % arctan_le_iff
% 5.68/5.99 thf(fact_6097_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6098_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6099_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.68/5.99 ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6100_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.68/5.99 ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6101_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6102_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.68/5.99 ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6103_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.68/5.99 ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6104_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6105_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_real,F: real > int,G: real > int] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6106_sum__mono,axiom,
% 5.68/5.99 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.68/5.99 ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ K5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono
% 5.68/5.99 thf(fact_6107_sum__product,axiom,
% 5.68/5.99 ! [F: int > int,A2: set_int,G: int > int,B4: set_int] :
% 5.68/5.99 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B4 ) )
% 5.68/5.99 = ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [I3: int] :
% 5.68/5.99 ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [J3: int] : ( times_times_int @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.68/5.99 @ B4 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_product
% 5.68/5.99 thf(fact_6108_sum__product,axiom,
% 5.68/5.99 ! [F: complex > complex,A2: set_complex,G: complex > complex,B4: set_complex] :
% 5.68/5.99 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B4 ) )
% 5.68/5.99 = ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [I3: complex] :
% 5.68/5.99 ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.68/5.99 @ B4 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_product
% 5.68/5.99 thf(fact_6109_sum__product,axiom,
% 5.68/5.99 ! [F: nat > nat,A2: set_nat,G: nat > nat,B4: set_nat] :
% 5.68/5.99 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B4 ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] :
% 5.68/5.99 ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.68/5.99 @ B4 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_product
% 5.68/5.99 thf(fact_6110_sum__product,axiom,
% 5.68/5.99 ! [F: nat > real,A2: set_nat,G: nat > real,B4: set_nat] :
% 5.68/5.99 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B4 ) )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] :
% 5.68/5.99 ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [J3: nat] : ( times_times_real @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.68/5.99 @ B4 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_product
% 5.68/5.99 thf(fact_6111_sum__distrib__right,axiom,
% 5.68/5.99 ! [F: int > int,A2: set_int,R2: int] :
% 5.68/5.99 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_right
% 5.68/5.99 thf(fact_6112_sum__distrib__right,axiom,
% 5.68/5.99 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.68/5.99 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_right
% 5.68/5.99 thf(fact_6113_sum__distrib__right,axiom,
% 5.68/5.99 ! [F: nat > nat,A2: set_nat,R2: nat] :
% 5.68/5.99 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_right
% 5.68/5.99 thf(fact_6114_sum__distrib__right,axiom,
% 5.68/5.99 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.68/5.99 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_right
% 5.68/5.99 thf(fact_6115_sum__distrib__left,axiom,
% 5.68/5.99 ! [R2: int,F: int > int,A2: set_int] :
% 5.68/5.99 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.68/5.99 = ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [N2: int] : ( times_times_int @ R2 @ ( F @ N2 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_left
% 5.68/5.99 thf(fact_6116_sum__distrib__left,axiom,
% 5.68/5.99 ! [R2: complex,F: complex > complex,A2: set_complex] :
% 5.68/5.99 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.68/5.99 = ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [N2: complex] : ( times_times_complex @ R2 @ ( F @ N2 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_left
% 5.68/5.99 thf(fact_6117_sum__distrib__left,axiom,
% 5.68/5.99 ! [R2: nat,F: nat > nat,A2: set_nat] :
% 5.68/5.99 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [N2: nat] : ( times_times_nat @ R2 @ ( F @ N2 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_left
% 5.68/5.99 thf(fact_6118_sum__distrib__left,axiom,
% 5.68/5.99 ! [R2: real,F: nat > real,A2: set_nat] :
% 5.68/5.99 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( F @ N2 ) )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_distrib_left
% 5.68/5.99 thf(fact_6119_sum_Odistrib,axiom,
% 5.68/5.99 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.68/5.99 ( ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.distrib
% 5.68/5.99 thf(fact_6120_sum_Odistrib,axiom,
% 5.68/5.99 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.68/5.99 ( ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.distrib
% 5.68/5.99 thf(fact_6121_sum_Odistrib,axiom,
% 5.68/5.99 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.68/5.99 ( ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.distrib
% 5.68/5.99 thf(fact_6122_sum_Odistrib,axiom,
% 5.68/5.99 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.distrib
% 5.68/5.99 thf(fact_6123_sum__divide__distrib,axiom,
% 5.68/5.99 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.68/5.99 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_divide_distrib
% 5.68/5.99 thf(fact_6124_sum__divide__distrib,axiom,
% 5.68/5.99 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.68/5.99 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R2 )
% 5.68/5.99 @ A2 ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_divide_distrib
% 5.68/5.99 thf(fact_6125_mod__sum__eq,axiom,
% 5.68/5.99 ! [F: int > int,A: int,A2: set_int] :
% 5.68/5.99 ( ( modulo_modulo_int
% 5.68/5.99 @ ( groups4538972089207619220nt_int
% 5.68/5.99 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.68/5.99 @ A2 )
% 5.68/5.99 @ A )
% 5.68/5.99 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % mod_sum_eq
% 5.68/5.99 thf(fact_6126_mod__sum__eq,axiom,
% 5.68/5.99 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.68/5.99 ( ( modulo_modulo_nat
% 5.68/5.99 @ ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.68/5.99 @ A2 )
% 5.68/5.99 @ A )
% 5.68/5.99 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % mod_sum_eq
% 5.68/5.99 thf(fact_6127_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > real] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6128_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > real] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6129_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > real] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6130_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > rat] :
% 5.68/5.99 ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6131_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > rat] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6132_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > rat] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6133_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > rat] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6134_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > nat] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6135_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6136_sum__nonneg,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg
% 5.68/5.99 thf(fact_6137_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > real] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6138_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > real] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6139_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > real] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6140_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > rat] :
% 5.68/5.99 ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6141_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > rat] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6142_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > rat] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6143_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > rat] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6144_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > nat] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6145_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6146_sum__nonpos,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonpos
% 5.68/5.99 thf(fact_6147_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: real > rat,I5: set_real,G: real > rat,I2: real] :
% 5.68/5.99 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6148_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: nat > rat,I5: set_nat,G: nat > rat,I2: nat] :
% 5.68/5.99 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.68/5.99 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_nat @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_nat @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6149_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: int > rat,I5: set_int,G: int > rat,I2: int] :
% 5.68/5.99 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.68/5.99 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_int @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6150_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: complex > rat,I5: set_complex,G: complex > rat,I2: complex] :
% 5.68/5.99 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6151_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: real > nat,I5: set_real,G: real > nat,I2: real] :
% 5.68/5.99 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6152_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: int > nat,I5: set_int,G: int > nat,I2: int] :
% 5.68/5.99 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.68/5.99 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_int @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6153_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: complex > nat,I5: set_complex,G: complex > nat,I2: complex] :
% 5.68/5.99 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6154_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: real > int,I5: set_real,G: real > int,I2: real] :
% 5.68/5.99 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6155_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: nat > int,I5: set_nat,G: nat > int,I2: nat] :
% 5.68/5.99 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.68/5.99 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_nat @ I2 @ I5 )
% 5.68/5.99 => ( ( finite_finite_nat @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6156_sum__mono__inv,axiom,
% 5.68/5.99 ! [F: complex > int,I5: set_complex,G: complex > int,I2: complex] :
% 5.68/5.99 ( ( ( groups5690904116761175830ex_int @ F @ I5 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ G @ I5 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = ( G @ I2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono_inv
% 5.68/5.99 thf(fact_6157_zero__less__eq__of__bool,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_less_eq_of_bool
% 5.68/5.99 thf(fact_6158_zero__less__eq__of__bool,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_less_eq_of_bool
% 5.68/5.99 thf(fact_6159_zero__less__eq__of__bool,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_less_eq_of_bool
% 5.68/5.99 thf(fact_6160_zero__less__eq__of__bool,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_less_eq_of_bool
% 5.68/5.99 thf(fact_6161_zero__less__eq__of__bool,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.68/5.99
% 5.68/5.99 % zero_less_eq_of_bool
% 5.68/5.99 thf(fact_6162_of__bool__less__eq__one,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_eq_one
% 5.68/5.99 thf(fact_6163_of__bool__less__eq__one,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_eq_one
% 5.68/5.99 thf(fact_6164_of__bool__less__eq__one,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_eq_one
% 5.68/5.99 thf(fact_6165_of__bool__less__eq__one,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_eq_one
% 5.68/5.99 thf(fact_6166_of__bool__less__eq__one,axiom,
% 5.68/5.99 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_less_eq_one
% 5.68/5.99 thf(fact_6167_num_Oexhaust,axiom,
% 5.68/5.99 ! [Y2: num] :
% 5.68/5.99 ( ( Y2 != one )
% 5.68/5.99 => ( ! [X23: num] :
% 5.68/5.99 ( Y2
% 5.68/5.99 != ( bit0 @ X23 ) )
% 5.68/5.99 => ~ ! [X33: num] :
% 5.68/5.99 ( Y2
% 5.68/5.99 != ( bit1 @ X33 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % num.exhaust
% 5.68/5.99 thf(fact_6168_xor__num_Ocases,axiom,
% 5.68/5.99 ! [X: product_prod_num_num] :
% 5.68/5.99 ( ( X
% 5.68/5.99 != ( product_Pair_num_num @ one @ one ) )
% 5.68/5.99 => ( ! [N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.68/5.99 => ( ! [N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.68/5.99 => ( ! [M5: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.68/5.99 => ( ! [M5: num,N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.68/5.99 => ( ! [M5: num,N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 5.68/5.99 => ( ! [M5: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.68/5.99 => ( ! [M5: num,N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.68/5.99 => ~ ! [M5: num,N3: num] :
% 5.68/5.99 ( X
% 5.68/5.99 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % xor_num.cases
% 5.68/5.99 thf(fact_6169_abs__zmult__eq__1,axiom,
% 5.68/5.99 ! [M: int,N: int] :
% 5.68/5.99 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.68/5.99 = one_one_int )
% 5.68/5.99 => ( ( abs_abs_int @ M )
% 5.68/5.99 = one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % abs_zmult_eq_1
% 5.68/5.99 thf(fact_6170_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_int,T: set_int,G: int > real,I2: int > int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ( finite_finite_int @ T )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: int] :
% 5.68/5.99 ( ( member_int @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6171_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_int,T: set_complex,G: complex > real,I2: complex > int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ T )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: complex] :
% 5.68/5.99 ( ( member_complex @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6172_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_complex,T: set_int,G: int > real,I2: int > complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ( finite_finite_int @ T )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: int] :
% 5.68/5.99 ( ( member_int @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6173_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ T )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: complex] :
% 5.68/5.99 ( ( member_complex @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6174_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_nat,T: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ S2 )
% 5.68/5.99 => ( ( finite_finite_nat @ T )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: nat] :
% 5.68/5.99 ( ( member_nat @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6175_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_nat,T: set_int,G: int > rat,I2: int > nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ S2 )
% 5.68/5.99 => ( ( finite_finite_int @ T )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: int] :
% 5.68/5.99 ( ( member_int @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6176_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_nat,T: set_complex,G: complex > rat,I2: complex > nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ S2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ T )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: complex] :
% 5.68/5.99 ( ( member_complex @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6177_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_int,T: set_nat,G: nat > rat,I2: nat > int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ( finite_finite_nat @ T )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: nat] :
% 5.68/5.99 ( ( member_nat @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6178_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_int,T: set_int,G: int > rat,I2: int > int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ( finite_finite_int @ T )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: int] :
% 5.68/5.99 ( ( member_int @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6179_sum__le__included,axiom,
% 5.68/5.99 ! [S2: set_int,T: set_complex,G: complex > rat,I2: complex > int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ T )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ T )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S2 )
% 5.68/5.99 => ? [Xa: complex] :
% 5.68/5.99 ( ( member_complex @ Xa @ T )
% 5.68/5.99 & ( ( I2 @ Xa )
% 5.68/5.99 = X3 )
% 5.68/5.99 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_le_included
% 5.68/5.99 thf(fact_6180_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 = ( ! [X2: real] :
% 5.68/5.99 ( ( member_real @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6181_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 = ( ! [X2: int] :
% 5.68/5.99 ( ( member_int @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6182_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 = ( ! [X2: complex] :
% 5.68/5.99 ( ( member_complex @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6183_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 = ( ! [X2: real] :
% 5.68/5.99 ( ( member_real @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6184_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 = ( ! [X2: nat] :
% 5.68/5.99 ( ( member_nat @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6185_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 = ( ! [X2: int] :
% 5.68/5.99 ( ( member_int @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6186_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 = ( ! [X2: complex] :
% 5.68/5.99 ( ( member_complex @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6187_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 = ( ! [X2: real] :
% 5.68/5.99 ( ( member_real @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6188_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 = ( ! [X2: int] :
% 5.68/5.99 ( ( member_int @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6189_sum__nonneg__eq__0__iff,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 = ( ! [X2: complex] :
% 5.68/5.99 ( ( member_complex @ X2 @ A2 )
% 5.68/5.99 => ( ( F @ X2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_eq_0_iff
% 5.68/5.99 thf(fact_6190_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > real,G: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: int] :
% 5.68/5.99 ( ( member_int @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6191_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: complex] :
% 5.68/5.99 ( ( member_complex @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6192_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: nat] :
% 5.68/5.99 ( ( member_nat @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6193_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: int] :
% 5.68/5.99 ( ( member_int @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6194_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: complex] :
% 5.68/5.99 ( ( member_complex @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6195_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: int] :
% 5.68/5.99 ( ( member_int @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6196_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: complex] :
% 5.68/5.99 ( ( member_complex @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6197_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: nat] :
% 5.68/5.99 ( ( member_nat @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6198_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: complex] :
% 5.68/5.99 ( ( member_complex @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6199_sum__strict__mono__ex1,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > int,G: int > int] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ? [X5: int] :
% 5.68/5.99 ( ( member_int @ X5 @ A2 )
% 5.68/5.99 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono_ex1
% 5.68/5.99 thf(fact_6200_sum_Orelated,axiom,
% 5.68/5.99 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.68/5.99 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.68/5.99 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_nat @ S3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6201_sum_Orelated,axiom,
% 5.68/5.99 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.68/5.99 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.68/5.99 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_int @ S3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups3049146728041665814omplex @ H2 @ S3 ) @ ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6202_sum_Orelated,axiom,
% 5.68/5.99 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.68/5.99 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.68/5.99 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_int @ S3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6203_sum_Orelated,axiom,
% 5.68/5.99 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.68/5.99 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.68/5.99 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6204_sum_Orelated,axiom,
% 5.68/5.99 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.68/5.99 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.68/5.99 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_nat @ S3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6205_sum_Orelated,axiom,
% 5.68/5.99 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.68/5.99 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.68/5.99 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_int @ S3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6206_sum_Orelated,axiom,
% 5.68/5.99 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.68/5.99 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.68/5.99 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6207_sum_Orelated,axiom,
% 5.68/5.99 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.68/5.99 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.68/5.99 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_int @ S3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S3 ) @ ( groups4541462559716669496nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6208_sum_Orelated,axiom,
% 5.68/5.99 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.68/5.99 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.68/5.99 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6209_sum_Orelated,axiom,
% 5.68/5.99 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.68/5.99 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.68/5.99 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.68/5.99 ( ( ( R @ X15 @ X23 )
% 5.68/5.99 & ( R @ Y15 @ Y23 ) )
% 5.68/5.99 => ( R @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.68/5.99 => ( ( finite_finite_nat @ S3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S3 )
% 5.68/5.99 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( R @ ( groups3539618377306564664at_int @ H2 @ S3 ) @ ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.related
% 5.68/5.99 thf(fact_6210_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6211_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > real,G: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_int )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6212_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > real,G: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_real )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6213_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6214_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_nat )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6215_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_int )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6216_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_real )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6217_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6218_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_int )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6219_sum__strict__mono,axiom,
% 5.68/5.99 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ A2 )
% 5.68/5.99 => ( ( A2 != bot_bot_set_real )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono
% 5.68/5.99 thf(fact_6220_numeral__Bit1,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1
% 5.68/5.99 thf(fact_6221_numeral__Bit1,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1
% 5.68/5.99 thf(fact_6222_numeral__Bit1,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1
% 5.68/5.99 thf(fact_6223_numeral__Bit1,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1
% 5.68/5.99 thf(fact_6224_numeral__Bit1,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1
% 5.68/5.99 thf(fact_6225_eval__nat__numeral_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.68/5.99 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % eval_nat_numeral(3)
% 5.68/5.99 thf(fact_6226_cong__exp__iff__simps_I10_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(10)
% 5.68/5.99 thf(fact_6227_cong__exp__iff__simps_I10_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(10)
% 5.68/5.99 thf(fact_6228_cong__exp__iff__simps_I10_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(10)
% 5.68/5.99 thf(fact_6229_cong__exp__iff__simps_I12_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(12)
% 5.68/5.99 thf(fact_6230_cong__exp__iff__simps_I12_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(12)
% 5.68/5.99 thf(fact_6231_cong__exp__iff__simps_I12_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(12)
% 5.68/5.99 thf(fact_6232_cong__exp__iff__simps_I13_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.68/5.99 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(13)
% 5.68/5.99 thf(fact_6233_cong__exp__iff__simps_I13_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.68/5.99 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(13)
% 5.68/5.99 thf(fact_6234_cong__exp__iff__simps_I13_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.68/5.99 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(13)
% 5.68/5.99 thf(fact_6235_power__minus__Bit1,axiom,
% 5.68/5.99 ! [X: real,K: num] :
% 5.68/5.99 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_minus_Bit1
% 5.68/5.99 thf(fact_6236_power__minus__Bit1,axiom,
% 5.68/5.99 ! [X: int,K: num] :
% 5.68/5.99 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_minus_Bit1
% 5.68/5.99 thf(fact_6237_power__minus__Bit1,axiom,
% 5.68/5.99 ! [X: complex,K: num] :
% 5.68/5.99 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_minus_Bit1
% 5.68/5.99 thf(fact_6238_power__minus__Bit1,axiom,
% 5.68/5.99 ! [X: code_integer,K: num] :
% 5.68/5.99 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_minus_Bit1
% 5.68/5.99 thf(fact_6239_power__minus__Bit1,axiom,
% 5.68/5.99 ! [X: rat,K: num] :
% 5.68/5.99 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_minus_Bit1
% 5.68/5.99 thf(fact_6240_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > real,B4: real,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6241_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > real,B4: real,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6242_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > real,B4: real,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6243_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > rat,B4: rat,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6244_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_nat,F: nat > rat,B4: rat,I2: nat] :
% 5.68/5.99 ( ( finite_finite_nat @ S2 )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_nat @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6245_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > rat,B4: rat,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6246_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > rat,B4: rat,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6247_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > nat,B4: nat,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6248_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > nat,B4: nat,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6249_sum__nonneg__leq__bound,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > nat,B4: nat,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.68/5.99 = B4 )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( F @ I2 ) @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_leq_bound
% 5.68/5.99 thf(fact_6250_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > real,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6251_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > real,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6252_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > real,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_real ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6253_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > rat,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6254_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_nat,F: nat > rat,I2: nat] :
% 5.68/5.99 ( ( finite_finite_nat @ S2 )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 => ( ( member_nat @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6255_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > rat,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6256_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > rat,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6257_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_real,F: real > nat,I2: real] :
% 5.68/5.99 ( ( finite_finite_real @ S2 )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 => ( ( member_real @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6258_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_int,F: int > nat,I2: int] :
% 5.68/5.99 ( ( finite_finite_int @ S2 )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 => ( ( member_int @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6259_sum__nonneg__0,axiom,
% 5.68/5.99 ! [S2: set_complex,F: complex > nat,I2: complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ S2 )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ S2 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 => ( ( member_complex @ I2 @ S2 )
% 5.68/5.99 => ( ( F @ I2 )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nonneg_0
% 5.68/5.99 thf(fact_6260_dvd__imp__le__int,axiom,
% 5.68/5.99 ! [I2: int,D: int] :
% 5.68/5.99 ( ( I2 != zero_zero_int )
% 5.68/5.99 => ( ( dvd_dvd_int @ D @ I2 )
% 5.68/5.99 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dvd_imp_le_int
% 5.68/5.99 thf(fact_6261_abs__mod__less,axiom,
% 5.68/5.99 ! [L2: int,K: int] :
% 5.68/5.99 ( ( L2 != zero_zero_int )
% 5.68/5.99 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % abs_mod_less
% 5.68/5.99 thf(fact_6262_numeral__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_code(3)
% 5.68/5.99 thf(fact_6263_numeral__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_code(3)
% 5.68/5.99 thf(fact_6264_numeral__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_code(3)
% 5.68/5.99 thf(fact_6265_numeral__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_code(3)
% 5.68/5.99 thf(fact_6266_numeral__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.68/5.99 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_code(3)
% 5.68/5.99 thf(fact_6267_power__numeral__odd,axiom,
% 5.68/5.99 ! [Z: complex,W: num] :
% 5.68/5.99 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.68/5.99 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_numeral_odd
% 5.68/5.99 thf(fact_6268_power__numeral__odd,axiom,
% 5.68/5.99 ! [Z: real,W: num] :
% 5.68/5.99 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.68/5.99 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_numeral_odd
% 5.68/5.99 thf(fact_6269_power__numeral__odd,axiom,
% 5.68/5.99 ! [Z: rat,W: num] :
% 5.68/5.99 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.68/5.99 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_numeral_odd
% 5.68/5.99 thf(fact_6270_power__numeral__odd,axiom,
% 5.68/5.99 ! [Z: nat,W: num] :
% 5.68/5.99 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.68/5.99 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_numeral_odd
% 5.68/5.99 thf(fact_6271_power__numeral__odd,axiom,
% 5.68/5.99 ! [Z: int,W: num] :
% 5.68/5.99 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.68/5.99 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % power_numeral_odd
% 5.68/5.99 thf(fact_6272_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_real,I2: real,F: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6273_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_int,I2: int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( member_int @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6274_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_complex,I2: complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6275_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_real,I2: real,F: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6276_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ I5 )
% 5.68/5.99 => ( ( member_nat @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6277_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_int,I2: int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( member_int @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6278_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_complex,I2: complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6279_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_real,I2: real,F: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( member_real @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6280_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_int,I2: int,F: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( member_int @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6281_sum__pos2,axiom,
% 5.68/5.99 ! [I5: set_complex,I2: complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( member_complex @ I2 @ I5 )
% 5.68/5.99 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos2
% 5.68/5.99 thf(fact_6282_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6283_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_int )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6284_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_real,F: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_real )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6285_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6286_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_nat )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6287_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_int )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6288_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_real,F: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_real )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6289_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6290_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_int,F: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_int )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6291_sum__pos,axiom,
% 5.68/5.99 ! [I5: set_real,F: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ I5 )
% 5.68/5.99 => ( ( I5 != bot_bot_set_real )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.68/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_pos
% 5.68/5.99 thf(fact_6292_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6293_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6294_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6295_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6296_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6297_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,G: real > nat,H2: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6298_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6299_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,G: real > int,H2: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1932886352136224148al_int @ G @ T3 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6300_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > int,H2: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6301_sum_Omono__neutral__cong__right,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_right
% 5.68/5.99 thf(fact_6302_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5754745047067104278omplex @ G @ S3 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6303_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6304_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6305_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1300246762558778688al_rat @ G @ S3 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6306_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6307_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,H2: real > nat,G: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1935376822645274424al_nat @ G @ S3 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6308_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6309_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_real,S3: set_real,H2: real > int,G: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups1932886352136224148al_int @ G @ S3 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6310_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6311_sum_Omono__neutral__cong__left,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( H2 @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ S3 )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = ( H2 @ X3 ) ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ S3 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_cong_left
% 5.68/5.99 thf(fact_6312_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6313_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6314_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6315_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6316_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6317_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 5.68/5.99 = ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6318_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ T3 )
% 5.68/5.99 = ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6319_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.68/5.99 = ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6320_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.68/5.99 = ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6321_sum_Omono__neutral__right,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 5.68/5.99 = ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_right
% 5.68/5.99 thf(fact_6322_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6323_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6324_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6325_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6326_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ S3 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6327_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ S3 )
% 5.68/5.99 = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6328_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_nat,S3: set_nat,G: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ S3 )
% 5.68/5.99 = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6329_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( groups3049146728041665814omplex @ G @ S3 )
% 5.68/5.99 = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6330_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( groups8778361861064173332t_real @ G @ S3 )
% 5.68/5.99 = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6331_sum_Omono__neutral__left,axiom,
% 5.68/5.99 ! [T3: set_int,S3: set_int,G: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ T3 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/5.99 => ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/5.99 => ( ( G @ X3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( groups3906332499630173760nt_rat @ G @ S3 )
% 5.68/5.99 = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.mono_neutral_left
% 5.68/5.99 thf(fact_6332_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6333_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6334_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6335_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6336_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6337_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > nat,H2: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6338_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6339_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > int,H2: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( ( groups1932886352136224148al_int @ G @ C4 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6340_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > int,H2: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6341_sum_Osame__carrierI,axiom,
% 5.68/5.99 ! [C4: set_nat,A2: set_nat,B4: set_nat,G: nat > complex,H2: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: nat] :
% 5.68/5.99 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [B2: nat] :
% 5.68/5.99 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( ( groups2073611262835488442omplex @ G @ C4 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ C4 ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrierI
% 5.68/5.99 thf(fact_6342_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.68/5.99 = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6343_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.68/5.99 = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6344_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.68/5.99 = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6345_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.68/5.99 = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6346_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.68/5.99 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6347_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > nat,H2: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.68/5.99 = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6348_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.68/5.99 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6349_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_real,A2: set_real,B4: set_real,G: real > int,H2: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: real] :
% 5.68/5.99 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups1932886352136224148al_int @ G @ C4 )
% 5.68/5.99 = ( groups1932886352136224148al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6350_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > int,H2: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: complex] :
% 5.68/5.99 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.68/5.99 = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6351_sum_Osame__carrier,axiom,
% 5.68/5.99 ! [C4: set_nat,A2: set_nat,B4: set_nat,G: nat > complex,H2: nat > complex] :
% 5.68/5.99 ( ( finite_finite_nat @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ C4 )
% 5.68/5.99 => ( ! [A3: nat] :
% 5.68/5.99 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.68/5.99 => ( ( G @ A3 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ! [B2: nat] :
% 5.68/5.99 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ C4 @ B4 ) )
% 5.68/5.99 => ( ( H2 @ B2 )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 => ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ B4 ) )
% 5.68/5.99 = ( ( groups2073611262835488442omplex @ G @ C4 )
% 5.68/5.99 = ( groups2073611262835488442omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.same_carrier
% 5.68/5.99 thf(fact_6352_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,G: complex > real] :
% 5.68/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.68/5.99 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5808333547571424918x_real @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6353_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,G: complex > rat] :
% 5.68/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.68/5.99 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5058264527183730370ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6354_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,G: complex > nat] :
% 5.68/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.68/5.99 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5693394587270226106ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6355_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,G: complex > int] :
% 5.68/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.68/5.99 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups5690904116761175830ex_int @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6356_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,G: nat > rat] :
% 5.68/5.99 ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.68/5.99 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B4 ) ) @ ( groups2906978787729119204at_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6357_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,G: nat > int] :
% 5.68/5.99 ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.68/5.99 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B4 ) ) @ ( groups3539618377306564664at_int @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6358_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_int,A2: set_int,G: int > real] :
% 5.68/5.99 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.68/5.99 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups8778361861064173332t_real @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6359_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_int,A2: set_int,G: int > rat] :
% 5.68/5.99 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.68/5.99 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups3906332499630173760nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6360_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_int,A2: set_int,G: int > nat] :
% 5.68/5.99 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.68/5.99 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups4541462559716669496nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6361_sum_Osubset__diff,axiom,
% 5.68/5.99 ! [B4: set_int,A2: set_int,G: int > int] :
% 5.68/5.99 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.68/5.99 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups4538972089207619220nt_int @ G @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.subset_diff
% 5.68/5.99 thf(fact_6362_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_complex,B4: set_complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6363_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_complex,B4: set_complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6364_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_complex,B4: set_complex,F: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6365_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_nat,B4: set_nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6366_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_nat,B4: set_nat,F: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6367_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_int,B4: set_int,F: int > real] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6368_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_int,B4: set_int,F: int > rat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6369_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_int,B4: set_int,F: int > int] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6370_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_complex,B4: set_complex,F: complex > complex] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6371_sum__diff,axiom,
% 5.68/5.99 ! [A2: set_nat,B4: set_nat,F: nat > real] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff
% 5.68/5.99 thf(fact_6372_numeral__Bit1__div__2,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.99 = ( numeral_numeral_nat @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1_div_2
% 5.68/5.99 thf(fact_6373_numeral__Bit1__div__2,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.99 = ( numeral_numeral_int @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_Bit1_div_2
% 5.68/5.99 thf(fact_6374_odd__numeral,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % odd_numeral
% 5.68/5.99 thf(fact_6375_odd__numeral,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % odd_numeral
% 5.68/5.99 thf(fact_6376_odd__numeral,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % odd_numeral
% 5.68/5.99 thf(fact_6377_subset__decode__imp__le,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.68/5.99 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % subset_decode_imp_le
% 5.68/5.99 thf(fact_6378_cong__exp__iff__simps_I3_J,axiom,
% 5.68/5.99 ! [N: num,Q2: num] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != zero_zero_nat ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(3)
% 5.68/5.99 thf(fact_6379_cong__exp__iff__simps_I3_J,axiom,
% 5.68/5.99 ! [N: num,Q2: num] :
% 5.68/5.99 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != zero_zero_int ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(3)
% 5.68/5.99 thf(fact_6380_cong__exp__iff__simps_I3_J,axiom,
% 5.68/5.99 ! [N: num,Q2: num] :
% 5.68/5.99 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 != zero_z3403309356797280102nteger ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(3)
% 5.68/5.99 thf(fact_6381_power3__eq__cube,axiom,
% 5.68/5.99 ! [A: complex] :
% 5.68/5.99 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % power3_eq_cube
% 5.68/5.99 thf(fact_6382_power3__eq__cube,axiom,
% 5.68/5.99 ! [A: real] :
% 5.68/5.99 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % power3_eq_cube
% 5.68/5.99 thf(fact_6383_power3__eq__cube,axiom,
% 5.68/5.99 ! [A: rat] :
% 5.68/5.99 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % power3_eq_cube
% 5.68/5.99 thf(fact_6384_power3__eq__cube,axiom,
% 5.68/5.99 ! [A: nat] :
% 5.68/5.99 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % power3_eq_cube
% 5.68/5.99 thf(fact_6385_power3__eq__cube,axiom,
% 5.68/5.99 ! [A: int] :
% 5.68/5.99 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.68/5.99
% 5.68/5.99 % power3_eq_cube
% 5.68/5.99 thf(fact_6386_numeral__3__eq__3,axiom,
% 5.68/5.99 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.68/5.99 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_3_eq_3
% 5.68/5.99 thf(fact_6387_Suc3__eq__add__3,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc3_eq_add_3
% 5.68/5.99 thf(fact_6388_zdvd__mult__cancel1,axiom,
% 5.68/5.99 ! [M: int,N: int] :
% 5.68/5.99 ( ( M != zero_zero_int )
% 5.68/5.99 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.68/5.99 = ( ( abs_abs_int @ N )
% 5.68/5.99 = one_one_int ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % zdvd_mult_cancel1
% 5.68/5.99 thf(fact_6389_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,F: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6390_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6391_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,F: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6392_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6393_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: nat] :
% 5.68/5.99 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6394_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,F: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6395_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6396_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,F: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: real] :
% 5.68/5.99 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6397_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,F: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: complex] :
% 5.68/5.99 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6398_sum__mono2,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,F: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.99 => ( ! [B2: nat] :
% 5.68/5.99 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_mono2
% 5.68/5.99 thf(fact_6399_num_Osize_I6_J,axiom,
% 5.68/5.99 ! [X32: num] :
% 5.68/5.99 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.68/5.99 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % num.size(6)
% 5.68/5.99 thf(fact_6400_of__bool__odd__eq__mod__2,axiom,
% 5.68/5.99 ! [A: nat] :
% 5.68/5.99 ( ( zero_n2687167440665602831ol_nat
% 5.68/5.99 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.99 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_odd_eq_mod_2
% 5.68/5.99 thf(fact_6401_of__bool__odd__eq__mod__2,axiom,
% 5.68/5.99 ! [A: int] :
% 5.68/5.99 ( ( zero_n2684676970156552555ol_int
% 5.68/5.99 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.99 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_odd_eq_mod_2
% 5.68/5.99 thf(fact_6402_of__bool__odd__eq__mod__2,axiom,
% 5.68/5.99 ! [A: code_integer] :
% 5.68/5.99 ( ( zero_n356916108424825756nteger
% 5.68/5.99 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.68/5.99 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % of_bool_odd_eq_mod_2
% 5.68/5.99 thf(fact_6403_cong__exp__iff__simps_I7_J,axiom,
% 5.68/5.99 ! [Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.68/5.99 = zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(7)
% 5.68/5.99 thf(fact_6404_cong__exp__iff__simps_I7_J,axiom,
% 5.68/5.99 ! [Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.68/5.99 = zero_zero_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(7)
% 5.68/5.99 thf(fact_6405_cong__exp__iff__simps_I7_J,axiom,
% 5.68/5.99 ! [Q2: num,N: num] :
% 5.68/5.99 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.68/5.99 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(7)
% 5.68/5.99 thf(fact_6406_cong__exp__iff__simps_I11_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num] :
% 5.68/5.99 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.68/5.99 = zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(11)
% 5.68/5.99 thf(fact_6407_cong__exp__iff__simps_I11_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num] :
% 5.68/5.99 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.68/5.99 = zero_zero_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(11)
% 5.68/5.99 thf(fact_6408_cong__exp__iff__simps_I11_J,axiom,
% 5.68/5.99 ! [M: num,Q2: num] :
% 5.68/5.99 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.68/5.99 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.68/5.99 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.68/5.99 = zero_z3403309356797280102nteger ) ) ).
% 5.68/5.99
% 5.68/5.99 % cong_exp_iff_simps(11)
% 5.68/5.99 thf(fact_6409_even__abs__add__iff,axiom,
% 5.68/5.99 ! [K: int,L2: int] :
% 5.68/5.99 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.68/5.99 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % even_abs_add_iff
% 5.68/5.99 thf(fact_6410_even__add__abs__iff,axiom,
% 5.68/5.99 ! [K: int,L2: int] :
% 5.68/5.99 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.68/5.99 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % even_add_abs_iff
% 5.68/5.99 thf(fact_6411_Suc__div__eq__add3__div,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.68/5.99 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_div_eq_add3_div
% 5.68/5.99 thf(fact_6412_Suc__mod__eq__add3__mod,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.68/5.99 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_mod_eq_add3_mod
% 5.68/5.99 thf(fact_6413_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,B: real,F: real > real] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6414_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6415_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,B: real,F: real > rat] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6416_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6417_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 5.68/5.99 ( ( finite_finite_nat @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.99 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6418_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,B: real,F: real > nat] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6419_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6420_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_real,A2: set_real,B: real,F: real > int] :
% 5.68/5.99 ( ( finite_finite_real @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/5.99 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6421_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/5.99 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6422_sum__strict__mono2,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 5.68/5.99 ( ( finite_finite_nat @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/5.99 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/5.99 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ B4 )
% 5.68/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B4 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_strict_mono2
% 5.68/5.99 thf(fact_6423_bits__induct,axiom,
% 5.68/5.99 ! [P: nat > $o,A: nat] :
% 5.68/5.99 ( ! [A3: nat] :
% 5.68/5.99 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ A3 ) )
% 5.68/5.99 => ( ! [A3: nat,B2: $o] :
% 5.68/5.99 ( ( P @ A3 )
% 5.68/5.99 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.68/5.99 => ( P @ A ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_induct
% 5.68/5.99 thf(fact_6424_bits__induct,axiom,
% 5.68/5.99 ! [P: int > $o,A: int] :
% 5.68/5.99 ( ! [A3: int] :
% 5.68/5.99 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ A3 ) )
% 5.68/5.99 => ( ! [A3: int,B2: $o] :
% 5.68/5.99 ( ( P @ A3 )
% 5.68/5.99 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.68/5.99 => ( P @ A ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_induct
% 5.68/5.99 thf(fact_6425_bits__induct,axiom,
% 5.68/5.99 ! [P: code_integer > $o,A: code_integer] :
% 5.68/5.99 ( ! [A3: code_integer] :
% 5.68/5.99 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ A3 ) )
% 5.68/5.99 => ( ! [A3: code_integer,B2: $o] :
% 5.68/5.99 ( ( P @ A3 )
% 5.68/5.99 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/5.99 = A3 )
% 5.68/5.99 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.68/5.99 => ( P @ A ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % bits_induct
% 5.68/5.99 thf(fact_6426_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.68/5.99 = one_one_Code_integer )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_le3102999989581377725nteger
% 5.68/5.99 @ ( abs_abs_Code_integer
% 5.68/5.99 @ ( minus_8373710615458151222nteger
% 5.68/5.99 @ ( groups7501900531339628137nteger
% 5.68/5.99 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6427_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 5.68/5.99 = one_one_Code_integer )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_le3102999989581377725nteger
% 5.68/5.99 @ ( abs_abs_Code_integer
% 5.68/5.99 @ ( minus_8373710615458151222nteger
% 5.68/5.99 @ ( groups7713935264441627589nteger
% 5.68/5.99 @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6428_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.68/5.99 ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.68/5.99 = one_one_Code_integer )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_le3102999989581377725nteger
% 5.68/5.99 @ ( abs_abs_Code_integer
% 5.68/5.99 @ ( minus_8373710615458151222nteger
% 5.68/5.99 @ ( groups7873554091576472773nteger
% 5.68/5.99 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6429_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.68/5.99 ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 5.68/5.99 = one_one_Code_integer )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_le3102999989581377725nteger
% 5.68/5.99 @ ( abs_abs_Code_integer
% 5.68/5.99 @ ( minus_8373710615458151222nteger
% 5.68/5.99 @ ( groups6621422865394947399nteger
% 5.68/5.99 @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6430_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 5.68/5.99 = one_one_real )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_real
% 5.68/5.99 @ ( abs_abs_real
% 5.68/5.99 @ ( minus_minus_real
% 5.68/5.99 @ ( groups8097168146408367636l_real
% 5.68/5.99 @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6431_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.68/5.99 ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 5.68/5.99 = one_one_real )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_real
% 5.68/5.99 @ ( abs_abs_real
% 5.68/5.99 @ ( minus_minus_real
% 5.68/5.99 @ ( groups8778361861064173332t_real
% 5.68/5.99 @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6432_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.68/5.99 ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 5.68/5.99 = one_one_real )
% 5.68/5.99 => ( ! [I4: complex] :
% 5.68/5.99 ( ( member_complex @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_real
% 5.68/5.99 @ ( abs_abs_real
% 5.68/5.99 @ ( minus_minus_real
% 5.68/5.99 @ ( groups5808333547571424918x_real
% 5.68/5.99 @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6433_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.68/5.99 = one_one_rat )
% 5.68/5.99 => ( ! [I4: nat] :
% 5.68/5.99 ( ( member_nat @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_rat
% 5.68/5.99 @ ( abs_abs_rat
% 5.68/5.99 @ ( minus_minus_rat
% 5.68/5.99 @ ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6434_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.68/5.99 ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 5.68/5.99 = one_one_rat )
% 5.68/5.99 => ( ! [I4: real] :
% 5.68/5.99 ( ( member_real @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_rat
% 5.68/5.99 @ ( abs_abs_rat
% 5.68/5.99 @ ( minus_minus_rat
% 5.68/5.99 @ ( groups1300246762558778688al_rat
% 5.68/5.99 @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6435_convex__sum__bound__le,axiom,
% 5.68/5.99 ! [I5: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.68/5.99 ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.68/5.99 => ( ( ( groups3906332499630173760nt_rat @ X @ I5 )
% 5.68/5.99 = one_one_rat )
% 5.68/5.99 => ( ! [I4: int] :
% 5.68/5.99 ( ( member_int @ I4 @ I5 )
% 5.68/5.99 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.68/5.99 => ( ord_less_eq_rat
% 5.68/5.99 @ ( abs_abs_rat
% 5.68/5.99 @ ( minus_minus_rat
% 5.68/5.99 @ ( groups3906332499630173760nt_rat
% 5.68/5.99 @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 @ B ) )
% 5.68/5.99 @ Delta ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % convex_sum_bound_le
% 5.68/5.99 thf(fact_6436_nat__intermed__int__val,axiom,
% 5.68/5.99 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( ( ord_less_eq_nat @ M @ I4 )
% 5.68/5.99 & ( ord_less_nat @ I4 @ N ) )
% 5.68/5.99 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.68/5.99 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.68/5.99 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.68/5.99 => ? [I4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ I4 )
% 5.68/5.99 & ( ord_less_eq_nat @ I4 @ N )
% 5.68/5.99 & ( ( F @ I4 )
% 5.68/5.99 = K ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % nat_intermed_int_val
% 5.68/5.99 thf(fact_6437_mod__exhaust__less__4,axiom,
% 5.68/5.99 ! [M: nat] :
% 5.68/5.99 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.99 = one_one_nat )
% 5.68/5.99 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.99 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/5.99 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.99 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % mod_exhaust_less_4
% 5.68/5.99 thf(fact_6438_decr__lemma,axiom,
% 5.68/5.99 ! [D: int,X: int,Z: int] :
% 5.68/5.99 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.99 => ( 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 ) ) ).
% 5.68/5.99
% 5.68/5.99 % decr_lemma
% 5.68/5.99 thf(fact_6439_incr__lemma,axiom,
% 5.68/5.99 ! [D: int,Z: int,X: int] :
% 5.68/5.99 ( ( ord_less_int @ zero_zero_int @ D )
% 5.68/5.99 => ( 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 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % incr_lemma
% 5.68/5.99 thf(fact_6440_exp__mod__exp,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_mod_exp
% 5.68/5.99 thf(fact_6441_exp__mod__exp,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_mod_exp
% 5.68/5.99 thf(fact_6442_exp__mod__exp,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_mod_exp
% 5.68/5.99 thf(fact_6443_nat__ivt__aux,axiom,
% 5.68/5.99 ! [N: nat,F: nat > int,K: int] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( ord_less_nat @ I4 @ N )
% 5.68/5.99 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.68/5.99 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.68/5.99 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.68/5.99 => ? [I4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ I4 @ N )
% 5.68/5.99 & ( ( F @ I4 )
% 5.68/5.99 = K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % nat_ivt_aux
% 5.68/5.99 thf(fact_6444_nat0__intermed__int__val,axiom,
% 5.68/5.99 ! [N: nat,F: nat > int,K: int] :
% 5.68/5.99 ( ! [I4: nat] :
% 5.68/5.99 ( ( ord_less_nat @ I4 @ N )
% 5.68/5.99 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.68/5.99 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.68/5.99 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.68/5.99 => ? [I4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ I4 @ N )
% 5.68/5.99 & ( ( F @ I4 )
% 5.68/5.99 = K ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % nat0_intermed_int_val
% 5.68/5.99 thf(fact_6445_exp__div__exp__eq,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_times_nat
% 5.68/5.99 @ ( zero_n2687167440665602831ol_nat
% 5.68/5.99 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.68/5.99 != zero_zero_nat )
% 5.68/5.99 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.68/5.99 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_div_exp_eq
% 5.68/5.99 thf(fact_6446_exp__div__exp__eq,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_times_int
% 5.68/5.99 @ ( zero_n2684676970156552555ol_int
% 5.68/5.99 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.68/5.99 != zero_zero_int )
% 5.68/5.99 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.68/5.99 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_div_exp_eq
% 5.68/5.99 thf(fact_6447_exp__div__exp__eq,axiom,
% 5.68/5.99 ! [M: nat,N: nat] :
% 5.68/5.99 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.68/5.99 = ( times_3573771949741848930nteger
% 5.68/5.99 @ ( zero_n356916108424825756nteger
% 5.68/5.99 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.68/5.99 != zero_z3403309356797280102nteger )
% 5.68/5.99 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.68/5.99 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % exp_div_exp_eq
% 5.68/5.99 thf(fact_6448_arctan__add,axiom,
% 5.68/5.99 ! [X: real,Y2: real] :
% 5.68/5.99 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/5.99 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/5.99 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 5.68/5.99 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % arctan_add
% 5.68/5.99 thf(fact_6449_odd__mod__4__div__2,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/5.99 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.68/5.99 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % odd_mod_4_div_2
% 5.68/5.99 thf(fact_6450_set__decode__def,axiom,
% 5.68/5.99 ( nat_set_decode
% 5.68/5.99 = ( ^ [X2: nat] :
% 5.68/5.99 ( collect_nat
% 5.68/5.99 @ ^ [N2: nat] :
% 5.68/5.99 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % set_decode_def
% 5.68/5.99 thf(fact_6451_signed__take__bit__numeral__minus__bit1,axiom,
% 5.68/5.99 ! [L2: num,K: num] :
% 5.68/5.99 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % signed_take_bit_numeral_minus_bit1
% 5.68/5.99 thf(fact_6452_dbl__dec__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.99 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(4)
% 5.68/5.99 thf(fact_6453_dbl__dec__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.99 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(4)
% 5.68/5.99 thf(fact_6454_dbl__dec__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(4)
% 5.68/5.99 thf(fact_6455_dbl__dec__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(4)
% 5.68/5.99 thf(fact_6456_dbl__dec__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.99 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(4)
% 5.68/5.99 thf(fact_6457_divmod__algorithm__code_I8_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(8)
% 5.68/5.99 thf(fact_6458_divmod__algorithm__code_I8_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(8)
% 5.68/5.99 thf(fact_6459_divmod__algorithm__code_I8_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_num @ M @ N )
% 5.68/5.99 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(8)
% 5.68/5.99 thf(fact_6460_divmod__algorithm__code_I7_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(7)
% 5.68/5.99 thf(fact_6461_divmod__algorithm__code_I7_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(7)
% 5.68/5.99 thf(fact_6462_divmod__algorithm__code_I7_J,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.68/5.99 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.68/5.99 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/5.99 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(7)
% 5.68/5.99 thf(fact_6463_signed__take__bit__numeral__bit1,axiom,
% 5.68/5.99 ! [L2: num,K: num] :
% 5.68/5.99 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % signed_take_bit_numeral_bit1
% 5.68/5.99 thf(fact_6464_dbl__inc__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.68/5.99 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(3)
% 5.68/5.99 thf(fact_6465_dbl__inc__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.68/5.99 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(3)
% 5.68/5.99 thf(fact_6466_dbl__inc__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.68/5.99 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(3)
% 5.68/5.99 thf(fact_6467_dbl__inc__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.68/5.99 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(3)
% 5.68/5.99 thf(fact_6468_dbl__dec__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.68/5.99 = one_one_complex ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(3)
% 5.68/5.99 thf(fact_6469_dbl__dec__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.68/5.99 = one_one_real ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(3)
% 5.68/5.99 thf(fact_6470_dbl__dec__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.68/5.99 = one_one_rat ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(3)
% 5.68/5.99 thf(fact_6471_dbl__dec__simps_I3_J,axiom,
% 5.68/5.99 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.68/5.99 = one_one_int ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(3)
% 5.68/5.99 thf(fact_6472_pred__numeral__simps_I1_J,axiom,
% 5.68/5.99 ( ( pred_numeral @ one )
% 5.68/5.99 = zero_zero_nat ) ).
% 5.68/5.99
% 5.68/5.99 % pred_numeral_simps(1)
% 5.68/5.99 thf(fact_6473_eq__numeral__Suc,axiom,
% 5.68/5.99 ! [K: num,N: nat] :
% 5.68/5.99 ( ( ( numeral_numeral_nat @ K )
% 5.68/5.99 = ( suc @ N ) )
% 5.68/5.99 = ( ( pred_numeral @ K )
% 5.68/5.99 = N ) ) ).
% 5.68/5.99
% 5.68/5.99 % eq_numeral_Suc
% 5.68/5.99 thf(fact_6474_Suc__eq__numeral,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( ( suc @ N )
% 5.68/5.99 = ( numeral_numeral_nat @ K ) )
% 5.68/5.99 = ( N
% 5.68/5.99 = ( pred_numeral @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % Suc_eq_numeral
% 5.68/5.99 thf(fact_6475_dbl__inc__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.68/5.99 = one_one_complex ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(2)
% 5.68/5.99 thf(fact_6476_dbl__inc__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.68/5.99 = one_one_real ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(2)
% 5.68/5.99 thf(fact_6477_dbl__inc__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.68/5.99 = one_one_rat ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(2)
% 5.68/5.99 thf(fact_6478_dbl__inc__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.68/5.99 = one_one_int ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(2)
% 5.68/5.99 thf(fact_6479_dbl__inc__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/5.99 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(4)
% 5.68/5.99 thf(fact_6480_dbl__inc__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/5.99 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(4)
% 5.68/5.99 thf(fact_6481_dbl__inc__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(4)
% 5.68/5.99 thf(fact_6482_dbl__inc__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(4)
% 5.68/5.99 thf(fact_6483_dbl__inc__simps_I4_J,axiom,
% 5.68/5.99 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/5.99 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(4)
% 5.68/5.99 thf(fact_6484_dbl__inc__simps_I5_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.68/5.99 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(5)
% 5.68/5.99 thf(fact_6485_dbl__inc__simps_I5_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.68/5.99 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(5)
% 5.68/5.99 thf(fact_6486_dbl__inc__simps_I5_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.68/5.99 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(5)
% 5.68/5.99 thf(fact_6487_dbl__inc__simps_I5_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.68/5.99 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(5)
% 5.68/5.99 thf(fact_6488_less__Suc__numeral,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.68/5.99 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % less_Suc_numeral
% 5.68/5.99 thf(fact_6489_less__numeral__Suc,axiom,
% 5.68/5.99 ! [K: num,N: nat] :
% 5.68/5.99 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.68/5.99 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % less_numeral_Suc
% 5.68/5.99 thf(fact_6490_pred__numeral__simps_I3_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.68/5.99 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % pred_numeral_simps(3)
% 5.68/5.99 thf(fact_6491_le__numeral__Suc,axiom,
% 5.68/5.99 ! [K: num,N: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.68/5.99 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % le_numeral_Suc
% 5.68/5.99 thf(fact_6492_le__Suc__numeral,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.68/5.99 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % le_Suc_numeral
% 5.68/5.99 thf(fact_6493_diff__numeral__Suc,axiom,
% 5.68/5.99 ! [K: num,N: nat] :
% 5.68/5.99 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.68/5.99 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.68/5.99
% 5.68/5.99 % diff_numeral_Suc
% 5.68/5.99 thf(fact_6494_diff__Suc__numeral,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.68/5.99 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % diff_Suc_numeral
% 5.68/5.99 thf(fact_6495_max__numeral__Suc,axiom,
% 5.68/5.99 ! [K: num,N: nat] :
% 5.68/5.99 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.68/5.99 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % max_numeral_Suc
% 5.68/5.99 thf(fact_6496_max__Suc__numeral,axiom,
% 5.68/5.99 ! [N: nat,K: num] :
% 5.68/5.99 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.68/5.99 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % max_Suc_numeral
% 5.68/5.99 thf(fact_6497_dbl__dec__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.68/5.99 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(2)
% 5.68/5.99 thf(fact_6498_dbl__dec__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.68/5.99 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(2)
% 5.68/5.99 thf(fact_6499_dbl__dec__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(2)
% 5.68/5.99 thf(fact_6500_dbl__dec__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(2)
% 5.68/5.99 thf(fact_6501_dbl__dec__simps_I2_J,axiom,
% 5.68/5.99 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.68/5.99 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(2)
% 5.68/5.99 thf(fact_6502_dbl__dec__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(1)
% 5.68/5.99 thf(fact_6503_dbl__dec__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(1)
% 5.68/5.99 thf(fact_6504_dbl__dec__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(1)
% 5.68/5.99 thf(fact_6505_dbl__dec__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(1)
% 5.68/5.99 thf(fact_6506_dbl__dec__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_dec_simps(1)
% 5.68/5.99 thf(fact_6507_dbl__inc__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(1)
% 5.68/5.99 thf(fact_6508_dbl__inc__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(1)
% 5.68/5.99 thf(fact_6509_dbl__inc__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.68/5.99 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(1)
% 5.68/5.99 thf(fact_6510_dbl__inc__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.68/5.99 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(1)
% 5.68/5.99 thf(fact_6511_dbl__inc__simps_I1_J,axiom,
% 5.68/5.99 ! [K: num] :
% 5.68/5.99 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.68/5.99 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_simps(1)
% 5.68/5.99 thf(fact_6512_sum_Ocl__ivl__Suc,axiom,
% 5.68/5.99 ! [N: nat,M: nat,G: nat > complex] :
% 5.68/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = zero_zero_complex ) )
% 5.68/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.cl_ivl_Suc
% 5.68/5.99 thf(fact_6513_sum_Ocl__ivl__Suc,axiom,
% 5.68/5.99 ! [N: nat,M: nat,G: nat > rat] :
% 5.68/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = zero_zero_rat ) )
% 5.68/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.cl_ivl_Suc
% 5.68/5.99 thf(fact_6514_sum_Ocl__ivl__Suc,axiom,
% 5.68/5.99 ! [N: nat,M: nat,G: nat > int] :
% 5.68/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = zero_zero_int ) )
% 5.68/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.cl_ivl_Suc
% 5.68/5.99 thf(fact_6515_sum_Ocl__ivl__Suc,axiom,
% 5.68/5.99 ! [N: nat,M: nat,G: nat > nat] :
% 5.68/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = zero_zero_nat ) )
% 5.68/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.cl_ivl_Suc
% 5.68/5.99 thf(fact_6516_sum_Ocl__ivl__Suc,axiom,
% 5.68/5.99 ! [N: nat,M: nat,G: nat > real] :
% 5.68/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = zero_zero_real ) )
% 5.68/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.cl_ivl_Suc
% 5.68/5.99 thf(fact_6517_dvd__numeral__simp,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.68/5.99 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dvd_numeral_simp
% 5.68/5.99 thf(fact_6518_dvd__numeral__simp,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.68/5.99 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dvd_numeral_simp
% 5.68/5.99 thf(fact_6519_dvd__numeral__simp,axiom,
% 5.68/5.99 ! [M: num,N: num] :
% 5.68/5.99 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.68/5.99 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dvd_numeral_simp
% 5.68/5.99 thf(fact_6520_divmod__algorithm__code_I2_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ( ( unique5052692396658037445od_int @ M @ one )
% 5.68/5.99 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(2)
% 5.68/5.99 thf(fact_6521_divmod__algorithm__code_I2_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.68/5.99 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(2)
% 5.68/5.99 thf(fact_6522_divmod__algorithm__code_I2_J,axiom,
% 5.68/5.99 ! [M: num] :
% 5.68/5.99 ( ( unique3479559517661332726nteger @ M @ one )
% 5.68/5.99 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(2)
% 5.68/5.99 thf(fact_6523_sum__zero__power,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > complex] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( C @ zero_zero_nat ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_complex ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power
% 5.68/5.99 thf(fact_6524_sum__zero__power,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > rat] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( C @ zero_zero_nat ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power
% 5.68/5.99 thf(fact_6525_sum__zero__power,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > real] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( C @ zero_zero_nat ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_real ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power
% 5.68/5.99 thf(fact_6526_divmod__algorithm__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.68/5.99 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(3)
% 5.68/5.99 thf(fact_6527_divmod__algorithm__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.68/5.99 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(3)
% 5.68/5.99 thf(fact_6528_divmod__algorithm__code_I3_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.68/5.99 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(3)
% 5.68/5.99 thf(fact_6529_divmod__algorithm__code_I4_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(4)
% 5.68/5.99 thf(fact_6530_divmod__algorithm__code_I4_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.68/5.99 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(4)
% 5.68/5.99 thf(fact_6531_divmod__algorithm__code_I4_J,axiom,
% 5.68/5.99 ! [N: num] :
% 5.68/5.99 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.68/5.99 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_algorithm_code(4)
% 5.68/5.99 thf(fact_6532_sum__zero__power_H,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex
% 5.68/5.99 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2073611262835488442omplex
% 5.68/5.99 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_complex ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power'
% 5.68/5.99 thf(fact_6533_sum__zero__power_H,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_rat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power'
% 5.68/5.99 thf(fact_6534_sum__zero__power_H,axiom,
% 5.68/5.99 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.68/5.99 ( ( ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.68/5.99 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.68/5.99 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = zero_zero_real ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_zero_power'
% 5.68/5.99 thf(fact_6535_signed__take__bit__numeral__bit0,axiom,
% 5.68/5.99 ! [L2: num,K: num] :
% 5.68/5.99 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.68/5.99 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % signed_take_bit_numeral_bit0
% 5.68/5.99 thf(fact_6536_signed__take__bit__numeral__minus__bit0,axiom,
% 5.68/5.99 ! [L2: num,K: num] :
% 5.68/5.99 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/5.99 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % signed_take_bit_numeral_minus_bit0
% 5.68/5.99 thf(fact_6537_sum__cong__Suc,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.68/5.99 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.68/5.99 => ( ( F @ ( suc @ X3 ) )
% 5.68/5.99 = ( G @ ( suc @ X3 ) ) ) )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.68/5.99 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_cong_Suc
% 5.68/5.99 thf(fact_6538_sum__cong__Suc,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.68/5.99 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.68/5.99 => ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.68/5.99 => ( ( F @ ( suc @ X3 ) )
% 5.68/5.99 = ( G @ ( suc @ X3 ) ) ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.68/5.99 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_cong_Suc
% 5.68/5.99 thf(fact_6539_numeral__eq__Suc,axiom,
% 5.68/5.99 ( numeral_numeral_nat
% 5.68/5.99 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % numeral_eq_Suc
% 5.68/5.99 thf(fact_6540_sum__subtractf__nat,axiom,
% 5.68/5.99 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.68/5.99 ( ! [X3: real] :
% 5.68/5.99 ( ( member_real @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( groups1935376822645274424al_nat
% 5.68/5.99 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_subtractf_nat
% 5.68/5.99 thf(fact_6541_sum__subtractf__nat,axiom,
% 5.68/5.99 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.68/5.99 ( ! [X3: int] :
% 5.68/5.99 ( ( member_int @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( groups4541462559716669496nt_nat
% 5.68/5.99 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_subtractf_nat
% 5.68/5.99 thf(fact_6542_sum__subtractf__nat,axiom,
% 5.68/5.99 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.68/5.99 ( ! [X3: complex] :
% 5.68/5.99 ( ( member_complex @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat
% 5.68/5.99 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_subtractf_nat
% 5.68/5.99 thf(fact_6543_sum__subtractf__nat,axiom,
% 5.68/5.99 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.68/5.99 ( ! [X3: product_prod_nat_nat] :
% 5.68/5.99 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( groups977919841031483927at_nat
% 5.68/5.99 @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_subtractf_nat
% 5.68/5.99 thf(fact_6544_sum__subtractf__nat,axiom,
% 5.68/5.99 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.68/5.99 ( ! [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.68/5.99 @ A2 )
% 5.68/5.99 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_subtractf_nat
% 5.68/5.99 thf(fact_6545_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.68/5.99 ! [G: nat > nat,M: nat,N: nat] :
% 5.68/5.99 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.shift_bounds_cl_Suc_ivl
% 5.68/5.99 thf(fact_6546_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.68/5.99 ! [G: nat > real,M: nat,N: nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.shift_bounds_cl_Suc_ivl
% 5.68/5.99 thf(fact_6547_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.68/5.99 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.68/5.99 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.shift_bounds_cl_nat_ivl
% 5.68/5.99 thf(fact_6548_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.68/5.99 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.shift_bounds_cl_nat_ivl
% 5.68/5.99 thf(fact_6549_sum__eq__Suc0__iff,axiom,
% 5.68/5.99 ! [A2: set_int,F: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ A2 )
% 5.68/5.99 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 = ( ? [X2: int] :
% 5.68/5.99 ( ( member_int @ X2 @ A2 )
% 5.68/5.99 & ( ( F @ X2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 & ! [Y: int] :
% 5.68/5.99 ( ( member_int @ Y @ A2 )
% 5.68/5.99 => ( ( X2 != Y )
% 5.68/5.99 => ( ( F @ Y )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_eq_Suc0_iff
% 5.68/5.99 thf(fact_6550_sum__eq__Suc0__iff,axiom,
% 5.68/5.99 ! [A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/5.99 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 = ( ? [X2: complex] :
% 5.68/5.99 ( ( member_complex @ X2 @ A2 )
% 5.68/5.99 & ( ( F @ X2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 & ! [Y: complex] :
% 5.68/5.99 ( ( member_complex @ Y @ A2 )
% 5.68/5.99 => ( ( X2 != Y )
% 5.68/5.99 => ( ( F @ Y )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_eq_Suc0_iff
% 5.68/5.99 thf(fact_6551_sum__eq__Suc0__iff,axiom,
% 5.68/5.99 ! [A2: set_nat,F: nat > nat] :
% 5.68/5.99 ( ( finite_finite_nat @ A2 )
% 5.68/5.99 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 = ( ? [X2: nat] :
% 5.68/5.99 ( ( member_nat @ X2 @ A2 )
% 5.68/5.99 & ( ( F @ X2 )
% 5.68/5.99 = ( suc @ zero_zero_nat ) )
% 5.68/5.99 & ! [Y: nat] :
% 5.68/5.99 ( ( member_nat @ Y @ A2 )
% 5.68/5.99 => ( ( X2 != Y )
% 5.68/5.99 => ( ( F @ Y )
% 5.68/5.99 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_eq_Suc0_iff
% 5.68/5.99 thf(fact_6552_sum__SucD,axiom,
% 5.68/5.99 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.68/5.99 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.68/5.99 = ( suc @ N ) )
% 5.68/5.99 => ? [X3: nat] :
% 5.68/5.99 ( ( member_nat @ X3 @ A2 )
% 5.68/5.99 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_SucD
% 5.68/5.99 thf(fact_6553_sum__power__add,axiom,
% 5.68/5.99 ! [X: complex,M: nat,I5: set_nat] :
% 5.68/5.99 ( ( groups2073611262835488442omplex
% 5.68/5.99 @ ^ [I3: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_power_add
% 5.68/5.99 thf(fact_6554_sum__power__add,axiom,
% 5.68/5.99 ! [X: rat,M: nat,I5: set_nat] :
% 5.68/5.99 ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_power_add
% 5.68/5.99 thf(fact_6555_sum__power__add,axiom,
% 5.68/5.99 ! [X: int,M: nat,I5: set_nat] :
% 5.68/5.99 ( ( groups3539618377306564664at_int
% 5.68/5.99 @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_power_add
% 5.68/5.99 thf(fact_6556_sum__power__add,axiom,
% 5.68/5.99 ! [X: real,M: nat,I5: set_nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.68/5.99 @ I5 )
% 5.68/5.99 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_power_add
% 5.68/5.99 thf(fact_6557_sum_OatLeastAtMost__rev,axiom,
% 5.68/5.99 ! [G: nat > nat,N: nat,M: nat] :
% 5.68/5.99 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeastAtMost_rev
% 5.68/5.99 thf(fact_6558_sum_OatLeastAtMost__rev,axiom,
% 5.68/5.99 ! [G: nat > real,N: nat,M: nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.68/5.99 = ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeastAtMost_rev
% 5.68/5.99 thf(fact_6559_pred__numeral__def,axiom,
% 5.68/5.99 ( pred_numeral
% 5.68/5.99 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % pred_numeral_def
% 5.68/5.99 thf(fact_6560_sum__nth__roots,axiom,
% 5.68/5.99 ! [N: nat,C: complex] :
% 5.68/5.99 ( ( ord_less_nat @ one_one_nat @ N )
% 5.68/5.99 => ( ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [X2: complex] : X2
% 5.68/5.99 @ ( collect_complex
% 5.68/5.99 @ ^ [Z2: complex] :
% 5.68/5.99 ( ( power_power_complex @ Z2 @ N )
% 5.68/5.99 = C ) ) )
% 5.68/5.99 = zero_zero_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_nth_roots
% 5.68/5.99 thf(fact_6561_sum__roots__unity,axiom,
% 5.68/5.99 ! [N: nat] :
% 5.68/5.99 ( ( ord_less_nat @ one_one_nat @ N )
% 5.68/5.99 => ( ( groups7754918857620584856omplex
% 5.68/5.99 @ ^ [X2: complex] : X2
% 5.68/5.99 @ ( collect_complex
% 5.68/5.99 @ ^ [Z2: complex] :
% 5.68/5.99 ( ( power_power_complex @ Z2 @ N )
% 5.68/5.99 = one_one_complex ) ) )
% 5.68/5.99 = zero_zero_complex ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_roots_unity
% 5.68/5.99 thf(fact_6562_sum__diff__nat,axiom,
% 5.68/5.99 ! [B4: set_complex,A2: set_complex,F: complex > nat] :
% 5.68/5.99 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/5.99 => ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/5.99 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff_nat
% 5.68/5.99 thf(fact_6563_sum__diff__nat,axiom,
% 5.68/5.99 ! [B4: set_int,A2: set_int,F: int > nat] :
% 5.68/5.99 ( ( finite_finite_int @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/5.99 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff_nat
% 5.68/5.99 thf(fact_6564_sum__diff__nat,axiom,
% 5.68/5.99 ! [B4: set_nat,A2: set_nat,F: nat > nat] :
% 5.68/5.99 ( ( finite_finite_nat @ B4 )
% 5.68/5.99 => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.68/5.99 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B4 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_diff_nat
% 5.68/5.99 thf(fact_6565_sum__shift__lb__Suc0__0,axiom,
% 5.68/5.99 ! [F: nat > complex,K: nat] :
% 5.68/5.99 ( ( ( F @ zero_zero_nat )
% 5.68/5.99 = zero_zero_complex )
% 5.68/5.99 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.68/5.99 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_shift_lb_Suc0_0
% 5.68/5.99 thf(fact_6566_sum__shift__lb__Suc0__0,axiom,
% 5.68/5.99 ! [F: nat > rat,K: nat] :
% 5.68/5.99 ( ( ( F @ zero_zero_nat )
% 5.68/5.99 = zero_zero_rat )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.68/5.99 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_shift_lb_Suc0_0
% 5.68/5.99 thf(fact_6567_sum__shift__lb__Suc0__0,axiom,
% 5.68/5.99 ! [F: nat > int,K: nat] :
% 5.68/5.99 ( ( ( F @ zero_zero_nat )
% 5.68/5.99 = zero_zero_int )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.68/5.99 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_shift_lb_Suc0_0
% 5.68/5.99 thf(fact_6568_sum__shift__lb__Suc0__0,axiom,
% 5.68/5.99 ! [F: nat > nat,K: nat] :
% 5.68/5.99 ( ( ( F @ zero_zero_nat )
% 5.68/5.99 = zero_zero_nat )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.68/5.99 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_shift_lb_Suc0_0
% 5.68/5.99 thf(fact_6569_sum__shift__lb__Suc0__0,axiom,
% 5.68/5.99 ! [F: nat > real,K: nat] :
% 5.68/5.99 ( ( ( F @ zero_zero_nat )
% 5.68/5.99 = zero_zero_real )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.68/5.99 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_shift_lb_Suc0_0
% 5.68/5.99 thf(fact_6570_sum_OatLeast0__atMost__Suc,axiom,
% 5.68/5.99 ! [G: nat > rat,N: nat] :
% 5.68/5.99 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast0_atMost_Suc
% 5.68/5.99 thf(fact_6571_sum_OatLeast0__atMost__Suc,axiom,
% 5.68/5.99 ! [G: nat > int,N: nat] :
% 5.68/5.99 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast0_atMost_Suc
% 5.68/5.99 thf(fact_6572_sum_OatLeast0__atMost__Suc,axiom,
% 5.68/5.99 ! [G: nat > nat,N: nat] :
% 5.68/5.99 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast0_atMost_Suc
% 5.68/5.99 thf(fact_6573_sum_OatLeast0__atMost__Suc,axiom,
% 5.68/5.99 ! [G: nat > real,N: nat] :
% 5.68/5.99 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast0_atMost_Suc
% 5.68/5.99 thf(fact_6574_sum_Onat__ivl__Suc_H,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.nat_ivl_Suc'
% 5.68/5.99 thf(fact_6575_sum_Onat__ivl__Suc_H,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > int] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.nat_ivl_Suc'
% 5.68/5.99 thf(fact_6576_sum_Onat__ivl__Suc_H,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.nat_ivl_Suc'
% 5.68/5.99 thf(fact_6577_sum_Onat__ivl__Suc_H,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > real] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.nat_ivl_Suc'
% 5.68/5.99 thf(fact_6578_sum_OatLeast__Suc__atMost,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast_Suc_atMost
% 5.68/5.99 thf(fact_6579_sum_OatLeast__Suc__atMost,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > int] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast_Suc_atMost
% 5.68/5.99 thf(fact_6580_sum_OatLeast__Suc__atMost,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast_Suc_atMost
% 5.68/5.99 thf(fact_6581_sum_OatLeast__Suc__atMost,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > real] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.atLeast_Suc_atMost
% 5.68/5.99 thf(fact_6582_dbl__inc__def,axiom,
% 5.68/5.99 ( neg_nu8557863876264182079omplex
% 5.68/5.99 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_def
% 5.68/5.99 thf(fact_6583_dbl__inc__def,axiom,
% 5.68/5.99 ( neg_nu8295874005876285629c_real
% 5.68/5.99 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_def
% 5.68/5.99 thf(fact_6584_dbl__inc__def,axiom,
% 5.68/5.99 ( neg_nu5219082963157363817nc_rat
% 5.68/5.99 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_def
% 5.68/5.99 thf(fact_6585_dbl__inc__def,axiom,
% 5.68/5.99 ( neg_nu5851722552734809277nc_int
% 5.68/5.99 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % dbl_inc_def
% 5.68/5.99 thf(fact_6586_sum_OSuc__reindex__ivl,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_rat @ ( G @ M )
% 5.68/5.99 @ ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.Suc_reindex_ivl
% 5.68/5.99 thf(fact_6587_sum_OSuc__reindex__ivl,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > int] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( G @ M )
% 5.68/5.99 @ ( groups3539618377306564664at_int
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.Suc_reindex_ivl
% 5.68/5.99 thf(fact_6588_sum_OSuc__reindex__ivl,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( G @ M )
% 5.68/5.99 @ ( groups3542108847815614940at_nat
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.Suc_reindex_ivl
% 5.68/5.99 thf(fact_6589_sum_OSuc__reindex__ivl,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > real] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.68/5.99 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/5.99 = ( plus_plus_real @ ( G @ M )
% 5.68/5.99 @ ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.Suc_reindex_ivl
% 5.68/5.99 thf(fact_6590_sum__Suc__diff,axiom,
% 5.68/5.99 ! [M: nat,N: nat,F: nat > rat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat
% 5.68/5.99 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_Suc_diff
% 5.68/5.99 thf(fact_6591_sum__Suc__diff,axiom,
% 5.68/5.99 ! [M: nat,N: nat,F: nat > int] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups3539618377306564664at_int
% 5.68/5.99 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_Suc_diff
% 5.68/5.99 thf(fact_6592_sum__Suc__diff,axiom,
% 5.68/5.99 ! [M: nat,N: nat,F: nat > real] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real
% 5.68/5.99 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.68/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/5.99 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum_Suc_diff
% 5.68/5.99 thf(fact_6593_sum_Oub__add__nat,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > rat,P4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/5.99 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/5.99 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.ub_add_nat
% 5.68/5.99 thf(fact_6594_sum_Oub__add__nat,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > int,P4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/5.99 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/5.99 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.ub_add_nat
% 5.68/5.99 thf(fact_6595_sum_Oub__add__nat,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > nat,P4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/5.99 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/5.99 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.ub_add_nat
% 5.68/5.99 thf(fact_6596_sum_Oub__add__nat,axiom,
% 5.68/5.99 ! [M: nat,N: nat,G: nat > real,P4: nat] :
% 5.68/5.99 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/5.99 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/5.99 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % sum.ub_add_nat
% 5.68/5.99 thf(fact_6597_divmod__int__def,axiom,
% 5.68/5.99 ( unique5052692396658037445od_int
% 5.68/5.99 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.68/5.99
% 5.68/5.99 % divmod_int_def
% 5.68/5.99 thf(fact_6598_divmod__def,axiom,
% 5.68/6.00 ( unique5052692396658037445od_int
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_def
% 5.68/6.00 thf(fact_6599_divmod__def,axiom,
% 5.68/6.00 ( unique5055182867167087721od_nat
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_def
% 5.68/6.00 thf(fact_6600_divmod__def,axiom,
% 5.68/6.00 ( unique3479559517661332726nteger
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_def
% 5.68/6.00 thf(fact_6601_divmod_H__nat__def,axiom,
% 5.68/6.00 ( unique5055182867167087721od_nat
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod'_nat_def
% 5.68/6.00 thf(fact_6602_dbl__dec__def,axiom,
% 5.68/6.00 ( neg_nu6511756317524482435omplex
% 5.68/6.00 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_def
% 5.68/6.00 thf(fact_6603_dbl__dec__def,axiom,
% 5.68/6.00 ( neg_nu6075765906172075777c_real
% 5.68/6.00 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_def
% 5.68/6.00 thf(fact_6604_dbl__dec__def,axiom,
% 5.68/6.00 ( neg_nu3179335615603231917ec_rat
% 5.68/6.00 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_def
% 5.68/6.00 thf(fact_6605_dbl__dec__def,axiom,
% 5.68/6.00 ( neg_nu3811975205180677377ec_int
% 5.68/6.00 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_def
% 5.68/6.00 thf(fact_6606_sum__natinterval__diff,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > complex] :
% 5.68/6.00 ( ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.68/6.00 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_complex ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_natinterval_diff
% 5.68/6.00 thf(fact_6607_sum__natinterval__diff,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > rat] :
% 5.68/6.00 ( ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.68/6.00 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_rat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_natinterval_diff
% 5.68/6.00 thf(fact_6608_sum__natinterval__diff,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > int] :
% 5.68/6.00 ( ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.68/6.00 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_int ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_natinterval_diff
% 5.68/6.00 thf(fact_6609_sum__natinterval__diff,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > real] :
% 5.68/6.00 ( ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.68/6.00 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_real ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_natinterval_diff
% 5.68/6.00 thf(fact_6610_sum__telescope_H_H,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > rat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.68/6.00 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_telescope''
% 5.68/6.00 thf(fact_6611_sum__telescope_H_H,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > int] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.68/6.00 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_telescope''
% 5.68/6.00 thf(fact_6612_sum__telescope_H_H,axiom,
% 5.68/6.00 ! [M: nat,N: nat,F: nat > real] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.68/6.00 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_telescope''
% 5.68/6.00 thf(fact_6613_mask__eq__sum__exp,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.68/6.00 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 @ ( collect_nat
% 5.68/6.00 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mask_eq_sum_exp
% 5.68/6.00 thf(fact_6614_mask__eq__sum__exp,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.68/6.00 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.00 @ ( collect_nat
% 5.68/6.00 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mask_eq_sum_exp
% 5.68/6.00 thf(fact_6615_sum__gp__multiplied,axiom,
% 5.68/6.00 ! [M: nat,N: nat,X: complex] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.68/6.00 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_multiplied
% 5.68/6.00 thf(fact_6616_sum__gp__multiplied,axiom,
% 5.68/6.00 ! [M: nat,N: nat,X: rat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.68/6.00 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_multiplied
% 5.68/6.00 thf(fact_6617_sum__gp__multiplied,axiom,
% 5.68/6.00 ! [M: nat,N: nat,X: int] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.68/6.00 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_multiplied
% 5.68/6.00 thf(fact_6618_sum__gp__multiplied,axiom,
% 5.68/6.00 ! [M: nat,N: nat,X: real] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.00 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.68/6.00 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_multiplied
% 5.68/6.00 thf(fact_6619_sum_Oin__pairs,axiom,
% 5.68/6.00 ! [G: nat > rat,M: nat,N: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.00 = ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.in_pairs
% 5.68/6.00 thf(fact_6620_sum_Oin__pairs,axiom,
% 5.68/6.00 ! [G: nat > int,M: nat,N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.00 = ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.in_pairs
% 5.68/6.00 thf(fact_6621_sum_Oin__pairs,axiom,
% 5.68/6.00 ! [G: nat > nat,M: nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.00 = ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.in_pairs
% 5.68/6.00 thf(fact_6622_sum_Oin__pairs,axiom,
% 5.68/6.00 ! [G: nat > real,M: nat,N: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.00 = ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.in_pairs
% 5.68/6.00 thf(fact_6623_mask__eq__sum__exp__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.00 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.00 @ ( collect_nat
% 5.68/6.00 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mask_eq_sum_exp_nat
% 5.68/6.00 thf(fact_6624_gauss__sum__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [X2: nat] : X2
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % gauss_sum_nat
% 5.68/6.00 thf(fact_6625_arith__series__nat,axiom,
% 5.68/6.00 ! [A: nat,D: nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( 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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % arith_series_nat
% 5.68/6.00 thf(fact_6626_Sum__Icc__nat,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [X2: nat] : X2
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( 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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Sum_Icc_nat
% 5.68/6.00 thf(fact_6627_divmod__divmod__step,axiom,
% 5.68/6.00 ( unique5055182867167087721od_nat
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_divmod_step
% 5.68/6.00 thf(fact_6628_divmod__divmod__step,axiom,
% 5.68/6.00 ( unique5052692396658037445od_int
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_divmod_step
% 5.68/6.00 thf(fact_6629_divmod__divmod__step,axiom,
% 5.68/6.00 ( unique3479559517661332726nteger
% 5.68/6.00 = ( ^ [M6: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_divmod_step
% 5.68/6.00 thf(fact_6630_one__div__minus__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_div_minus_numeral
% 5.68/6.00 thf(fact_6631_minus__one__div__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % minus_one_div_numeral
% 5.68/6.00 thf(fact_6632_infinite__int__iff__unbounded__le,axiom,
% 5.68/6.00 ! [S3: set_int] :
% 5.68/6.00 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.68/6.00 = ( ! [M6: int] :
% 5.68/6.00 ? [N2: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N2 ) )
% 5.68/6.00 & ( member_int @ N2 @ S3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % infinite_int_iff_unbounded_le
% 5.68/6.00 thf(fact_6633_minus__numeral__div__numeral,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % minus_numeral_div_numeral
% 5.68/6.00 thf(fact_6634_numeral__div__minus__numeral,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_div_minus_numeral
% 5.68/6.00 thf(fact_6635_Divides_Oadjust__div__eq,axiom,
% 5.68/6.00 ! [Q2: int,R2: int] :
% 5.68/6.00 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.68/6.00 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Divides.adjust_div_eq
% 5.68/6.00 thf(fact_6636_infinite__nat__iff__unbounded,axiom,
% 5.68/6.00 ! [S3: set_nat] :
% 5.68/6.00 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.68/6.00 = ( ! [M6: nat] :
% 5.68/6.00 ? [N2: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M6 @ N2 )
% 5.68/6.00 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % infinite_nat_iff_unbounded
% 5.68/6.00 thf(fact_6637_unbounded__k__infinite,axiom,
% 5.68/6.00 ! [K: nat,S3: set_nat] :
% 5.68/6.00 ( ! [M5: nat] :
% 5.68/6.00 ( ( ord_less_nat @ K @ M5 )
% 5.68/6.00 => ? [N7: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M5 @ N7 )
% 5.68/6.00 & ( member_nat @ N7 @ S3 ) ) )
% 5.68/6.00 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % unbounded_k_infinite
% 5.68/6.00 thf(fact_6638_infinite__nat__iff__unbounded__le,axiom,
% 5.68/6.00 ! [S3: set_nat] :
% 5.68/6.00 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.68/6.00 = ( ! [M6: nat] :
% 5.68/6.00 ? [N2: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.00 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % infinite_nat_iff_unbounded_le
% 5.68/6.00 thf(fact_6639_sum__gp,axiom,
% 5.68/6.00 ! [N: nat,M: nat,X: complex] :
% 5.68/6.00 ( ( ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_complex ) )
% 5.68/6.00 & ( ~ ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( ( X = one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.68/6.00 & ( ( X != one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp
% 5.68/6.00 thf(fact_6640_sum__gp,axiom,
% 5.68/6.00 ! [N: nat,M: nat,X: rat] :
% 5.68/6.00 ( ( ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_rat ) )
% 5.68/6.00 & ( ~ ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( ( X = one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.68/6.00 & ( ( X != one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp
% 5.68/6.00 thf(fact_6641_sum__gp,axiom,
% 5.68/6.00 ! [N: nat,M: nat,X: real] :
% 5.68/6.00 ( ( ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = zero_zero_real ) )
% 5.68/6.00 & ( ~ ( ord_less_nat @ N @ M )
% 5.68/6.00 => ( ( ( X = one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.68/6.00 & ( ( X != one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp
% 5.68/6.00 thf(fact_6642_divmod__BitM__2__eq,axiom,
% 5.68/6.00 ! [M: num] :
% 5.68/6.00 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.68/6.00 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_BitM_2_eq
% 5.68/6.00 thf(fact_6643_gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.00 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_6644_gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.00 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_6645_of__int__code__if,axiom,
% 5.68/6.00 ( ring_1_of_int_real
% 5.68/6.00 = ( ^ [K3: int] :
% 5.68/6.00 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.68/6.00 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.00 @ ( if_real
% 5.68/6.00 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_code_if
% 5.68/6.00 thf(fact_6646_of__int__code__if,axiom,
% 5.68/6.00 ( ring_1_of_int_int
% 5.68/6.00 = ( ^ [K3: int] :
% 5.68/6.00 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.68/6.00 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.00 @ ( if_int
% 5.68/6.00 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_code_if
% 5.68/6.00 thf(fact_6647_of__int__code__if,axiom,
% 5.68/6.00 ( ring_17405671764205052669omplex
% 5.68/6.00 = ( ^ [K3: int] :
% 5.68/6.00 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.68/6.00 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.00 @ ( if_complex
% 5.68/6.00 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_code_if
% 5.68/6.00 thf(fact_6648_of__int__code__if,axiom,
% 5.68/6.00 ( ring_18347121197199848620nteger
% 5.68/6.00 = ( ^ [K3: int] :
% 5.68/6.00 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.68/6.00 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.00 @ ( if_Code_integer
% 5.68/6.00 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_code_if
% 5.68/6.00 thf(fact_6649_of__int__code__if,axiom,
% 5.68/6.00 ( ring_1_of_int_rat
% 5.68/6.00 = ( ^ [K3: int] :
% 5.68/6.00 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.68/6.00 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.00 @ ( if_rat
% 5.68/6.00 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_code_if
% 5.68/6.00 thf(fact_6650_divmod__algorithm__code_I6_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc4245557441103728435nt_int
% 5.68/6.00 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.68/6.00 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(6)
% 5.68/6.00 thf(fact_6651_divmod__algorithm__code_I6_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc2626176000494625587at_nat
% 5.68/6.00 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.68/6.00 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(6)
% 5.68/6.00 thf(fact_6652_divmod__algorithm__code_I6_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc6916734918728496179nteger
% 5.68/6.00 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.68/6.00 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(6)
% 5.68/6.00 thf(fact_6653_sum__gp__offset,axiom,
% 5.68/6.00 ! [X: complex,M: nat,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.68/6.00 & ( ( X != one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_offset
% 5.68/6.00 thf(fact_6654_sum__gp__offset,axiom,
% 5.68/6.00 ! [X: rat,M: nat,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.68/6.00 & ( ( X != one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_offset
% 5.68/6.00 thf(fact_6655_sum__gp__offset,axiom,
% 5.68/6.00 ! [X: real,M: nat,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.68/6.00 & ( ( X != one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.00 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_offset
% 5.68/6.00 thf(fact_6656_of__nat__eq__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ M )
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( M = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_iff
% 5.68/6.00 thf(fact_6657_of__nat__eq__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ( semiri5074537144036343181t_real @ M )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( M = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_iff
% 5.68/6.00 thf(fact_6658_of__nat__eq__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.68/6.00 = ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( M = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_iff
% 5.68/6.00 thf(fact_6659_of__nat__eq__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ( semiri681578069525770553at_rat @ M )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( M = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_iff
% 5.68/6.00 thf(fact_6660_int__eq__iff__numeral,axiom,
% 5.68/6.00 ! [M: nat,V: num] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ M )
% 5.68/6.00 = ( numeral_numeral_int @ V ) )
% 5.68/6.00 = ( M
% 5.68/6.00 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_eq_iff_numeral
% 5.68/6.00 thf(fact_6661_abs__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.68/6.00 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % abs_of_nat
% 5.68/6.00 thf(fact_6662_abs__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % abs_of_nat
% 5.68/6.00 thf(fact_6663_abs__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % abs_of_nat
% 5.68/6.00 thf(fact_6664_abs__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % abs_of_nat
% 5.68/6.00 thf(fact_6665_negative__zle,axiom,
% 5.68/6.00 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.68/6.00
% 5.68/6.00 % negative_zle
% 5.68/6.00 thf(fact_6666_case__prod__conv,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.68/6.00 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.68/6.00 = ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_conv
% 5.68/6.00 thf(fact_6667_case__prod__conv,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.68/6.00 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.68/6.00 = ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_conv
% 5.68/6.00 thf(fact_6668_case__prod__conv,axiom,
% 5.68/6.00 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.68/6.00 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.68/6.00 = ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_conv
% 5.68/6.00 thf(fact_6669_case__prod__conv,axiom,
% 5.68/6.00 ! [F: int > int > $o,A: int,B: int] :
% 5.68/6.00 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.68/6.00 = ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_conv
% 5.68/6.00 thf(fact_6670_case__prod__conv,axiom,
% 5.68/6.00 ! [F: int > int > int,A: int,B: int] :
% 5.68/6.00 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.68/6.00 = ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_conv
% 5.68/6.00 thf(fact_6671_of__nat__0,axiom,
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.68/6.00 = zero_zero_complex ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0
% 5.68/6.00 thf(fact_6672_of__nat__0,axiom,
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.68/6.00 = zero_zero_int ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0
% 5.68/6.00 thf(fact_6673_of__nat__0,axiom,
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.68/6.00 = zero_zero_real ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0
% 5.68/6.00 thf(fact_6674_of__nat__0,axiom,
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.68/6.00 = zero_zero_nat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0
% 5.68/6.00 thf(fact_6675_of__nat__0,axiom,
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.68/6.00 = zero_zero_rat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0
% 5.68/6.00 thf(fact_6676_of__nat__0__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( zero_zero_complex
% 5.68/6.00 = ( semiri8010041392384452111omplex @ N ) )
% 5.68/6.00 = ( zero_zero_nat = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_eq_iff
% 5.68/6.00 thf(fact_6677_of__nat__0__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( zero_zero_int
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( zero_zero_nat = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_eq_iff
% 5.68/6.00 thf(fact_6678_of__nat__0__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( zero_zero_real
% 5.68/6.00 = ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( zero_zero_nat = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_eq_iff
% 5.68/6.00 thf(fact_6679_of__nat__0__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( zero_zero_nat
% 5.68/6.00 = ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( zero_zero_nat = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_eq_iff
% 5.68/6.00 thf(fact_6680_of__nat__0__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( zero_zero_rat
% 5.68/6.00 = ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( zero_zero_nat = N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_eq_iff
% 5.68/6.00 thf(fact_6681_of__nat__eq__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ( semiri8010041392384452111omplex @ M )
% 5.68/6.00 = zero_zero_complex )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_0_iff
% 5.68/6.00 thf(fact_6682_of__nat__eq__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ M )
% 5.68/6.00 = zero_zero_int )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_0_iff
% 5.68/6.00 thf(fact_6683_of__nat__eq__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ( semiri5074537144036343181t_real @ M )
% 5.68/6.00 = zero_zero_real )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_0_iff
% 5.68/6.00 thf(fact_6684_of__nat__eq__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.68/6.00 = zero_zero_nat )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_0_iff
% 5.68/6.00 thf(fact_6685_of__nat__eq__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ( semiri681578069525770553at_rat @ M )
% 5.68/6.00 = zero_zero_rat )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_0_iff
% 5.68/6.00 thf(fact_6686_of__nat__less__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_iff
% 5.68/6.00 thf(fact_6687_of__nat__less__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_iff
% 5.68/6.00 thf(fact_6688_of__nat__less__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_iff
% 5.68/6.00 thf(fact_6689_of__nat__less__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_iff
% 5.68/6.00 thf(fact_6690_of__nat__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_numeral
% 5.68/6.00 thf(fact_6691_of__nat__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_numeral
% 5.68/6.00 thf(fact_6692_of__nat__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numeral_numeral_real @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_numeral
% 5.68/6.00 thf(fact_6693_of__nat__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numeral_numeral_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_numeral
% 5.68/6.00 thf(fact_6694_of__nat__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numeral_numeral_rat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_numeral
% 5.68/6.00 thf(fact_6695_of__nat__le__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_iff
% 5.68/6.00 thf(fact_6696_of__nat__le__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_iff
% 5.68/6.00 thf(fact_6697_of__nat__le__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_iff
% 5.68/6.00 thf(fact_6698_of__nat__le__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_iff
% 5.68/6.00 thf(fact_6699_of__nat__add,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_add
% 5.68/6.00 thf(fact_6700_of__nat__add,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.68/6.00 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_add
% 5.68/6.00 thf(fact_6701_of__nat__add,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.68/6.00 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_add
% 5.68/6.00 thf(fact_6702_of__nat__add,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.68/6.00 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_add
% 5.68/6.00 thf(fact_6703_of__nat__mult,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.68/6.00 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mult
% 5.68/6.00 thf(fact_6704_of__nat__mult,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.68/6.00 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mult
% 5.68/6.00 thf(fact_6705_of__nat__mult,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.68/6.00 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mult
% 5.68/6.00 thf(fact_6706_of__nat__mult,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.68/6.00 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mult
% 5.68/6.00 thf(fact_6707_of__nat__1,axiom,
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.68/6.00 = one_one_complex ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1
% 5.68/6.00 thf(fact_6708_of__nat__1,axiom,
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.68/6.00 = one_one_int ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1
% 5.68/6.00 thf(fact_6709_of__nat__1,axiom,
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.68/6.00 = one_one_real ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1
% 5.68/6.00 thf(fact_6710_of__nat__1,axiom,
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.68/6.00 = one_one_nat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1
% 5.68/6.00 thf(fact_6711_of__nat__1,axiom,
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.68/6.00 = one_one_rat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1
% 5.68/6.00 thf(fact_6712_of__nat__1__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( one_one_complex
% 5.68/6.00 = ( semiri8010041392384452111omplex @ N ) )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1_eq_iff
% 5.68/6.00 thf(fact_6713_of__nat__1__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( one_one_int
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1_eq_iff
% 5.68/6.00 thf(fact_6714_of__nat__1__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( one_one_real
% 5.68/6.00 = ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1_eq_iff
% 5.68/6.00 thf(fact_6715_of__nat__1__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( one_one_nat
% 5.68/6.00 = ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1_eq_iff
% 5.68/6.00 thf(fact_6716_of__nat__1__eq__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( one_one_rat
% 5.68/6.00 = ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_1_eq_iff
% 5.68/6.00 thf(fact_6717_of__nat__eq__1__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ( semiri8010041392384452111omplex @ N )
% 5.68/6.00 = one_one_complex )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_1_iff
% 5.68/6.00 thf(fact_6718_of__nat__eq__1__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ N )
% 5.68/6.00 = one_one_int )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_1_iff
% 5.68/6.00 thf(fact_6719_of__nat__eq__1__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ( semiri5074537144036343181t_real @ N )
% 5.68/6.00 = one_one_real )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_1_iff
% 5.68/6.00 thf(fact_6720_of__nat__eq__1__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.68/6.00 = one_one_nat )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_1_iff
% 5.68/6.00 thf(fact_6721_of__nat__eq__1__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ( semiri681578069525770553at_rat @ N )
% 5.68/6.00 = one_one_rat )
% 5.68/6.00 = ( N = one_one_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_1_iff
% 5.68/6.00 thf(fact_6722_of__int__le__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_iff
% 5.68/6.00 thf(fact_6723_of__int__le__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_iff
% 5.68/6.00 thf(fact_6724_of__int__le__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_iff
% 5.68/6.00 thf(fact_6725_of__int__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.68/6.00 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral
% 5.68/6.00 thf(fact_6726_of__int__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.68/6.00 = ( numeral_numeral_real @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral
% 5.68/6.00 thf(fact_6727_of__int__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.68/6.00 = ( numeral_numeral_rat @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral
% 5.68/6.00 thf(fact_6728_of__int__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.68/6.00 = ( numeral_numeral_int @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral
% 5.68/6.00 thf(fact_6729_of__int__eq__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.68/6.00 = ( numera6690914467698888265omplex @ N ) )
% 5.68/6.00 = ( Z
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_iff
% 5.68/6.00 thf(fact_6730_of__int__eq__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ( ring_1_of_int_real @ Z )
% 5.68/6.00 = ( numeral_numeral_real @ N ) )
% 5.68/6.00 = ( Z
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_iff
% 5.68/6.00 thf(fact_6731_of__int__eq__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ( ring_1_of_int_rat @ Z )
% 5.68/6.00 = ( numeral_numeral_rat @ N ) )
% 5.68/6.00 = ( Z
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_iff
% 5.68/6.00 thf(fact_6732_of__int__eq__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ( ring_1_of_int_int @ Z )
% 5.68/6.00 = ( numeral_numeral_int @ N ) )
% 5.68/6.00 = ( Z
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_iff
% 5.68/6.00 thf(fact_6733_of__int__less__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_iff
% 5.68/6.00 thf(fact_6734_of__int__less__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_iff
% 5.68/6.00 thf(fact_6735_of__int__less__iff,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_int @ W @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_iff
% 5.68/6.00 thf(fact_6736_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ( semiri8010041392384452111omplex @ X )
% 5.68/6.00 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6737_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ X )
% 5.68/6.00 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6738_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ( semiri5074537144036343181t_real @ X )
% 5.68/6.00 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6739_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.68/6.00 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6740_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ( semiri681578069525770553at_rat @ X )
% 5.68/6.00 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6741_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.68/6.00 = ( semiri8010041392384452111omplex @ X ) )
% 5.68/6.00 = ( ( power_power_nat @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6742_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.68/6.00 = ( semiri1314217659103216013at_int @ X ) )
% 5.68/6.00 = ( ( power_power_nat @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6743_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ X ) )
% 5.68/6.00 = ( ( power_power_nat @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6744_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.68/6.00 = ( semiri1316708129612266289at_nat @ X ) )
% 5.68/6.00 = ( ( power_power_nat @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6745_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ X ) )
% 5.68/6.00 = ( ( power_power_nat @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_eq_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6746_of__nat__power,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.68/6.00 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power
% 5.68/6.00 thf(fact_6747_of__nat__power,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.68/6.00 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power
% 5.68/6.00 thf(fact_6748_of__nat__power,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.68/6.00 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power
% 5.68/6.00 thf(fact_6749_of__nat__power,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.68/6.00 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power
% 5.68/6.00 thf(fact_6750_of__nat__power,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.68/6.00 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power
% 5.68/6.00 thf(fact_6751_of__int__mult,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.68/6.00 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_mult
% 5.68/6.00 thf(fact_6752_of__int__mult,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.68/6.00 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_mult
% 5.68/6.00 thf(fact_6753_of__int__mult,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.68/6.00 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_mult
% 5.68/6.00 thf(fact_6754_of__int__add,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.68/6.00 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_add
% 5.68/6.00 thf(fact_6755_of__int__add,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.68/6.00 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_add
% 5.68/6.00 thf(fact_6756_of__int__add,axiom,
% 5.68/6.00 ! [W: int,Z: int] :
% 5.68/6.00 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.68/6.00 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_add
% 5.68/6.00 thf(fact_6757_negative__zless,axiom,
% 5.68/6.00 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.68/6.00
% 5.68/6.00 % negative_zless
% 5.68/6.00 thf(fact_6758_of__int__power,axiom,
% 5.68/6.00 ! [Z: int,N: nat] :
% 5.68/6.00 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.68/6.00 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power
% 5.68/6.00 thf(fact_6759_of__int__power,axiom,
% 5.68/6.00 ! [Z: int,N: nat] :
% 5.68/6.00 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.68/6.00 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power
% 5.68/6.00 thf(fact_6760_of__int__power,axiom,
% 5.68/6.00 ! [Z: int,N: nat] :
% 5.68/6.00 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.68/6.00 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power
% 5.68/6.00 thf(fact_6761_of__int__power,axiom,
% 5.68/6.00 ! [Z: int,N: nat] :
% 5.68/6.00 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.68/6.00 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power
% 5.68/6.00 thf(fact_6762_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.68/6.00 = ( ring_1_of_int_rat @ X ) )
% 5.68/6.00 = ( ( power_power_int @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6763_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.68/6.00 = ( ring_1_of_int_real @ X ) )
% 5.68/6.00 = ( ( power_power_int @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6764_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.68/6.00 = ( ring_1_of_int_int @ X ) )
% 5.68/6.00 = ( ( power_power_int @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6765_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.68/6.00 = ( ring_17405671764205052669omplex @ X ) )
% 5.68/6.00 = ( ( power_power_int @ B @ W )
% 5.68/6.00 = X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6766_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_rat @ X )
% 5.68/6.00 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6767_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_real @ X )
% 5.68/6.00 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6768_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_int @ X )
% 5.68/6.00 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6769_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ( ring_17405671764205052669omplex @ X )
% 5.68/6.00 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.68/6.00 = ( X
% 5.68/6.00 = ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6770_of__nat__of__bool,axiom,
% 5.68/6.00 ! [P: $o] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/6.00 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_of_bool
% 5.68/6.00 thf(fact_6771_of__nat__of__bool,axiom,
% 5.68/6.00 ! [P: $o] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/6.00 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_of_bool
% 5.68/6.00 thf(fact_6772_of__nat__of__bool,axiom,
% 5.68/6.00 ! [P: $o] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/6.00 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_of_bool
% 5.68/6.00 thf(fact_6773_of__nat__of__bool,axiom,
% 5.68/6.00 ! [P: $o] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/6.00 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_of_bool
% 5.68/6.00 thf(fact_6774_of__nat__of__bool,axiom,
% 5.68/6.00 ! [P: $o] :
% 5.68/6.00 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.68/6.00 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_of_bool
% 5.68/6.00 thf(fact_6775_dbl__dec__simps_I5_J,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.68/6.00 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_simps(5)
% 5.68/6.00 thf(fact_6776_dbl__dec__simps_I5_J,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.68/6.00 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_simps(5)
% 5.68/6.00 thf(fact_6777_dbl__dec__simps_I5_J,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.68/6.00 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_simps(5)
% 5.68/6.00 thf(fact_6778_dbl__dec__simps_I5_J,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.68/6.00 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % dbl_dec_simps(5)
% 5.68/6.00 thf(fact_6779_of__nat__le__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_0_iff
% 5.68/6.00 thf(fact_6780_of__nat__le__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_0_iff
% 5.68/6.00 thf(fact_6781_of__nat__le__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_0_iff
% 5.68/6.00 thf(fact_6782_of__nat__le__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.68/6.00 = ( M = zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_0_iff
% 5.68/6.00 thf(fact_6783_of__nat__Suc,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.68/6.00 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_Suc
% 5.68/6.00 thf(fact_6784_of__nat__Suc,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.68/6.00 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_Suc
% 5.68/6.00 thf(fact_6785_of__nat__Suc,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.68/6.00 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_Suc
% 5.68/6.00 thf(fact_6786_of__nat__Suc,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.68/6.00 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_Suc
% 5.68/6.00 thf(fact_6787_of__nat__Suc,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.68/6.00 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_Suc
% 5.68/6.00 thf(fact_6788_numeral__less__real__of__nat__iff,axiom,
% 5.68/6.00 ! [W: num,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_less_real_of_nat_iff
% 5.68/6.00 thf(fact_6789_real__of__nat__less__numeral__iff,axiom,
% 5.68/6.00 ! [N: nat,W: num] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.68/6.00 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_less_numeral_iff
% 5.68/6.00 thf(fact_6790_numeral__le__real__of__nat__iff,axiom,
% 5.68/6.00 ! [N: num,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_le_real_of_nat_iff
% 5.68/6.00 thf(fact_6791_pred__numeral__simps_I2_J,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.68/6.00 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % pred_numeral_simps(2)
% 5.68/6.00 thf(fact_6792_of__nat__0__less__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_less_iff
% 5.68/6.00 thf(fact_6793_of__nat__0__less__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_less_iff
% 5.68/6.00 thf(fact_6794_of__nat__0__less__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_less_iff
% 5.68/6.00 thf(fact_6795_of__nat__0__less__iff,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_less_iff
% 5.68/6.00 thf(fact_6796_of__int__le__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_0_iff
% 5.68/6.00 thf(fact_6797_of__int__le__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_0_iff
% 5.68/6.00 thf(fact_6798_of__int__le__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_0_iff
% 5.68/6.00 thf(fact_6799_of__int__0__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_le_iff
% 5.68/6.00 thf(fact_6800_of__int__0__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_le_iff
% 5.68/6.00 thf(fact_6801_of__int__0__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_le_iff
% 5.68/6.00 thf(fact_6802_of__int__0__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_less_iff
% 5.68/6.00 thf(fact_6803_of__int__0__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_less_iff
% 5.68/6.00 thf(fact_6804_of__int__0__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_0_less_iff
% 5.68/6.00 thf(fact_6805_of__int__less__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.68/6.00 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_0_iff
% 5.68/6.00 thf(fact_6806_of__int__less__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.68/6.00 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_0_iff
% 5.68/6.00 thf(fact_6807_of__int__less__0__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.68/6.00 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_0_iff
% 5.68/6.00 thf(fact_6808_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6809_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6810_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6811_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6812_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6813_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6814_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6815_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6816_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: nat] :
% 5.68/6.00 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.68/6.00 = ( semiri8010041392384452111omplex @ Y2 ) )
% 5.68/6.00 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6817_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: nat] :
% 5.68/6.00 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = ( semiri1314217659103216013at_int @ Y2 ) )
% 5.68/6.00 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6818_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: nat] :
% 5.68/6.00 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ Y2 ) )
% 5.68/6.00 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6819_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: nat] :
% 5.68/6.00 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = ( semiri1316708129612266289at_nat @ Y2 ) )
% 5.68/6.00 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6820_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: nat] :
% 5.68/6.00 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ Y2 ) )
% 5.68/6.00 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6821_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: nat,X: num,N: nat] :
% 5.68/6.00 ( ( ( semiri8010041392384452111omplex @ Y2 )
% 5.68/6.00 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6822_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: nat,X: num,N: nat] :
% 5.68/6.00 ( ( ( semiri1314217659103216013at_int @ Y2 )
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6823_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: nat,X: num,N: nat] :
% 5.68/6.00 ( ( ( semiri5074537144036343181t_real @ Y2 )
% 5.68/6.00 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6824_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: nat,X: num,N: nat] :
% 5.68/6.00 ( ( ( semiri1316708129612266289at_nat @ Y2 )
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6825_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: nat,X: num,N: nat] :
% 5.68/6.00 ( ( ( semiri681578069525770553at_rat @ Y2 )
% 5.68/6.00 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6826_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6827_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6828_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6829_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,B: nat,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6830_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6831_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6832_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6833_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: nat,W: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_of_nat_power_cancel_iff
% 5.68/6.00 thf(fact_6834_of__int__numeral__le__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_le_iff
% 5.68/6.00 thf(fact_6835_of__int__numeral__le__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_le_iff
% 5.68/6.00 thf(fact_6836_of__int__numeral__le__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_le_iff
% 5.68/6.00 thf(fact_6837_of__int__le__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_iff
% 5.68/6.00 thf(fact_6838_of__int__le__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_iff
% 5.68/6.00 thf(fact_6839_of__int__le__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_iff
% 5.68/6.00 thf(fact_6840_of__int__less__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.68/6.00 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_iff
% 5.68/6.00 thf(fact_6841_of__int__less__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.68/6.00 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_iff
% 5.68/6.00 thf(fact_6842_of__int__less__numeral__iff,axiom,
% 5.68/6.00 ! [Z: int,N: num] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.00 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_iff
% 5.68/6.00 thf(fact_6843_of__int__numeral__less__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_less_iff
% 5.68/6.00 thf(fact_6844_of__int__numeral__less__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_less_iff
% 5.68/6.00 thf(fact_6845_of__int__numeral__less__iff,axiom,
% 5.68/6.00 ! [N: num,Z: int] :
% 5.68/6.00 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_numeral_less_iff
% 5.68/6.00 thf(fact_6846_of__int__le__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_1_iff
% 5.68/6.00 thf(fact_6847_of__int__le__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_1_iff
% 5.68/6.00 thf(fact_6848_of__int__le__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.68/6.00 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_1_iff
% 5.68/6.00 thf(fact_6849_of__int__1__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_le_iff
% 5.68/6.00 thf(fact_6850_of__int__1__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_le_iff
% 5.68/6.00 thf(fact_6851_of__int__1__le__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_le_iff
% 5.68/6.00 thf(fact_6852_of__int__less__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.68/6.00 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_1_iff
% 5.68/6.00 thf(fact_6853_of__int__less__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.68/6.00 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_1_iff
% 5.68/6.00 thf(fact_6854_of__int__less__1__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.68/6.00 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_1_iff
% 5.68/6.00 thf(fact_6855_of__int__1__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.68/6.00 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_less_iff
% 5.68/6.00 thf(fact_6856_of__int__1__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.68/6.00 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_less_iff
% 5.68/6.00 thf(fact_6857_of__int__1__less__iff,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.68/6.00 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_1_less_iff
% 5.68/6.00 thf(fact_6858_of__int__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6859_of__int__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6860_of__int__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6861_of__int__le__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6862_of__int__le__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6863_of__int__le__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6864_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.68/6.00 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6865_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_real @ Y2 )
% 5.68/6.00 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6866_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.68/6.00 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6867_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_int @ Y2 )
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6868_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.68/6.00 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6869_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.68/6.00 = ( ring_1_of_int_real @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6870_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.68/6.00 = ( ring_1_of_int_rat @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6871_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = ( ring_1_of_int_int @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6872_of__int__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6873_of__int__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6874_of__int__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: int,B: int,W: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.68/6.00 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6875_of__int__less__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6876_of__int__less__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6877_of__int__less__of__int__power__cancel__iff,axiom,
% 5.68/6.00 ! [B: int,W: nat,X: int] :
% 5.68/6.00 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_of_int_power_cancel_iff
% 5.68/6.00 thf(fact_6878_of__nat__zero__less__power__iff,axiom,
% 5.68/6.00 ! [X: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.68/6.00 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_zero_less_power_iff
% 5.68/6.00 thf(fact_6879_of__nat__zero__less__power__iff,axiom,
% 5.68/6.00 ! [X: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.68/6.00 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_zero_less_power_iff
% 5.68/6.00 thf(fact_6880_of__nat__zero__less__power__iff,axiom,
% 5.68/6.00 ! [X: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.68/6.00 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_zero_less_power_iff
% 5.68/6.00 thf(fact_6881_of__nat__zero__less__power__iff,axiom,
% 5.68/6.00 ! [X: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.68/6.00 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_zero_less_power_iff
% 5.68/6.00 thf(fact_6882_even__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % even_of_nat
% 5.68/6.00 thf(fact_6883_even__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % even_of_nat
% 5.68/6.00 thf(fact_6884_even__of__nat,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % even_of_nat
% 5.68/6.00 thf(fact_6885_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6886_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6887_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6888_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.68/6.00 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6889_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6890_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6891_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6892_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6893_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6894_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6895_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6896_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [X: nat,I2: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6897_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6898_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6899_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6900_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.68/6.00 ! [I2: num,N: nat,X: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.68/6.00 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_nat_cancel_iff
% 5.68/6.00 thf(fact_6901_of__int__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6902_of__int__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6903_of__int__le__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6904_numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6905_numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6906_numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6907_numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6908_numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6909_numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6910_of__int__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6911_of__int__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6912_of__int__less__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6913_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 5.68/6.00 = ( ring_1_of_int_real @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6914_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = ( ring_1_of_int_int @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6915_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 5.68/6.00 = ( ring_17405671764205052669omplex @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6916_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 5.68/6.00 = ( ring_18347121197199848620nteger @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6917_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,Y2: int] :
% 5.68/6.00 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 5.68/6.00 = ( ring_1_of_int_rat @ Y2 ) )
% 5.68/6.00 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.68/6.00 = Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_eq_of_int_cancel_iff
% 5.68/6.00 thf(fact_6918_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_real @ Y2 )
% 5.68/6.00 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6919_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_int @ Y2 )
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6920_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_17405671764205052669omplex @ Y2 )
% 5.68/6.00 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6921_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_18347121197199848620nteger @ Y2 )
% 5.68/6.00 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6922_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [Y2: int,X: num,N: nat] :
% 5.68/6.00 ( ( ( ring_1_of_int_rat @ Y2 )
% 5.68/6.00 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.68/6.00 = ( Y2
% 5.68/6.00 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_eq_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6923_divmod__algorithm__code_I5_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc4245557441103728435nt_int
% 5.68/6.00 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.68/6.00 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(5)
% 5.68/6.00 thf(fact_6924_divmod__algorithm__code_I5_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc2626176000494625587at_nat
% 5.68/6.00 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.68/6.00 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(5)
% 5.68/6.00 thf(fact_6925_divmod__algorithm__code_I5_J,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.00 = ( produc6916734918728496179nteger
% 5.68/6.00 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.68/6.00 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_algorithm_code(5)
% 5.68/6.00 thf(fact_6926_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6927_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6928_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6929_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_le_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6930_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6931_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6932_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6933_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.68/6.00 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_le_of_int_cancel_iff
% 5.68/6.00 thf(fact_6934_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6935_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6936_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6937_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.68/6.00 ! [A: int,X: num,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.68/6.00 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_less_neg_numeral_power_cancel_iff
% 5.68/6.00 thf(fact_6938_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6939_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6940_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6941_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.68/6.00 ! [X: num,N: nat,A: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.68/6.00 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_numeral_power_less_of_int_cancel_iff
% 5.68/6.00 thf(fact_6942_of__nat__less__of__int__iff,axiom,
% 5.68/6.00 ! [N: nat,X: int] :
% 5.68/6.00 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_int_iff
% 5.68/6.00 thf(fact_6943_of__nat__less__of__int__iff,axiom,
% 5.68/6.00 ! [N: nat,X: int] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_int_iff
% 5.68/6.00 thf(fact_6944_of__nat__less__of__int__iff,axiom,
% 5.68/6.00 ! [N: nat,X: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 5.68/6.00 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_of_int_iff
% 5.68/6.00 thf(fact_6945_mult__of__int__commute,axiom,
% 5.68/6.00 ! [X: int,Y2: real] :
% 5.68/6.00 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_real @ Y2 @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_int_commute
% 5.68/6.00 thf(fact_6946_mult__of__int__commute,axiom,
% 5.68/6.00 ! [X: int,Y2: rat] :
% 5.68/6.00 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_rat @ Y2 @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_int_commute
% 5.68/6.00 thf(fact_6947_mult__of__int__commute,axiom,
% 5.68/6.00 ! [X: int,Y2: int] :
% 5.68/6.00 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_int @ Y2 @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_int_commute
% 5.68/6.00 thf(fact_6948_mult__of__nat__commute,axiom,
% 5.68/6.00 ! [X: nat,Y2: int] :
% 5.68/6.00 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_int @ Y2 @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_nat_commute
% 5.68/6.00 thf(fact_6949_mult__of__nat__commute,axiom,
% 5.68/6.00 ! [X: nat,Y2: real] :
% 5.68/6.00 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_real @ Y2 @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_nat_commute
% 5.68/6.00 thf(fact_6950_mult__of__nat__commute,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_nat @ Y2 @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_nat_commute
% 5.68/6.00 thf(fact_6951_mult__of__nat__commute,axiom,
% 5.68/6.00 ! [X: nat,Y2: rat] :
% 5.68/6.00 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y2 )
% 5.68/6.00 = ( times_times_rat @ Y2 @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mult_of_nat_commute
% 5.68/6.00 thf(fact_6952_old_Oprod_Ocase,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.68/6.00 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.68/6.00 = ( F @ X1 @ X22 ) ) ).
% 5.68/6.00
% 5.68/6.00 % old.prod.case
% 5.68/6.00 thf(fact_6953_old_Oprod_Ocase,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.68/6.00 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.68/6.00 = ( F @ X1 @ X22 ) ) ).
% 5.68/6.00
% 5.68/6.00 % old.prod.case
% 5.68/6.00 thf(fact_6954_old_Oprod_Ocase,axiom,
% 5.68/6.00 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.68/6.00 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.68/6.00 = ( F @ X1 @ X22 ) ) ).
% 5.68/6.00
% 5.68/6.00 % old.prod.case
% 5.68/6.00 thf(fact_6955_old_Oprod_Ocase,axiom,
% 5.68/6.00 ! [F: int > int > $o,X1: int,X22: int] :
% 5.68/6.00 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.68/6.00 = ( F @ X1 @ X22 ) ) ).
% 5.68/6.00
% 5.68/6.00 % old.prod.case
% 5.68/6.00 thf(fact_6956_old_Oprod_Ocase,axiom,
% 5.68/6.00 ! [F: int > int > int,X1: int,X22: int] :
% 5.68/6.00 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.68/6.00 = ( F @ X1 @ X22 ) ) ).
% 5.68/6.00
% 5.68/6.00 % old.prod.case
% 5.68/6.00 thf(fact_6957_semiring__norm_I26_J,axiom,
% 5.68/6.00 ( ( bitM @ one )
% 5.68/6.00 = one ) ).
% 5.68/6.00
% 5.68/6.00 % semiring_norm(26)
% 5.68/6.00 thf(fact_6958_case__prodE2,axiom,
% 5.68/6.00 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.68/6.00 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.68/6.00 => ~ ! [X3: nat,Y3: nat] :
% 5.68/6.00 ( ( Z
% 5.68/6.00 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE2
% 5.68/6.00 thf(fact_6959_case__prodE2,axiom,
% 5.68/6.00 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.68/6.00 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.68/6.00 => ~ ! [X3: nat,Y3: nat] :
% 5.68/6.00 ( ( Z
% 5.68/6.00 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE2
% 5.68/6.00 thf(fact_6960_case__prodE2,axiom,
% 5.68/6.00 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.68/6.00 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( Z
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE2
% 5.68/6.00 thf(fact_6961_case__prodE2,axiom,
% 5.68/6.00 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.68/6.00 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( Z
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE2
% 5.68/6.00 thf(fact_6962_case__prodE2,axiom,
% 5.68/6.00 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.68/6.00 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( Z
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE2
% 5.68/6.00 thf(fact_6963_case__prod__eta,axiom,
% 5.68/6.00 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.68/6.00 ( ( produc27273713700761075at_nat
% 5.68/6.00 @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 5.68/6.00 = F ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_eta
% 5.68/6.00 thf(fact_6964_case__prod__eta,axiom,
% 5.68/6.00 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.68/6.00 ( ( produc8739625826339149834_nat_o
% 5.68/6.00 @ ^ [X2: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y ) ) )
% 5.68/6.00 = F ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_eta
% 5.68/6.00 thf(fact_6965_case__prod__eta,axiom,
% 5.68/6.00 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.68/6.00 ( ( produc4245557441103728435nt_int
% 5.68/6.00 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.68/6.00 = F ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_eta
% 5.68/6.00 thf(fact_6966_case__prod__eta,axiom,
% 5.68/6.00 ! [F: product_prod_int_int > $o] :
% 5.68/6.00 ( ( produc4947309494688390418_int_o
% 5.68/6.00 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.68/6.00 = F ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_eta
% 5.68/6.00 thf(fact_6967_case__prod__eta,axiom,
% 5.68/6.00 ! [F: product_prod_int_int > int] :
% 5.68/6.00 ( ( produc8211389475949308722nt_int
% 5.68/6.00 @ ^ [X2: int,Y: int] : ( F @ ( product_Pair_int_int @ X2 @ Y ) ) )
% 5.68/6.00 = F ) ).
% 5.68/6.00
% 5.68/6.00 % case_prod_eta
% 5.68/6.00 thf(fact_6968_cond__case__prod__eta,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.68/6.00 ( ! [X3: nat,Y3: nat] :
% 5.68/6.00 ( ( F @ X3 @ Y3 )
% 5.68/6.00 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.68/6.00 => ( ( produc27273713700761075at_nat @ F )
% 5.68/6.00 = G ) ) ).
% 5.68/6.00
% 5.68/6.00 % cond_case_prod_eta
% 5.68/6.00 thf(fact_6969_cond__case__prod__eta,axiom,
% 5.68/6.00 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.68/6.00 ( ! [X3: nat,Y3: nat] :
% 5.68/6.00 ( ( F @ X3 @ Y3 )
% 5.68/6.00 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.68/6.00 => ( ( produc8739625826339149834_nat_o @ F )
% 5.68/6.00 = G ) ) ).
% 5.68/6.00
% 5.68/6.00 % cond_case_prod_eta
% 5.68/6.00 thf(fact_6970_cond__case__prod__eta,axiom,
% 5.68/6.00 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.68/6.00 ( ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( F @ X3 @ Y3 )
% 5.68/6.00 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.68/6.00 => ( ( produc4245557441103728435nt_int @ F )
% 5.68/6.00 = G ) ) ).
% 5.68/6.00
% 5.68/6.00 % cond_case_prod_eta
% 5.68/6.00 thf(fact_6971_cond__case__prod__eta,axiom,
% 5.68/6.00 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.68/6.00 ( ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( F @ X3 @ Y3 )
% 5.68/6.00 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.68/6.00 => ( ( produc4947309494688390418_int_o @ F )
% 5.68/6.00 = G ) ) ).
% 5.68/6.00
% 5.68/6.00 % cond_case_prod_eta
% 5.68/6.00 thf(fact_6972_cond__case__prod__eta,axiom,
% 5.68/6.00 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.68/6.00 ( ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( F @ X3 @ Y3 )
% 5.68/6.00 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.68/6.00 => ( ( produc8211389475949308722nt_int @ F )
% 5.68/6.00 = G ) ) ).
% 5.68/6.00
% 5.68/6.00 % cond_case_prod_eta
% 5.68/6.00 thf(fact_6973_of__nat__0__le__iff,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_le_iff
% 5.68/6.00 thf(fact_6974_of__nat__0__le__iff,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_le_iff
% 5.68/6.00 thf(fact_6975_of__nat__0__le__iff,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_le_iff
% 5.68/6.00 thf(fact_6976_of__nat__0__le__iff,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_0_le_iff
% 5.68/6.00 thf(fact_6977_of__nat__less__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_0_iff
% 5.68/6.00 thf(fact_6978_of__nat__less__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_0_iff
% 5.68/6.00 thf(fact_6979_of__nat__less__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_0_iff
% 5.68/6.00 thf(fact_6980_of__nat__less__0__iff,axiom,
% 5.68/6.00 ! [M: nat] :
% 5.68/6.00 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_0_iff
% 5.68/6.00 thf(fact_6981_of__nat__neq__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.68/6.00 != zero_zero_complex ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_neq_0
% 5.68/6.00 thf(fact_6982_of__nat__neq__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.68/6.00 != zero_zero_int ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_neq_0
% 5.68/6.00 thf(fact_6983_of__nat__neq__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.68/6.00 != zero_zero_real ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_neq_0
% 5.68/6.00 thf(fact_6984_of__nat__neq__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.68/6.00 != zero_zero_nat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_neq_0
% 5.68/6.00 thf(fact_6985_of__nat__neq__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.68/6.00 != zero_zero_rat ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_neq_0
% 5.68/6.00 thf(fact_6986_div__mult2__eq_H,axiom,
% 5.68/6.00 ! [A: int,M: nat,N: nat] :
% 5.68/6.00 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.00 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % div_mult2_eq'
% 5.68/6.00 thf(fact_6987_div__mult2__eq_H,axiom,
% 5.68/6.00 ! [A: nat,M: nat,N: nat] :
% 5.68/6.00 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.68/6.00 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % div_mult2_eq'
% 5.68/6.00 thf(fact_6988_less__imp__of__nat__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M @ N )
% 5.68/6.00 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % less_imp_of_nat_less
% 5.68/6.00 thf(fact_6989_less__imp__of__nat__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M @ N )
% 5.68/6.00 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % less_imp_of_nat_less
% 5.68/6.00 thf(fact_6990_less__imp__of__nat__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M @ N )
% 5.68/6.00 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % less_imp_of_nat_less
% 5.68/6.00 thf(fact_6991_less__imp__of__nat__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ M @ N )
% 5.68/6.00 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % less_imp_of_nat_less
% 5.68/6.00 thf(fact_6992_of__nat__less__imp__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 => ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_imp_less
% 5.68/6.00 thf(fact_6993_of__nat__less__imp__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.00 => ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_imp_less
% 5.68/6.00 thf(fact_6994_of__nat__less__imp__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 => ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_imp_less
% 5.68/6.00 thf(fact_6995_of__nat__less__imp__less,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.68/6.00 => ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_imp_less
% 5.68/6.00 thf(fact_6996_of__nat__mono,axiom,
% 5.68/6.00 ! [I2: nat,J: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.00 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mono
% 5.68/6.00 thf(fact_6997_of__nat__mono,axiom,
% 5.68/6.00 ! [I2: nat,J: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.00 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mono
% 5.68/6.00 thf(fact_6998_of__nat__mono,axiom,
% 5.68/6.00 ! [I2: nat,J: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.00 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mono
% 5.68/6.00 thf(fact_6999_of__nat__mono,axiom,
% 5.68/6.00 ! [I2: nat,J: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.00 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mono
% 5.68/6.00 thf(fact_7000_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.68/6.00 thf(fact_7001_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.68/6.00 thf(fact_7002_of__nat__dvd__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_dvd_iff
% 5.68/6.00 thf(fact_7003_of__nat__dvd__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_dvd_iff
% 5.68/6.00 thf(fact_7004_of__nat__dvd__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.68/6.00 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_dvd_iff
% 5.68/6.00 thf(fact_7005_int__ops_I3_J,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_ops(3)
% 5.68/6.00 thf(fact_7006_nat__int__comparison_I2_J,axiom,
% 5.68/6.00 ( ord_less_nat
% 5.68/6.00 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_int_comparison(2)
% 5.68/6.00 thf(fact_7007_int__of__nat__induct,axiom,
% 5.68/6.00 ! [P: int > $o,Z: int] :
% 5.68/6.00 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.68/6.00 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.68/6.00 => ( P @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_of_nat_induct
% 5.68/6.00 thf(fact_7008_int__cases,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ! [N3: nat] :
% 5.68/6.00 ( Z
% 5.68/6.00 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( Z
% 5.68/6.00 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_cases
% 5.68/6.00 thf(fact_7009_zle__int,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.00 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % zle_int
% 5.68/6.00 thf(fact_7010_nat__int__comparison_I3_J,axiom,
% 5.68/6.00 ( ord_less_eq_nat
% 5.68/6.00 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_int_comparison(3)
% 5.68/6.00 thf(fact_7011_zero__le__imp__eq__int,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.00 => ? [N3: nat] :
% 5.68/6.00 ( K
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zero_le_imp_eq_int
% 5.68/6.00 thf(fact_7012_nonneg__int__cases,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( K
% 5.68/6.00 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nonneg_int_cases
% 5.68/6.00 thf(fact_7013_of__nat__mod,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.68/6.00 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mod
% 5.68/6.00 thf(fact_7014_of__nat__mod,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.68/6.00 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mod
% 5.68/6.00 thf(fact_7015_of__nat__mod,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.68/6.00 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_mod
% 5.68/6.00 thf(fact_7016_zadd__int__left,axiom,
% 5.68/6.00 ! [M: nat,N: nat,Z: int] :
% 5.68/6.00 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.68/6.00
% 5.68/6.00 % zadd_int_left
% 5.68/6.00 thf(fact_7017_int__ops_I5_J,axiom,
% 5.68/6.00 ! [A: nat,B: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_ops(5)
% 5.68/6.00 thf(fact_7018_int__plus,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_plus
% 5.68/6.00 thf(fact_7019_int__ops_I7_J,axiom,
% 5.68/6.00 ! [A: nat,B: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.68/6.00 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_ops(7)
% 5.68/6.00 thf(fact_7020_zle__iff__zadd,axiom,
% 5.68/6.00 ( ord_less_eq_int
% 5.68/6.00 = ( ^ [W3: int,Z2: int] :
% 5.68/6.00 ? [N2: nat] :
% 5.68/6.00 ( Z2
% 5.68/6.00 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zle_iff_zadd
% 5.68/6.00 thf(fact_7021_zdiv__int,axiom,
% 5.68/6.00 ! [A: nat,B: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.68/6.00 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zdiv_int
% 5.68/6.00 thf(fact_7022_of__nat__max,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y2 ) )
% 5.68/6.00 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_max
% 5.68/6.00 thf(fact_7023_of__nat__max,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y2 ) )
% 5.68/6.00 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_max
% 5.68/6.00 thf(fact_7024_of__nat__max,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y2 ) )
% 5.68/6.00 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_max
% 5.68/6.00 thf(fact_7025_of__nat__max,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y2 ) )
% 5.68/6.00 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_max
% 5.68/6.00 thf(fact_7026_of__nat__max,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y2 ) )
% 5.68/6.00 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_max
% 5.68/6.00 thf(fact_7027_semiring__norm_I28_J,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( bitM @ ( bit1 @ N ) )
% 5.68/6.00 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % semiring_norm(28)
% 5.68/6.00 thf(fact_7028_semiring__norm_I27_J,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( bitM @ ( bit0 @ N ) )
% 5.68/6.00 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % semiring_norm(27)
% 5.68/6.00 thf(fact_7029_nat__less__as__int,axiom,
% 5.68/6.00 ( ord_less_nat
% 5.68/6.00 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_less_as_int
% 5.68/6.00 thf(fact_7030_nat__leq__as__int,axiom,
% 5.68/6.00 ( ord_less_eq_nat
% 5.68/6.00 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_leq_as_int
% 5.68/6.00 thf(fact_7031_of__nat__diff,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_diff
% 5.68/6.00 thf(fact_7032_of__nat__diff,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_diff
% 5.68/6.00 thf(fact_7033_of__nat__diff,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_diff
% 5.68/6.00 thf(fact_7034_of__nat__diff,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.68/6.00 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_diff
% 5.68/6.00 thf(fact_7035_reals__Archimedean3,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.00 => ! [Y4: real] :
% 5.68/6.00 ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % reals_Archimedean3
% 5.68/6.00 thf(fact_7036_real__of__int__div4,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_int_div4
% 5.68/6.00 thf(fact_7037_int__cases4,axiom,
% 5.68/6.00 ! [M: int] :
% 5.68/6.00 ( ! [N3: nat] :
% 5.68/6.00 ( M
% 5.68/6.00 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.68/6.00 => ( M
% 5.68/6.00 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_cases4
% 5.68/6.00 thf(fact_7038_real__of__nat__div4,axiom,
% 5.68/6.00 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_div4
% 5.68/6.00 thf(fact_7039_int__zle__neg,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.68/6.00 = ( ( N = zero_zero_nat )
% 5.68/6.00 & ( M = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_zle_neg
% 5.68/6.00 thf(fact_7040_int__Suc,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_Suc
% 5.68/6.00 thf(fact_7041_int__ops_I4_J,axiom,
% 5.68/6.00 ! [A: nat] :
% 5.68/6.00 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.68/6.00 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_ops(4)
% 5.68/6.00 thf(fact_7042_zless__iff__Suc__zadd,axiom,
% 5.68/6.00 ( ord_less_int
% 5.68/6.00 = ( ^ [W3: int,Z2: int] :
% 5.68/6.00 ? [N2: nat] :
% 5.68/6.00 ( Z2
% 5.68/6.00 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zless_iff_Suc_zadd
% 5.68/6.00 thf(fact_7043_nonpos__int__cases,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( K
% 5.68/6.00 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nonpos_int_cases
% 5.68/6.00 thf(fact_7044_negative__zle__0,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.68/6.00
% 5.68/6.00 % negative_zle_0
% 5.68/6.00 thf(fact_7045_real__of__nat__div,axiom,
% 5.68/6.00 ! [D: nat,N: nat] :
% 5.68/6.00 ( ( dvd_dvd_nat @ D @ N )
% 5.68/6.00 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.68/6.00 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_div
% 5.68/6.00 thf(fact_7046_real__of__int__div,axiom,
% 5.68/6.00 ! [D: int,N: int] :
% 5.68/6.00 ( ( dvd_dvd_int @ D @ N )
% 5.68/6.00 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.68/6.00 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_int_div
% 5.68/6.00 thf(fact_7047_eval__nat__numeral_I2_J,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.68/6.00 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % eval_nat_numeral(2)
% 5.68/6.00 thf(fact_7048_BitM__plus__one,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.68/6.00 = ( bit0 @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % BitM_plus_one
% 5.68/6.00 thf(fact_7049_one__plus__BitM,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.68/6.00 = ( bit0 @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_plus_BitM
% 5.68/6.00 thf(fact_7050_of__int__nonneg,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_nonneg
% 5.68/6.00 thf(fact_7051_of__int__nonneg,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_nonneg
% 5.68/6.00 thf(fact_7052_of__int__nonneg,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_nonneg
% 5.68/6.00 thf(fact_7053_of__int__leD,axiom,
% 5.68/6.00 ! [N: int,X: code_integer] :
% 5.68/6.00 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_leD
% 5.68/6.00 thf(fact_7054_of__int__leD,axiom,
% 5.68/6.00 ! [N: int,X: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_leD
% 5.68/6.00 thf(fact_7055_of__int__leD,axiom,
% 5.68/6.00 ! [N: int,X: rat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_leD
% 5.68/6.00 thf(fact_7056_of__int__leD,axiom,
% 5.68/6.00 ! [N: int,X: int] :
% 5.68/6.00 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_leD
% 5.68/6.00 thf(fact_7057_of__int__pos,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_pos
% 5.68/6.00 thf(fact_7058_of__int__pos,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_pos
% 5.68/6.00 thf(fact_7059_of__int__pos,axiom,
% 5.68/6.00 ! [Z: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/6.00 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_pos
% 5.68/6.00 thf(fact_7060_of__int__lessD,axiom,
% 5.68/6.00 ! [N: int,X: code_integer] :
% 5.68/6.00 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_lessD
% 5.68/6.00 thf(fact_7061_of__int__lessD,axiom,
% 5.68/6.00 ! [N: int,X: real] :
% 5.68/6.00 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_lessD
% 5.68/6.00 thf(fact_7062_of__int__lessD,axiom,
% 5.68/6.00 ! [N: int,X: rat] :
% 5.68/6.00 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_lessD
% 5.68/6.00 thf(fact_7063_of__int__lessD,axiom,
% 5.68/6.00 ! [N: int,X: int] :
% 5.68/6.00 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.68/6.00 => ( ( N = zero_zero_int )
% 5.68/6.00 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_lessD
% 5.68/6.00 thf(fact_7064_mod__mult2__eq_H,axiom,
% 5.68/6.00 ! [A: code_integer,M: nat,N: nat] :
% 5.68/6.00 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.68/6.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mod_mult2_eq'
% 5.68/6.00 thf(fact_7065_mod__mult2__eq_H,axiom,
% 5.68/6.00 ! [A: int,M: nat,N: nat] :
% 5.68/6.00 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.00 = ( 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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mod_mult2_eq'
% 5.68/6.00 thf(fact_7066_mod__mult2__eq_H,axiom,
% 5.68/6.00 ! [A: nat,M: nat,N: nat] :
% 5.68/6.00 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.68/6.00 = ( 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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mod_mult2_eq'
% 5.68/6.00 thf(fact_7067_of__int__neg__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.00 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_neg_numeral
% 5.68/6.00 thf(fact_7068_of__int__neg__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_neg_numeral
% 5.68/6.00 thf(fact_7069_of__int__neg__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.00 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_neg_numeral
% 5.68/6.00 thf(fact_7070_of__int__neg__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.00 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_neg_numeral
% 5.68/6.00 thf(fact_7071_of__int__neg__numeral,axiom,
% 5.68/6.00 ! [K: num] :
% 5.68/6.00 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.00 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_int_neg_numeral
% 5.68/6.00 thf(fact_7072_field__char__0__class_Oof__nat__div,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.68/6.00 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % field_char_0_class.of_nat_div
% 5.68/6.00 thf(fact_7073_field__char__0__class_Oof__nat__div,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % field_char_0_class.of_nat_div
% 5.68/6.00 thf(fact_7074_field__char__0__class_Oof__nat__div,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.68/6.00 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % field_char_0_class.of_nat_div
% 5.68/6.00 thf(fact_7075_int__le__real__less,axiom,
% 5.68/6.00 ( ord_less_eq_int
% 5.68/6.00 = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_le_real_less
% 5.68/6.00 thf(fact_7076_int__less__real__le,axiom,
% 5.68/6.00 ( ord_less_int
% 5.68/6.00 = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_less_real_le
% 5.68/6.00 thf(fact_7077_pos__int__cases,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ K )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( ( K
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.68/6.00 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % pos_int_cases
% 5.68/6.00 thf(fact_7078_zero__less__imp__eq__int,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_int @ zero_zero_int @ K )
% 5.68/6.00 => ? [N3: nat] :
% 5.68/6.00 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.68/6.00 & ( K
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zero_less_imp_eq_int
% 5.68/6.00 thf(fact_7079_int__cases3,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( K != zero_zero_int )
% 5.68/6.00 => ( ! [N3: nat] :
% 5.68/6.00 ( ( K
% 5.68/6.00 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.68/6.00 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( ( K
% 5.68/6.00 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.68/6.00 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % int_cases3
% 5.68/6.00 thf(fact_7080_nat__less__real__le,axiom,
% 5.68/6.00 ( ord_less_nat
% 5.68/6.00 = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_less_real_le
% 5.68/6.00 thf(fact_7081_nat__le__real__less,axiom,
% 5.68/6.00 ( ord_less_eq_nat
% 5.68/6.00 = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_le_real_less
% 5.68/6.00 thf(fact_7082_zmult__zless__mono2__lemma,axiom,
% 5.68/6.00 ! [I2: int,J: int,K: nat] :
% 5.68/6.00 ( ( ord_less_int @ I2 @ J )
% 5.68/6.00 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.00 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zmult_zless_mono2_lemma
% 5.68/6.00 thf(fact_7083_not__zle__0__negative,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % not_zle_0_negative
% 5.68/6.00 thf(fact_7084_negative__zless__0,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.68/6.00
% 5.68/6.00 % negative_zless_0
% 5.68/6.00 thf(fact_7085_negD,axiom,
% 5.68/6.00 ! [X: int] :
% 5.68/6.00 ( ( ord_less_int @ X @ zero_zero_int )
% 5.68/6.00 => ? [N3: nat] :
% 5.68/6.00 ( X
% 5.68/6.00 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % negD
% 5.68/6.00 thf(fact_7086_real__of__int__div__aux,axiom,
% 5.68/6.00 ! [X: int,D: int] :
% 5.68/6.00 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.68/6.00 = ( 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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_int_div_aux
% 5.68/6.00 thf(fact_7087_real__of__nat__div__aux,axiom,
% 5.68/6.00 ! [X: nat,D: nat] :
% 5.68/6.00 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.68/6.00 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_div_aux
% 5.68/6.00 thf(fact_7088_numeral__BitM,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.68/6.00 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_BitM
% 5.68/6.00 thf(fact_7089_numeral__BitM,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.68/6.00 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_BitM
% 5.68/6.00 thf(fact_7090_numeral__BitM,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.68/6.00 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_BitM
% 5.68/6.00 thf(fact_7091_numeral__BitM,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.68/6.00 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.68/6.00
% 5.68/6.00 % numeral_BitM
% 5.68/6.00 thf(fact_7092_odd__numeral__BitM,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % odd_numeral_BitM
% 5.68/6.00 thf(fact_7093_odd__numeral__BitM,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % odd_numeral_BitM
% 5.68/6.00 thf(fact_7094_odd__numeral__BitM,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % odd_numeral_BitM
% 5.68/6.00 thf(fact_7095_of__nat__less__two__power,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_two_power
% 5.68/6.00 thf(fact_7096_of__nat__less__two__power,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_two_power
% 5.68/6.00 thf(fact_7097_of__nat__less__two__power,axiom,
% 5.68/6.00 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_less_two_power
% 5.68/6.00 thf(fact_7098_inverse__of__nat__le,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( N != zero_zero_nat )
% 5.68/6.00 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % inverse_of_nat_le
% 5.68/6.00 thf(fact_7099_inverse__of__nat__le,axiom,
% 5.68/6.00 ! [N: nat,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.00 => ( ( N != zero_zero_nat )
% 5.68/6.00 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % inverse_of_nat_le
% 5.68/6.00 thf(fact_7100_real__archimedian__rdiv__eq__0,axiom,
% 5.68/6.00 ! [X: real,C: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.68/6.00 => ( ! [M5: nat] :
% 5.68/6.00 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 5.68/6.00 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X ) @ C ) )
% 5.68/6.00 => ( X = zero_zero_real ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_archimedian_rdiv_eq_0
% 5.68/6.00 thf(fact_7101_real__of__int__div2,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_int_div2
% 5.68/6.00 thf(fact_7102_real__of__int__div3,axiom,
% 5.68/6.00 ! [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 ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_int_div3
% 5.68/6.00 thf(fact_7103_neg__int__cases,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( ord_less_int @ K @ zero_zero_int )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ( ( K
% 5.68/6.00 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.68/6.00 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % neg_int_cases
% 5.68/6.00 thf(fact_7104_zdiff__int__split,axiom,
% 5.68/6.00 ! [P: int > $o,X: nat,Y2: nat] :
% 5.68/6.00 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y2 ) ) )
% 5.68/6.00 = ( ( ( ord_less_eq_nat @ Y2 @ X )
% 5.68/6.00 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 5.68/6.00 & ( ( ord_less_nat @ X @ Y2 )
% 5.68/6.00 => ( P @ zero_zero_int ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % zdiff_int_split
% 5.68/6.00 thf(fact_7105_real__of__nat__div2,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_div2
% 5.68/6.00 thf(fact_7106_real__of__nat__div3,axiom,
% 5.68/6.00 ! [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 ) ).
% 5.68/6.00
% 5.68/6.00 % real_of_nat_div3
% 5.68/6.00 thf(fact_7107_ln__realpow,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.00 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.68/6.00 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % ln_realpow
% 5.68/6.00 thf(fact_7108_even__of__int__iff,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.68/6.00 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % even_of_int_iff
% 5.68/6.00 thf(fact_7109_even__of__int__iff,axiom,
% 5.68/6.00 ! [K: int] :
% 5.68/6.00 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.68/6.00 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % even_of_int_iff
% 5.68/6.00 thf(fact_7110_linear__plus__1__le__power,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.00 => ( 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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % linear_plus_1_le_power
% 5.68/6.00 thf(fact_7111_Bernoulli__inequality,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.00 => ( 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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Bernoulli_inequality
% 5.68/6.00 thf(fact_7112_divmod__step__nat__def,axiom,
% 5.68/6.00 ( unique5026877609467782581ep_nat
% 5.68/6.00 = ( ^ [L: num] :
% 5.68/6.00 ( produc2626176000494625587at_nat
% 5.68/6.00 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_step_nat_def
% 5.68/6.00 thf(fact_7113_divmod__step__int__def,axiom,
% 5.68/6.00 ( unique5024387138958732305ep_int
% 5.68/6.00 = ( ^ [L: num] :
% 5.68/6.00 ( produc4245557441103728435nt_int
% 5.68/6.00 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_step_int_def
% 5.68/6.00 thf(fact_7114_Bernoulli__inequality__even,axiom,
% 5.68/6.00 ! [N: nat,X: real] :
% 5.68/6.00 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.00 => ( 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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Bernoulli_inequality_even
% 5.68/6.00 thf(fact_7115_double__arith__series,axiom,
% 5.68/6.00 ! [A: complex,D: complex,N: nat] :
% 5.68/6.00 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.68/6.00 @ ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_arith_series
% 5.68/6.00 thf(fact_7116_double__arith__series,axiom,
% 5.68/6.00 ! [A: int,D: int,N: nat] :
% 5.68/6.00 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.68/6.00 @ ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_arith_series
% 5.68/6.00 thf(fact_7117_double__arith__series,axiom,
% 5.68/6.00 ! [A: rat,D: rat,N: nat] :
% 5.68/6.00 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.68/6.00 @ ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_arith_series
% 5.68/6.00 thf(fact_7118_double__arith__series,axiom,
% 5.68/6.00 ! [A: nat,D: nat,N: nat] :
% 5.68/6.00 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.68/6.00 @ ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_arith_series
% 5.68/6.00 thf(fact_7119_double__arith__series,axiom,
% 5.68/6.00 ! [A: real,D: real,N: nat] :
% 5.68/6.00 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_arith_series
% 5.68/6.00 thf(fact_7120_double__gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum
% 5.68/6.00 thf(fact_7121_double__gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum
% 5.68/6.00 thf(fact_7122_double__gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum
% 5.68/6.00 thf(fact_7123_double__gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum
% 5.68/6.00 thf(fact_7124_double__gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.00 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum
% 5.68/6.00 thf(fact_7125_divmod__step__def,axiom,
% 5.68/6.00 ( unique5026877609467782581ep_nat
% 5.68/6.00 = ( ^ [L: num] :
% 5.68/6.00 ( produc2626176000494625587at_nat
% 5.68/6.00 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_step_def
% 5.68/6.00 thf(fact_7126_divmod__step__def,axiom,
% 5.68/6.00 ( unique5024387138958732305ep_int
% 5.68/6.00 = ( ^ [L: num] :
% 5.68/6.00 ( produc4245557441103728435nt_int
% 5.68/6.00 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_step_def
% 5.68/6.00 thf(fact_7127_divmod__step__def,axiom,
% 5.68/6.00 ( unique4921790084139445826nteger
% 5.68/6.00 = ( ^ [L: num] :
% 5.68/6.00 ( produc6916734918728496179nteger
% 5.68/6.00 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_step_def
% 5.68/6.00 thf(fact_7128_arith__series,axiom,
% 5.68/6.00 ! [A: int,D: int,N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % arith_series
% 5.68/6.00 thf(fact_7129_arith__series,axiom,
% 5.68/6.00 ! [A: nat,D: nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.68/6.00 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % arith_series
% 5.68/6.00 thf(fact_7130_gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % gauss_sum
% 5.68/6.00 thf(fact_7131_gauss__sum,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.68/6.00 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % gauss_sum
% 5.68/6.00 thf(fact_7132_double__gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.68/6.00 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_7133_double__gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.68/6.00 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_7134_double__gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.68/6.00 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_7135_double__gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.68/6.00 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_7136_double__gauss__sum__from__Suc__0,axiom,
% 5.68/6.00 ! [N: nat] :
% 5.68/6.00 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.68/6.00 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % double_gauss_sum_from_Suc_0
% 5.68/6.00 thf(fact_7137_nat__approx__posE,axiom,
% 5.68/6.00 ! [E: real] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_approx_posE
% 5.68/6.00 thf(fact_7138_nat__approx__posE,axiom,
% 5.68/6.00 ! [E: rat] :
% 5.68/6.00 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.68/6.00 => ~ ! [N3: nat] :
% 5.68/6.00 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % nat_approx_posE
% 5.68/6.00 thf(fact_7139_floor__exists1,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [X3: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 5.68/6.00 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.68/6.00 & ! [Y4: int] :
% 5.68/6.00 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 5.68/6.00 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.68/6.00 => ( Y4 = X3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % floor_exists1
% 5.68/6.00 thf(fact_7140_floor__exists1,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [X3: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 5.68/6.00 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.68/6.00 & ! [Y4: int] :
% 5.68/6.00 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 5.68/6.00 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.68/6.00 => ( Y4 = X3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % floor_exists1
% 5.68/6.00 thf(fact_7141_floor__exists,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [Z3: int] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 5.68/6.00 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % floor_exists
% 5.68/6.00 thf(fact_7142_floor__exists,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [Z3: int] :
% 5.68/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 5.68/6.00 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % floor_exists
% 5.68/6.00 thf(fact_7143_monoseq__arctan__series,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.00 => ( topolo6980174941875973593q_real
% 5.68/6.00 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % monoseq_arctan_series
% 5.68/6.00 thf(fact_7144_lemma__termdiff3,axiom,
% 5.68/6.00 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.68/6.00 ( ( H2 != zero_zero_real )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( 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 @ H2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff3
% 5.68/6.00 thf(fact_7145_lemma__termdiff3,axiom,
% 5.68/6.00 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.68/6.00 ( ( H2 != zero_zero_complex )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( 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 @ H2 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff3
% 5.68/6.00 thf(fact_7146_ex__less__of__nat__mult,axiom,
% 5.68/6.00 ! [X: real,Y2: real] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.00 => ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_less_of_nat_mult
% 5.68/6.00 thf(fact_7147_ex__less__of__nat__mult,axiom,
% 5.68/6.00 ! [X: rat,Y2: rat] :
% 5.68/6.00 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.68/6.00 => ? [N3: nat] : ( ord_less_rat @ Y2 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_less_of_nat_mult
% 5.68/6.00 thf(fact_7148_case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc8763457246119570046nteger,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.68/6.00 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( C @ A3 @ B2 ) )
% 5.68/6.00 => ( produc127349428274296955eger_o @ C @ P4 ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2
% 5.68/6.00 thf(fact_7149_case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.68/6.00 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( C @ A3 @ B2 ) )
% 5.68/6.00 => ( produc6253627499356882019eger_o @ C @ P4 ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2
% 5.68/6.00 thf(fact_7150_case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.68/6.00 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 5.68/6.00 => ( C @ A3 @ B2 ) )
% 5.68/6.00 => ( produc1573362020775583542_int_o @ C @ P4 ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2
% 5.68/6.00 thf(fact_7151_case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.68/6.00 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.68/6.00 => ( C @ A3 @ B2 ) )
% 5.68/6.00 => ( produc2558449545302689196_int_o @ C @ P4 ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2
% 5.68/6.00 thf(fact_7152_case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,C: int > int > $o] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( C @ A3 @ B2 ) )
% 5.68/6.00 => ( produc4947309494688390418_int_o @ C @ P4 ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2
% 5.68/6.00 thf(fact_7153_case__prodI,axiom,
% 5.68/6.00 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( F @ A @ B )
% 5.68/6.00 => ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI
% 5.68/6.00 thf(fact_7154_case__prodI,axiom,
% 5.68/6.00 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( F @ A @ B )
% 5.68/6.00 => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI
% 5.68/6.00 thf(fact_7155_case__prodI,axiom,
% 5.68/6.00 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.68/6.00 ( ( F @ A @ B )
% 5.68/6.00 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI
% 5.68/6.00 thf(fact_7156_case__prodI,axiom,
% 5.68/6.00 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.68/6.00 ( ( F @ A @ B )
% 5.68/6.00 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI
% 5.68/6.00 thf(fact_7157_case__prodI,axiom,
% 5.68/6.00 ! [F: int > int > $o,A: int,B: int] :
% 5.68/6.00 ( ( F @ A @ B )
% 5.68/6.00 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI
% 5.68/6.00 thf(fact_7158_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,Z: nat,C: int > int > set_nat] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7159_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,Z: real,C: int > int > set_real] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7160_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,Z: int,C: int > int > set_int] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7161_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,Z: complex,C: int > int > set_complex] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member_complex @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7162_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: product_prod_int_int,Z: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat] :
% 5.68/6.00 ( ! [A3: int,B2: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member8440522571783428010at_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member8440522571783428010at_nat @ Z @ ( produc1656060378719767003at_nat @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7163_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc8763457246119570046nteger,Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 5.68/6.00 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7164_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc8763457246119570046nteger,Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real] :
% 5.68/6.00 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7165_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc8763457246119570046nteger,Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 5.68/6.00 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7166_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc8763457246119570046nteger,Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex] :
% 5.68/6.00 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.68/6.00 => ( member_complex @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7167_mem__case__prodI2,axiom,
% 5.68/6.00 ! [P4: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 5.68/6.00 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.68/6.00 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI2
% 5.68/6.00 thf(fact_7168_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: nat,C: int > int > set_nat,A: int,B: int] :
% 5.68/6.00 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7169_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: real,C: int > int > set_real,A: int,B: int] :
% 5.68/6.00 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7170_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: int,C: int > int > set_int,A: int,B: int] :
% 5.68/6.00 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7171_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: complex,C: int > int > set_complex,A: int,B: int] :
% 5.68/6.00 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7172_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat,A: int,B: int] :
% 5.68/6.00 ( ( member8440522571783428010at_nat @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member8440522571783428010at_nat @ Z @ ( produc1656060378719767003at_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7173_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7174_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7175_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7176_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7177_mem__case__prodI,axiom,
% 5.68/6.00 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.68/6.00 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.68/6.00 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodI
% 5.68/6.00 thf(fact_7178_case__prodI2_H,axiom,
% 5.68/6.00 ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.68/6.00 ( ! [A3: nat,B2: nat] :
% 5.68/6.00 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 5.68/6.00 = P4 )
% 5.68/6.00 => ( C @ A3 @ B2 @ X ) )
% 5.68/6.00 => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodI2'
% 5.68/6.00 thf(fact_7179_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: nat,C: int > int > set_nat,P4: product_prod_int_int] :
% 5.68/6.00 ( ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7180_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: real,C: int > int > set_real,P4: product_prod_int_int] :
% 5.68/6.00 ( ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7181_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: int,C: int > int > set_int,P4: product_prod_int_int] :
% 5.68/6.00 ( ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7182_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: complex,C: int > int > set_complex,P4: product_prod_int_int] :
% 5.68/6.00 ( ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7183_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: product_prod_nat_nat,C: int > int > set_Pr1261947904930325089at_nat,P4: product_prod_int_int] :
% 5.68/6.00 ( ( member8440522571783428010at_nat @ Z @ ( produc1656060378719767003at_nat @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member8440522571783428010at_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7184_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P4: produc8763457246119570046nteger] :
% 5.68/6.00 ( ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7185_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,P4: produc8763457246119570046nteger] :
% 5.68/6.00 ( ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7186_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P4: produc8763457246119570046nteger] :
% 5.68/6.00 ( ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7187_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,P4: produc8763457246119570046nteger] :
% 5.68/6.00 ( ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7188_mem__case__prodE,axiom,
% 5.68/6.00 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc7773217078559923341nt_int] :
% 5.68/6.00 ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) )
% 5.68/6.00 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % mem_case_prodE
% 5.68/6.00 thf(fact_7189_case__prodE,axiom,
% 5.68/6.00 ! [C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc8763457246119570046nteger] :
% 5.68/6.00 ( ( produc127349428274296955eger_o @ C @ P4 )
% 5.68/6.00 => ~ ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc6137756002093451184nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE
% 5.68/6.00 thf(fact_7190_case__prodE,axiom,
% 5.68/6.00 ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc1908205239877642774nteger] :
% 5.68/6.00 ( ( produc6253627499356882019eger_o @ C @ P4 )
% 5.68/6.00 => ~ ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc8603105652947943368nteger @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE
% 5.68/6.00 thf(fact_7191_case__prodE,axiom,
% 5.68/6.00 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc2285326912895808259nt_int] :
% 5.68/6.00 ( ( produc1573362020775583542_int_o @ C @ P4 )
% 5.68/6.00 => ~ ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE
% 5.68/6.00 thf(fact_7192_case__prodE,axiom,
% 5.68/6.00 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc7773217078559923341nt_int] :
% 5.68/6.00 ( ( produc2558449545302689196_int_o @ C @ P4 )
% 5.68/6.00 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE
% 5.68/6.00 thf(fact_7193_case__prodE,axiom,
% 5.68/6.00 ! [C: int > int > $o,P4: product_prod_int_int] :
% 5.68/6.00 ( ( produc4947309494688390418_int_o @ C @ P4 )
% 5.68/6.00 => ~ ! [X3: int,Y3: int] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE
% 5.68/6.00 thf(fact_7194_case__prodD,axiom,
% 5.68/6.00 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) )
% 5.68/6.00 => ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD
% 5.68/6.00 thf(fact_7195_case__prodD,axiom,
% 5.68/6.00 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.68/6.00 ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 5.68/6.00 => ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD
% 5.68/6.00 thf(fact_7196_case__prodD,axiom,
% 5.68/6.00 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.68/6.00 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 5.68/6.00 => ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD
% 5.68/6.00 thf(fact_7197_case__prodD,axiom,
% 5.68/6.00 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.68/6.00 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 5.68/6.00 => ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD
% 5.68/6.00 thf(fact_7198_case__prodD,axiom,
% 5.68/6.00 ! [F: int > int > $o,A: int,B: int] :
% 5.68/6.00 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.68/6.00 => ( F @ A @ B ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD
% 5.68/6.00 thf(fact_7199_case__prodE_H,axiom,
% 5.68/6.00 ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.68/6.00 ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 5.68/6.00 => ~ ! [X3: nat,Y3: nat] :
% 5.68/6.00 ( ( P4
% 5.68/6.00 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.68/6.00 => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodE'
% 5.68/6.00 thf(fact_7200_case__prodD_H,axiom,
% 5.68/6.00 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.68/6.00 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.68/6.00 => ( R @ A @ B @ C ) ) ).
% 5.68/6.00
% 5.68/6.00 % case_prodD'
% 5.68/6.00 thf(fact_7201_complex__mod__minus__le__complex__mod,axiom,
% 5.68/6.00 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % complex_mod_minus_le_complex_mod
% 5.68/6.00 thf(fact_7202_complex__mod__triangle__ineq2,axiom,
% 5.68/6.00 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.68/6.00
% 5.68/6.00 % complex_mod_triangle_ineq2
% 5.68/6.00 thf(fact_7203_Divides_Oadjust__div__def,axiom,
% 5.68/6.00 ( adjust_div
% 5.68/6.00 = ( produc8211389475949308722nt_int
% 5.68/6.00 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Divides.adjust_div_def
% 5.68/6.00 thf(fact_7204_monoseq__realpow,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.00 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.00 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % monoseq_realpow
% 5.68/6.00 thf(fact_7205_real__arch__simple,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_arch_simple
% 5.68/6.00 thf(fact_7206_real__arch__simple,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % real_arch_simple
% 5.68/6.00 thf(fact_7207_reals__Archimedean2,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % reals_Archimedean2
% 5.68/6.00 thf(fact_7208_reals__Archimedean2,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % reals_Archimedean2
% 5.68/6.00 thf(fact_7209_exists__least__lemma,axiom,
% 5.68/6.00 ! [P: nat > $o] :
% 5.68/6.00 ( ~ ( P @ zero_zero_nat )
% 5.68/6.00 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.68/6.00 => ? [N3: nat] :
% 5.68/6.00 ( ~ ( P @ N3 )
% 5.68/6.00 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % exists_least_lemma
% 5.68/6.00 thf(fact_7210_ex__le__of__int,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_le_of_int
% 5.68/6.00 thf(fact_7211_ex__le__of__int,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_le_of_int
% 5.68/6.00 thf(fact_7212_ex__less__of__int,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_less_of_int
% 5.68/6.00 thf(fact_7213_ex__less__of__int,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.68/6.00
% 5.68/6.00 % ex_less_of_int
% 5.68/6.00 thf(fact_7214_ex__of__int__less,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ).
% 5.68/6.00
% 5.68/6.00 % ex_of_int_less
% 5.68/6.00 thf(fact_7215_ex__of__int__less,axiom,
% 5.68/6.00 ! [X: rat] :
% 5.68/6.00 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ).
% 5.68/6.00
% 5.68/6.00 % ex_of_int_less
% 5.68/6.00 thf(fact_7216_norm__divide__numeral,axiom,
% 5.68/6.00 ! [A: real,W: num] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_divide_numeral
% 5.68/6.00 thf(fact_7217_norm__divide__numeral,axiom,
% 5.68/6.00 ! [A: complex,W: num] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_divide_numeral
% 5.68/6.00 thf(fact_7218_norm__mult__numeral1,axiom,
% 5.68/6.00 ! [W: num,A: real] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.68/6.00 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_numeral1
% 5.68/6.00 thf(fact_7219_norm__mult__numeral1,axiom,
% 5.68/6.00 ! [W: num,A: complex] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.68/6.00 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_numeral1
% 5.68/6.00 thf(fact_7220_norm__mult__numeral2,axiom,
% 5.68/6.00 ! [A: real,W: num] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.68/6.00 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_numeral2
% 5.68/6.00 thf(fact_7221_norm__mult__numeral2,axiom,
% 5.68/6.00 ! [A: complex,W: num] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.00 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_numeral2
% 5.68/6.00 thf(fact_7222_norm__neg__numeral,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/6.00 = ( numeral_numeral_real @ W ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_neg_numeral
% 5.68/6.00 thf(fact_7223_norm__neg__numeral,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.00 = ( numeral_numeral_real @ W ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_neg_numeral
% 5.68/6.00 thf(fact_7224_norm__le__zero__iff,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.68/6.00 = ( X = zero_zero_real ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_le_zero_iff
% 5.68/6.00 thf(fact_7225_norm__le__zero__iff,axiom,
% 5.68/6.00 ! [X: complex] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.68/6.00 = ( X = zero_zero_complex ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_le_zero_iff
% 5.68/6.00 thf(fact_7226_norm__numeral,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.68/6.00 = ( numeral_numeral_real @ W ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_numeral
% 5.68/6.00 thf(fact_7227_norm__numeral,axiom,
% 5.68/6.00 ! [W: num] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.68/6.00 = ( numeral_numeral_real @ W ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_numeral
% 5.68/6.00 thf(fact_7228_Collect__case__prod__mono,axiom,
% 5.68/6.00 ! [A2: int > int > $o,B4: int > int > $o] :
% 5.68/6.00 ( ( ord_le6741204236512500942_int_o @ A2 @ B4 )
% 5.68/6.00 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B4 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % Collect_case_prod_mono
% 5.68/6.00 thf(fact_7229_norm__ge__zero,axiom,
% 5.68/6.00 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_ge_zero
% 5.68/6.00 thf(fact_7230_norm__mult,axiom,
% 5.68/6.00 ! [X: real,Y2: real] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) )
% 5.68/6.00 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult
% 5.68/6.00 thf(fact_7231_norm__mult,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) )
% 5.68/6.00 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult
% 5.68/6.00 thf(fact_7232_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_real,F: real > complex,G: real > real] :
% 5.68/6.00 ( ! [X3: real] :
% 5.68/6.00 ( ( member_real @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S3 ) ) @ ( groups8097168146408367636l_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7233_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_int,F: int > complex,G: int > real] :
% 5.68/6.00 ( ! [X3: int] :
% 5.68/6.00 ( ( member_int @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S3 ) ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7234_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 5.68/6.00 ( ! [X3: product_prod_nat_nat] :
% 5.68/6.00 ( ( member8440522571783428010at_nat @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S3 ) ) @ ( groups4567486121110086003t_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7235_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_nat,F: nat > complex,G: nat > real] :
% 5.68/6.00 ( ! [X3: nat] :
% 5.68/6.00 ( ( member_nat @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7236_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_complex,F: complex > complex,G: complex > real] :
% 5.68/6.00 ( ! [X3: complex] :
% 5.68/6.00 ( ( member_complex @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S3 ) ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7237_sum__norm__le,axiom,
% 5.68/6.00 ! [S3: set_nat,F: nat > real,G: nat > real] :
% 5.68/6.00 ( ! [X3: nat] :
% 5.68/6.00 ( ( member_nat @ X3 @ S3 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_norm_le
% 5.68/6.00 thf(fact_7238_norm__divide,axiom,
% 5.68/6.00 ! [A: real,B: real] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_divide
% 5.68/6.00 thf(fact_7239_norm__divide,axiom,
% 5.68/6.00 ! [A: complex,B: complex] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_divide
% 5.68/6.00 thf(fact_7240_norm__power,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 5.68/6.00 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power
% 5.68/6.00 thf(fact_7241_norm__power,axiom,
% 5.68/6.00 ! [X: complex,N: nat] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 5.68/6.00 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power
% 5.68/6.00 thf(fact_7242_norm__sum,axiom,
% 5.68/6.00 ! [F: nat > complex,A2: set_nat] :
% 5.68/6.00 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.68/6.00 @ A2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_sum
% 5.68/6.00 thf(fact_7243_norm__sum,axiom,
% 5.68/6.00 ! [F: complex > complex,A2: set_complex] :
% 5.68/6.00 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.68/6.00 @ ( groups5808333547571424918x_real
% 5.68/6.00 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.68/6.00 @ A2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_sum
% 5.68/6.00 thf(fact_7244_norm__sum,axiom,
% 5.68/6.00 ! [F: nat > real,A2: set_nat] :
% 5.68/6.00 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 5.68/6.00 @ A2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_sum
% 5.68/6.00 thf(fact_7245_norm__uminus__minus,axiom,
% 5.68/6.00 ! [X: real,Y2: real] :
% 5.68/6.00 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y2 ) )
% 5.68/6.00 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_uminus_minus
% 5.68/6.00 thf(fact_7246_norm__uminus__minus,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex] :
% 5.68/6.00 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y2 ) )
% 5.68/6.00 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_uminus_minus
% 5.68/6.00 thf(fact_7247_nonzero__norm__divide,axiom,
% 5.68/6.00 ! [B: real,A: real] :
% 5.68/6.00 ( ( B != zero_zero_real )
% 5.68/6.00 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nonzero_norm_divide
% 5.68/6.00 thf(fact_7248_nonzero__norm__divide,axiom,
% 5.68/6.00 ! [B: complex,A: complex] :
% 5.68/6.00 ( ( B != zero_zero_complex )
% 5.68/6.00 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/6.00 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % nonzero_norm_divide
% 5.68/6.00 thf(fact_7249_power__eq__imp__eq__norm,axiom,
% 5.68/6.00 ! [W: real,N: nat,Z: real] :
% 5.68/6.00 ( ( ( power_power_real @ W @ N )
% 5.68/6.00 = ( power_power_real @ Z @ N ) )
% 5.68/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.00 => ( ( real_V7735802525324610683m_real @ W )
% 5.68/6.00 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_eq_imp_eq_norm
% 5.68/6.00 thf(fact_7250_power__eq__imp__eq__norm,axiom,
% 5.68/6.00 ! [W: complex,N: nat,Z: complex] :
% 5.68/6.00 ( ( ( power_power_complex @ W @ N )
% 5.68/6.00 = ( power_power_complex @ Z @ N ) )
% 5.68/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.00 => ( ( real_V1022390504157884413omplex @ W )
% 5.68/6.00 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_eq_imp_eq_norm
% 5.68/6.00 thf(fact_7251_norm__mult__less,axiom,
% 5.68/6.00 ! [X: real,R2: real,Y2: real,S2: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S2 )
% 5.68/6.00 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_less
% 5.68/6.00 thf(fact_7252_norm__mult__less,axiom,
% 5.68/6.00 ! [X: complex,R2: real,Y2: complex,S2: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S2 )
% 5.68/6.00 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_less
% 5.68/6.00 thf(fact_7253_norm__mult__ineq,axiom,
% 5.68/6.00 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y2 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_ineq
% 5.68/6.00 thf(fact_7254_norm__mult__ineq,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y2 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_mult_ineq
% 5.68/6.00 thf(fact_7255_norm__add__less,axiom,
% 5.68/6.00 ! [X: real,R2: real,Y2: real,S2: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y2 ) @ S2 )
% 5.68/6.00 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_add_less
% 5.68/6.00 thf(fact_7256_norm__add__less,axiom,
% 5.68/6.00 ! [X: complex,R2: real,Y2: complex,S2: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y2 ) @ S2 )
% 5.68/6.00 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_add_less
% 5.68/6.00 thf(fact_7257_norm__triangle__lt,axiom,
% 5.68/6.00 ! [X: real,Y2: real,E: real] :
% 5.68/6.00 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_lt
% 5.68/6.00 thf(fact_7258_norm__triangle__lt,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex,E: real] :
% 5.68/6.00 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_lt
% 5.68/6.00 thf(fact_7259_norm__power__ineq,axiom,
% 5.68/6.00 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power_ineq
% 5.68/6.00 thf(fact_7260_norm__power__ineq,axiom,
% 5.68/6.00 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power_ineq
% 5.68/6.00 thf(fact_7261_norm__add__leD,axiom,
% 5.68/6.00 ! [A: real,B: real,C: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_add_leD
% 5.68/6.00 thf(fact_7262_norm__add__leD,axiom,
% 5.68/6.00 ! [A: complex,B: complex,C: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_add_leD
% 5.68/6.00 thf(fact_7263_norm__triangle__le,axiom,
% 5.68/6.00 ! [X: real,Y2: real,E: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_le
% 5.68/6.00 thf(fact_7264_norm__triangle__le,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex,E: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_le
% 5.68/6.00 thf(fact_7265_norm__triangle__ineq,axiom,
% 5.68/6.00 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq
% 5.68/6.00 thf(fact_7266_norm__triangle__ineq,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq
% 5.68/6.00 thf(fact_7267_norm__triangle__mono,axiom,
% 5.68/6.00 ! [A: real,R2: real,B: real,S2: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_mono
% 5.68/6.00 thf(fact_7268_norm__triangle__mono,axiom,
% 5.68/6.00 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_mono
% 5.68/6.00 thf(fact_7269_norm__diff__triangle__less,axiom,
% 5.68/6.00 ! [X: real,Y2: real,E1: real,Z: real,E22: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y2 ) ) @ E1 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y2 @ Z ) ) @ E22 )
% 5.68/6.00 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_less
% 5.68/6.00 thf(fact_7270_norm__diff__triangle__less,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 5.68/6.00 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 5.68/6.00 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 5.68/6.00 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_less
% 5.68/6.00 thf(fact_7271_norm__triangle__sub,axiom,
% 5.68/6.00 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_sub
% 5.68/6.00 thf(fact_7272_norm__triangle__sub,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_sub
% 5.68/6.00 thf(fact_7273_norm__triangle__ineq4,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq4
% 5.68/6.00 thf(fact_7274_norm__triangle__ineq4,axiom,
% 5.68/6.00 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq4
% 5.68/6.00 thf(fact_7275_norm__diff__triangle__le,axiom,
% 5.68/6.00 ! [X: real,Y2: real,E1: real,Z: real,E22: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y2 ) ) @ E1 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y2 @ Z ) ) @ E22 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_le
% 5.68/6.00 thf(fact_7276_norm__diff__triangle__le,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex,E1: real,Z: complex,E22: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E1 )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y2 @ Z ) ) @ E22 )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_le
% 5.68/6.00 thf(fact_7277_norm__triangle__le__diff,axiom,
% 5.68/6.00 ! [X: real,Y2: real,E: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_le_diff
% 5.68/6.00 thf(fact_7278_norm__triangle__le__diff,axiom,
% 5.68/6.00 ! [X: complex,Y2: complex,E: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) ) @ E )
% 5.68/6.00 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y2 ) ) @ E ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_le_diff
% 5.68/6.00 thf(fact_7279_norm__diff__ineq,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_ineq
% 5.68/6.00 thf(fact_7280_norm__diff__ineq,axiom,
% 5.68/6.00 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_ineq
% 5.68/6.00 thf(fact_7281_norm__triangle__ineq2,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq2
% 5.68/6.00 thf(fact_7282_norm__triangle__ineq2,axiom,
% 5.68/6.00 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq2
% 5.68/6.00 thf(fact_7283_power__eq__1__iff,axiom,
% 5.68/6.00 ! [W: real,N: nat] :
% 5.68/6.00 ( ( ( power_power_real @ W @ N )
% 5.68/6.00 = one_one_real )
% 5.68/6.00 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.68/6.00 = one_one_real )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_eq_1_iff
% 5.68/6.00 thf(fact_7284_power__eq__1__iff,axiom,
% 5.68/6.00 ! [W: complex,N: nat] :
% 5.68/6.00 ( ( ( power_power_complex @ W @ N )
% 5.68/6.00 = one_one_complex )
% 5.68/6.00 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.68/6.00 = one_one_real )
% 5.68/6.00 | ( N = zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_eq_1_iff
% 5.68/6.00 thf(fact_7285_norm__diff__triangle__ineq,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_ineq
% 5.68/6.00 thf(fact_7286_norm__diff__triangle__ineq,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_diff_triangle_ineq
% 5.68/6.00 thf(fact_7287_norm__triangle__ineq3,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq3
% 5.68/6.00 thf(fact_7288_norm__triangle__ineq3,axiom,
% 5.68/6.00 ! [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 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_triangle_ineq3
% 5.68/6.00 thf(fact_7289_square__norm__one,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.00 = one_one_real )
% 5.68/6.00 => ( ( real_V7735802525324610683m_real @ X )
% 5.68/6.00 = one_one_real ) ) ).
% 5.68/6.00
% 5.68/6.00 % square_norm_one
% 5.68/6.00 thf(fact_7290_square__norm__one,axiom,
% 5.68/6.00 ! [X: complex] :
% 5.68/6.00 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.00 = one_one_complex )
% 5.68/6.00 => ( ( real_V1022390504157884413omplex @ X )
% 5.68/6.00 = one_one_real ) ) ).
% 5.68/6.00
% 5.68/6.00 % square_norm_one
% 5.68/6.00 thf(fact_7291_norm__power__diff,axiom,
% 5.68/6.00 ! [Z: real,W: real,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.68/6.00 => ( 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 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power_diff
% 5.68/6.00 thf(fact_7292_norm__power__diff,axiom,
% 5.68/6.00 ! [Z: complex,W: complex,M: nat] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.68/6.00 => ( 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 ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % norm_power_diff
% 5.68/6.00 thf(fact_7293_ln__series,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.00 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.00 => ( ( ln_ln_real @ X )
% 5.68/6.00 = ( suminf_real
% 5.68/6.00 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % ln_series
% 5.68/6.00 thf(fact_7294_of__nat__code__if,axiom,
% 5.68/6.00 ( semiri8010041392384452111omplex
% 5.68/6.00 = ( ^ [N2: nat] :
% 5.68/6.00 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.68/6.00 @ ( produc1917071388513777916omplex
% 5.68/6.00 @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 5.68/6.00 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_code_if
% 5.68/6.00 thf(fact_7295_of__nat__code__if,axiom,
% 5.68/6.00 ( semiri1314217659103216013at_int
% 5.68/6.00 = ( ^ [N2: nat] :
% 5.68/6.00 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.68/6.00 @ ( produc6840382203811409530at_int
% 5.68/6.00 @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 5.68/6.00 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_code_if
% 5.68/6.00 thf(fact_7296_of__nat__code__if,axiom,
% 5.68/6.00 ( semiri5074537144036343181t_real
% 5.68/6.00 = ( ^ [N2: nat] :
% 5.68/6.00 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.68/6.00 @ ( produc1703576794950452218t_real
% 5.68/6.00 @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 5.68/6.00 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_code_if
% 5.68/6.00 thf(fact_7297_of__nat__code__if,axiom,
% 5.68/6.00 ( semiri1316708129612266289at_nat
% 5.68/6.00 = ( ^ [N2: nat] :
% 5.68/6.00 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.68/6.00 @ ( produc6842872674320459806at_nat
% 5.68/6.00 @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 5.68/6.00 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_code_if
% 5.68/6.00 thf(fact_7298_of__nat__code__if,axiom,
% 5.68/6.00 ( semiri681578069525770553at_rat
% 5.68/6.00 = ( ^ [N2: nat] :
% 5.68/6.00 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.68/6.00 @ ( produc6207742614233964070at_rat
% 5.68/6.00 @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 5.68/6.00 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % of_nat_code_if
% 5.68/6.00 thf(fact_7299_divmod__nat__if,axiom,
% 5.68/6.00 ( divmod_nat
% 5.68/6.00 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.00 ( if_Pro6206227464963214023at_nat
% 5.68/6.00 @ ( ( N2 = zero_zero_nat )
% 5.68/6.00 | ( ord_less_nat @ M6 @ N2 ) )
% 5.68/6.00 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.68/6.00 @ ( produc2626176000494625587at_nat
% 5.68/6.00 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.68/6.00 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % divmod_nat_if
% 5.68/6.00 thf(fact_7300_arctan__series,axiom,
% 5.68/6.00 ! [X: real] :
% 5.68/6.00 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.00 => ( ( arctan @ X )
% 5.68/6.00 = ( suminf_real
% 5.68/6.00 @ ^ [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 ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % arctan_series
% 5.68/6.00 thf(fact_7301_round__unique,axiom,
% 5.68/6.00 ! [X: real,Y2: int] :
% 5.68/6.00 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y2 ) )
% 5.68/6.00 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 => ( ( archim8280529875227126926d_real @ X )
% 5.68/6.00 = Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_unique
% 5.68/6.00 thf(fact_7302_round__unique,axiom,
% 5.68/6.00 ! [X: rat,Y2: int] :
% 5.68/6.00 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y2 ) )
% 5.68/6.00 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.00 => ( ( archim7778729529865785530nd_rat @ X )
% 5.68/6.00 = Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_unique
% 5.68/6.00 thf(fact_7303_lemma__termdiff2,axiom,
% 5.68/6.00 ! [H2: complex,Z: complex,N: nat] :
% 5.68/6.00 ( ( H2 != zero_zero_complex )
% 5.68/6.00 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.00 = ( times_times_complex @ H2
% 5.68/6.00 @ ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [P5: nat] :
% 5.68/6.00 ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff2
% 5.68/6.00 thf(fact_7304_lemma__termdiff2,axiom,
% 5.68/6.00 ! [H2: rat,Z: rat,N: nat] :
% 5.68/6.00 ( ( H2 != zero_zero_rat )
% 5.68/6.00 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.00 = ( times_times_rat @ H2
% 5.68/6.00 @ ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [P5: nat] :
% 5.68/6.00 ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff2
% 5.68/6.00 thf(fact_7305_lemma__termdiff2,axiom,
% 5.68/6.00 ! [H2: real,Z: real,N: nat] :
% 5.68/6.00 ( ( H2 != zero_zero_real )
% 5.68/6.00 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.00 = ( times_times_real @ H2
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [P5: nat] :
% 5.68/6.00 ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff2
% 5.68/6.00 thf(fact_7306_lessThan__iff,axiom,
% 5.68/6.00 ! [I2: rat,K: rat] :
% 5.68/6.00 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.68/6.00 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_iff
% 5.68/6.00 thf(fact_7307_lessThan__iff,axiom,
% 5.68/6.00 ! [I2: num,K: num] :
% 5.68/6.00 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.68/6.00 = ( ord_less_num @ I2 @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_iff
% 5.68/6.00 thf(fact_7308_lessThan__iff,axiom,
% 5.68/6.00 ! [I2: nat,K: nat] :
% 5.68/6.00 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.68/6.00 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_iff
% 5.68/6.00 thf(fact_7309_lessThan__iff,axiom,
% 5.68/6.00 ! [I2: int,K: int] :
% 5.68/6.00 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.68/6.00 = ( ord_less_int @ I2 @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_iff
% 5.68/6.00 thf(fact_7310_lessThan__iff,axiom,
% 5.68/6.00 ! [I2: real,K: real] :
% 5.68/6.00 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.68/6.00 = ( ord_less_real @ I2 @ K ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_iff
% 5.68/6.00 thf(fact_7311_lessThan__subset__iff,axiom,
% 5.68/6.00 ! [X: rat,Y2: rat] :
% 5.68/6.00 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y2 ) )
% 5.68/6.00 = ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_subset_iff
% 5.68/6.00 thf(fact_7312_lessThan__subset__iff,axiom,
% 5.68/6.00 ! [X: num,Y2: num] :
% 5.68/6.00 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y2 ) )
% 5.68/6.00 = ( ord_less_eq_num @ X @ Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_subset_iff
% 5.68/6.00 thf(fact_7313_lessThan__subset__iff,axiom,
% 5.68/6.00 ! [X: nat,Y2: nat] :
% 5.68/6.00 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y2 ) )
% 5.68/6.00 = ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_subset_iff
% 5.68/6.00 thf(fact_7314_lessThan__subset__iff,axiom,
% 5.68/6.00 ! [X: int,Y2: int] :
% 5.68/6.00 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y2 ) )
% 5.68/6.00 = ( ord_less_eq_int @ X @ Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_subset_iff
% 5.68/6.00 thf(fact_7315_lessThan__subset__iff,axiom,
% 5.68/6.00 ! [X: real,Y2: real] :
% 5.68/6.00 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y2 ) )
% 5.68/6.00 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_subset_iff
% 5.68/6.00 thf(fact_7316_round__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_numeral
% 5.68/6.00 thf(fact_7317_round__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.68/6.00 = ( numeral_numeral_int @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_numeral
% 5.68/6.00 thf(fact_7318_sum_OlessThan__Suc,axiom,
% 5.68/6.00 ! [G: nat > rat,N: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc
% 5.68/6.00 thf(fact_7319_sum_OlessThan__Suc,axiom,
% 5.68/6.00 ! [G: nat > int,N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc
% 5.68/6.00 thf(fact_7320_sum_OlessThan__Suc,axiom,
% 5.68/6.00 ! [G: nat > nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc
% 5.68/6.00 thf(fact_7321_sum_OlessThan__Suc,axiom,
% 5.68/6.00 ! [G: nat > real,N: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc
% 5.68/6.00 thf(fact_7322_round__neg__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_neg_numeral
% 5.68/6.00 thf(fact_7323_round__neg__numeral,axiom,
% 5.68/6.00 ! [N: num] :
% 5.68/6.00 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.68/6.00 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_neg_numeral
% 5.68/6.00 thf(fact_7324_powser__zero,axiom,
% 5.68/6.00 ! [F: nat > complex] :
% 5.68/6.00 ( ( suminf_complex
% 5.68/6.00 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.68/6.00 = ( F @ zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % powser_zero
% 5.68/6.00 thf(fact_7325_powser__zero,axiom,
% 5.68/6.00 ! [F: nat > real] :
% 5.68/6.00 ( ( suminf_real
% 5.68/6.00 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.68/6.00 = ( F @ zero_zero_nat ) ) ).
% 5.68/6.00
% 5.68/6.00 % powser_zero
% 5.68/6.00 thf(fact_7326_lessThan__def,axiom,
% 5.68/6.00 ( set_ord_lessThan_rat
% 5.68/6.00 = ( ^ [U2: rat] :
% 5.68/6.00 ( collect_rat
% 5.68/6.00 @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_def
% 5.68/6.00 thf(fact_7327_lessThan__def,axiom,
% 5.68/6.00 ( set_ord_lessThan_num
% 5.68/6.00 = ( ^ [U2: num] :
% 5.68/6.00 ( collect_num
% 5.68/6.00 @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_def
% 5.68/6.00 thf(fact_7328_lessThan__def,axiom,
% 5.68/6.00 ( set_ord_lessThan_nat
% 5.68/6.00 = ( ^ [U2: nat] :
% 5.68/6.00 ( collect_nat
% 5.68/6.00 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_def
% 5.68/6.00 thf(fact_7329_lessThan__def,axiom,
% 5.68/6.00 ( set_ord_lessThan_int
% 5.68/6.00 = ( ^ [U2: int] :
% 5.68/6.00 ( collect_int
% 5.68/6.00 @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_def
% 5.68/6.00 thf(fact_7330_lessThan__def,axiom,
% 5.68/6.00 ( set_or5984915006950818249n_real
% 5.68/6.00 = ( ^ [U2: real] :
% 5.68/6.00 ( collect_real
% 5.68/6.00 @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_def
% 5.68/6.00 thf(fact_7331_lessThan__strict__subset__iff,axiom,
% 5.68/6.00 ! [M: rat,N: rat] :
% 5.68/6.00 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.68/6.00 = ( ord_less_rat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_strict_subset_iff
% 5.68/6.00 thf(fact_7332_lessThan__strict__subset__iff,axiom,
% 5.68/6.00 ! [M: num,N: num] :
% 5.68/6.00 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.68/6.00 = ( ord_less_num @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_strict_subset_iff
% 5.68/6.00 thf(fact_7333_lessThan__strict__subset__iff,axiom,
% 5.68/6.00 ! [M: nat,N: nat] :
% 5.68/6.00 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_strict_subset_iff
% 5.68/6.00 thf(fact_7334_lessThan__strict__subset__iff,axiom,
% 5.68/6.00 ! [M: int,N: int] :
% 5.68/6.00 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.68/6.00 = ( ord_less_int @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_strict_subset_iff
% 5.68/6.00 thf(fact_7335_lessThan__strict__subset__iff,axiom,
% 5.68/6.00 ! [M: real,N: real] :
% 5.68/6.00 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.68/6.00 = ( ord_less_real @ M @ N ) ) ).
% 5.68/6.00
% 5.68/6.00 % lessThan_strict_subset_iff
% 5.68/6.00 thf(fact_7336_finite__nat__bounded,axiom,
% 5.68/6.00 ! [S3: set_nat] :
% 5.68/6.00 ( ( finite_finite_nat @ S3 )
% 5.68/6.00 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % finite_nat_bounded
% 5.68/6.00 thf(fact_7337_finite__nat__iff__bounded,axiom,
% 5.68/6.00 ( finite_finite_nat
% 5.68/6.00 = ( ^ [S4: set_nat] :
% 5.68/6.00 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % finite_nat_iff_bounded
% 5.68/6.00 thf(fact_7338_round__mono,axiom,
% 5.68/6.00 ! [X: rat,Y2: rat] :
% 5.68/6.00 ( ( ord_less_eq_rat @ X @ Y2 )
% 5.68/6.00 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y2 ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_mono
% 5.68/6.00 thf(fact_7339_sum_Onat__diff__reindex,axiom,
% 5.68/6.00 ! [G: nat > nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.nat_diff_reindex
% 5.68/6.00 thf(fact_7340_sum_Onat__diff__reindex,axiom,
% 5.68/6.00 ! [G: nat > real,N: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.nat_diff_reindex
% 5.68/6.00 thf(fact_7341_sum__diff__distrib,axiom,
% 5.68/6.00 ! [Q: int > nat,P: int > nat,N: int] :
% 5.68/6.00 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.68/6.00 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 5.68/6.00 = ( groups4541462559716669496nt_nat
% 5.68/6.00 @ ^ [X2: int] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.68/6.00 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_diff_distrib
% 5.68/6.00 thf(fact_7342_sum__diff__distrib,axiom,
% 5.68/6.00 ! [Q: real > nat,P: real > nat,N: real] :
% 5.68/6.00 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.68/6.00 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.68/6.00 = ( groups1935376822645274424al_nat
% 5.68/6.00 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.68/6.00 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_diff_distrib
% 5.68/6.00 thf(fact_7343_sum__diff__distrib,axiom,
% 5.68/6.00 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.68/6.00 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.68/6.00 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.68/6.00 = ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_diff_distrib
% 5.68/6.00 thf(fact_7344_sum_OlessThan__Suc__shift,axiom,
% 5.68/6.00 ! [G: nat > rat,N: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.68/6.00 @ ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc_shift
% 5.68/6.00 thf(fact_7345_sum_OlessThan__Suc__shift,axiom,
% 5.68/6.00 ! [G: nat > int,N: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.68/6.00 @ ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc_shift
% 5.68/6.00 thf(fact_7346_sum_OlessThan__Suc__shift,axiom,
% 5.68/6.00 ! [G: nat > nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.68/6.00 @ ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc_shift
% 5.68/6.00 thf(fact_7347_sum_OlessThan__Suc__shift,axiom,
% 5.68/6.00 ! [G: nat > real,N: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.00 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.lessThan_Suc_shift
% 5.68/6.00 thf(fact_7348_sumr__diff__mult__const2,axiom,
% 5.68/6.00 ! [F: nat > int,N: nat,R2: int] :
% 5.68/6.00 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 5.68/6.00 = ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ R2 )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sumr_diff_mult_const2
% 5.68/6.00 thf(fact_7349_sumr__diff__mult__const2,axiom,
% 5.68/6.00 ! [F: nat > rat,N: nat,R2: rat] :
% 5.68/6.00 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 5.68/6.00 = ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ R2 )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sumr_diff_mult_const2
% 5.68/6.00 thf(fact_7350_sumr__diff__mult__const2,axiom,
% 5.68/6.00 ! [F: nat > real,N: nat,R2: real] :
% 5.68/6.00 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 5.68/6.00 = ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ R2 )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sumr_diff_mult_const2
% 5.68/6.00 thf(fact_7351_sum__lessThan__telescope,axiom,
% 5.68/6.00 ! [F: nat > rat,M: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope
% 5.68/6.00 thf(fact_7352_sum__lessThan__telescope,axiom,
% 5.68/6.00 ! [F: nat > int,M: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope
% 5.68/6.00 thf(fact_7353_sum__lessThan__telescope,axiom,
% 5.68/6.00 ! [F: nat > real,M: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope
% 5.68/6.00 thf(fact_7354_sum__lessThan__telescope_H,axiom,
% 5.68/6.00 ! [F: nat > rat,M: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope'
% 5.68/6.00 thf(fact_7355_sum__lessThan__telescope_H,axiom,
% 5.68/6.00 ! [F: nat > int,M: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope'
% 5.68/6.00 thf(fact_7356_sum__lessThan__telescope_H,axiom,
% 5.68/6.00 ! [F: nat > real,M: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_lessThan_telescope'
% 5.68/6.00 thf(fact_7357_sum_OatLeast1__atMost__eq,axiom,
% 5.68/6.00 ! [G: nat > nat,N: nat] :
% 5.68/6.00 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.00 = ( groups3542108847815614940at_nat
% 5.68/6.00 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.atLeast1_atMost_eq
% 5.68/6.00 thf(fact_7358_sum_OatLeast1__atMost__eq,axiom,
% 5.68/6.00 ! [G: nat > real,N: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.00 = ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum.atLeast1_atMost_eq
% 5.68/6.00 thf(fact_7359_power__diff__1__eq,axiom,
% 5.68/6.00 ! [X: complex,N: nat] :
% 5.68/6.00 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 5.68/6.00 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_1_eq
% 5.68/6.00 thf(fact_7360_power__diff__1__eq,axiom,
% 5.68/6.00 ! [X: rat,N: nat] :
% 5.68/6.00 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 5.68/6.00 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_1_eq
% 5.68/6.00 thf(fact_7361_power__diff__1__eq,axiom,
% 5.68/6.00 ! [X: int,N: nat] :
% 5.68/6.00 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 5.68/6.00 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_1_eq
% 5.68/6.00 thf(fact_7362_power__diff__1__eq,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 5.68/6.00 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_1_eq
% 5.68/6.00 thf(fact_7363_one__diff__power__eq,axiom,
% 5.68/6.00 ! [X: complex,N: nat] :
% 5.68/6.00 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.68/6.00 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_diff_power_eq
% 5.68/6.00 thf(fact_7364_one__diff__power__eq,axiom,
% 5.68/6.00 ! [X: rat,N: nat] :
% 5.68/6.00 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.68/6.00 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_diff_power_eq
% 5.68/6.00 thf(fact_7365_one__diff__power__eq,axiom,
% 5.68/6.00 ! [X: int,N: nat] :
% 5.68/6.00 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.68/6.00 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_diff_power_eq
% 5.68/6.00 thf(fact_7366_one__diff__power__eq,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.68/6.00 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % one_diff_power_eq
% 5.68/6.00 thf(fact_7367_geometric__sum,axiom,
% 5.68/6.00 ! [X: complex,N: nat] :
% 5.68/6.00 ( ( X != one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % geometric_sum
% 5.68/6.00 thf(fact_7368_geometric__sum,axiom,
% 5.68/6.00 ! [X: rat,N: nat] :
% 5.68/6.00 ( ( X != one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % geometric_sum
% 5.68/6.00 thf(fact_7369_geometric__sum,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( X != one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % geometric_sum
% 5.68/6.00 thf(fact_7370_round__diff__minimal,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_diff_minimal
% 5.68/6.00 thf(fact_7371_round__diff__minimal,axiom,
% 5.68/6.00 ! [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 ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % round_diff_minimal
% 5.68/6.00 thf(fact_7372_sum__gp__strict,axiom,
% 5.68/6.00 ! [X: complex,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.68/6.00 & ( ( X != one_one_complex )
% 5.68/6.00 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_strict
% 5.68/6.00 thf(fact_7373_sum__gp__strict,axiom,
% 5.68/6.00 ! [X: rat,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.68/6.00 & ( ( X != one_one_rat )
% 5.68/6.00 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_strict
% 5.68/6.00 thf(fact_7374_sum__gp__strict,axiom,
% 5.68/6.00 ! [X: real,N: nat] :
% 5.68/6.00 ( ( ( X = one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.00 & ( ( X != one_one_real )
% 5.68/6.00 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.00 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % sum_gp_strict
% 5.68/6.00 thf(fact_7375_lemma__termdiff1,axiom,
% 5.68/6.00 ! [Z: complex,H2: complex,M: nat] :
% 5.68/6.00 ( ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff1
% 5.68/6.00 thf(fact_7376_lemma__termdiff1,axiom,
% 5.68/6.00 ! [Z: rat,H2: rat,M: nat] :
% 5.68/6.00 ( ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff1
% 5.68/6.00 thf(fact_7377_lemma__termdiff1,axiom,
% 5.68/6.00 ! [Z: int,H2: int,M: nat] :
% 5.68/6.00 ( ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff1
% 5.68/6.00 thf(fact_7378_lemma__termdiff1,axiom,
% 5.68/6.00 ! [Z: real,H2: real,M: nat] :
% 5.68/6.00 ( ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) )
% 5.68/6.00 = ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % lemma_termdiff1
% 5.68/6.00 thf(fact_7379_power__diff__sumr2,axiom,
% 5.68/6.00 ! [X: complex,N: nat,Y2: complex] :
% 5.68/6.00 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y2 @ N ) )
% 5.68/6.00 = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 5.68/6.00 @ ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_sumr2
% 5.68/6.00 thf(fact_7380_power__diff__sumr2,axiom,
% 5.68/6.00 ! [X: rat,N: nat,Y2: rat] :
% 5.68/6.00 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y2 @ N ) )
% 5.68/6.00 = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 5.68/6.00 @ ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_sumr2
% 5.68/6.00 thf(fact_7381_power__diff__sumr2,axiom,
% 5.68/6.00 ! [X: int,N: nat,Y2: int] :
% 5.68/6.00 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y2 @ N ) )
% 5.68/6.00 = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 5.68/6.00 @ ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_sumr2
% 5.68/6.00 thf(fact_7382_power__diff__sumr2,axiom,
% 5.68/6.00 ! [X: real,N: nat,Y2: real] :
% 5.68/6.00 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) )
% 5.68/6.00 = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % power_diff_sumr2
% 5.68/6.00 thf(fact_7383_diff__power__eq__sum,axiom,
% 5.68/6.00 ! [X: complex,N: nat,Y2: complex] :
% 5.68/6.00 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y2 @ ( suc @ N ) ) )
% 5.68/6.00 = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 5.68/6.00 @ ( groups2073611262835488442omplex
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % diff_power_eq_sum
% 5.68/6.00 thf(fact_7384_diff__power__eq__sum,axiom,
% 5.68/6.00 ! [X: rat,N: nat,Y2: rat] :
% 5.68/6.00 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y2 @ ( suc @ N ) ) )
% 5.68/6.00 = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 5.68/6.00 @ ( groups2906978787729119204at_rat
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % diff_power_eq_sum
% 5.68/6.00 thf(fact_7385_diff__power__eq__sum,axiom,
% 5.68/6.00 ! [X: int,N: nat,Y2: int] :
% 5.68/6.00 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y2 @ ( suc @ N ) ) )
% 5.68/6.00 = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 5.68/6.00 @ ( groups3539618377306564664at_int
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % diff_power_eq_sum
% 5.68/6.00 thf(fact_7386_diff__power__eq__sum,axiom,
% 5.68/6.00 ! [X: real,N: nat,Y2: real] :
% 5.68/6.00 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y2 @ ( suc @ N ) ) )
% 5.68/6.00 = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 5.68/6.00 @ ( groups6591440286371151544t_real
% 5.68/6.00 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.68/6.00 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.68/6.00
% 5.68/6.00 % diff_power_eq_sum
% 5.68/6.00 thf(fact_7387_real__sum__nat__ivl__bounded2,axiom,
% 5.68/6.01 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.68/6.01 ( ! [P7: nat] :
% 5.68/6.01 ( ( ord_less_nat @ P7 @ N )
% 5.68/6.01 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.68/6.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.68/6.01 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sum_nat_ivl_bounded2
% 5.68/6.01 thf(fact_7388_real__sum__nat__ivl__bounded2,axiom,
% 5.68/6.01 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.68/6.01 ( ! [P7: nat] :
% 5.68/6.01 ( ( ord_less_nat @ P7 @ N )
% 5.68/6.01 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.68/6.01 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.68/6.01 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sum_nat_ivl_bounded2
% 5.68/6.01 thf(fact_7389_real__sum__nat__ivl__bounded2,axiom,
% 5.68/6.01 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.68/6.01 ( ! [P7: nat] :
% 5.68/6.01 ( ( ord_less_nat @ P7 @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.68/6.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.68/6.01 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sum_nat_ivl_bounded2
% 5.68/6.01 thf(fact_7390_real__sum__nat__ivl__bounded2,axiom,
% 5.68/6.01 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.68/6.01 ( ! [P7: nat] :
% 5.68/6.01 ( ( ord_less_nat @ P7 @ N )
% 5.68/6.01 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.68/6.01 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sum_nat_ivl_bounded2
% 5.68/6.01 thf(fact_7391_divmod__nat__def,axiom,
% 5.68/6.01 ( divmod_nat
% 5.68/6.01 = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % divmod_nat_def
% 5.68/6.01 thf(fact_7392_one__diff__power__eq_H,axiom,
% 5.68/6.01 ! [X: complex,N: nat] :
% 5.68/6.01 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.68/6.01 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.68/6.01 @ ( groups2073611262835488442omplex
% 5.68/6.01 @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % one_diff_power_eq'
% 5.68/6.01 thf(fact_7393_one__diff__power__eq_H,axiom,
% 5.68/6.01 ! [X: rat,N: nat] :
% 5.68/6.01 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.68/6.01 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.68/6.01 @ ( groups2906978787729119204at_rat
% 5.68/6.01 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % one_diff_power_eq'
% 5.68/6.01 thf(fact_7394_one__diff__power__eq_H,axiom,
% 5.68/6.01 ! [X: int,N: nat] :
% 5.68/6.01 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.68/6.01 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.68/6.01 @ ( groups3539618377306564664at_int
% 5.68/6.01 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % one_diff_power_eq'
% 5.68/6.01 thf(fact_7395_one__diff__power__eq_H,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.68/6.01 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % one_diff_power_eq'
% 5.68/6.01 thf(fact_7396_sum__split__even__odd,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real,N: nat] :
% 5.68/6.01 ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_split_even_odd
% 5.68/6.01 thf(fact_7397_of__int__round__le,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_le
% 5.68/6.01 thf(fact_7398_of__int__round__le,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_le
% 5.68/6.01 thf(fact_7399_of__int__round__ge,axiom,
% 5.68/6.01 ! [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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_ge
% 5.68/6.01 thf(fact_7400_of__int__round__ge,axiom,
% 5.68/6.01 ! [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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_ge
% 5.68/6.01 thf(fact_7401_of__int__round__gt,axiom,
% 5.68/6.01 ! [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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_gt
% 5.68/6.01 thf(fact_7402_of__int__round__gt,axiom,
% 5.68/6.01 ! [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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_gt
% 5.68/6.01 thf(fact_7403_of__int__round__abs__le,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_abs_le
% 5.68/6.01 thf(fact_7404_of__int__round__abs__le,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % of_int_round_abs_le
% 5.68/6.01 thf(fact_7405_round__unique_H,axiom,
% 5.68/6.01 ! [X: real,N: int] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 => ( ( archim8280529875227126926d_real @ X )
% 5.68/6.01 = N ) ) ).
% 5.68/6.01
% 5.68/6.01 % round_unique'
% 5.68/6.01 thf(fact_7406_round__unique_H,axiom,
% 5.68/6.01 ! [X: rat,N: int] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 => ( ( archim7778729529865785530nd_rat @ X )
% 5.68/6.01 = N ) ) ).
% 5.68/6.01
% 5.68/6.01 % round_unique'
% 5.68/6.01 thf(fact_7407_suminf__geometric,axiom,
% 5.68/6.01 ! [C: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.68/6.01 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_geometric
% 5.68/6.01 thf(fact_7408_suminf__geometric,axiom,
% 5.68/6.01 ! [C: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.68/6.01 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_geometric
% 5.68/6.01 thf(fact_7409_sum__bounds__lt__plus1,axiom,
% 5.68/6.01 ! [F: nat > nat,Mm: nat] :
% 5.68/6.01 ( ( groups3542108847815614940at_nat
% 5.68/6.01 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.68/6.01 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_bounds_lt_plus1
% 5.68/6.01 thf(fact_7410_sum__bounds__lt__plus1,axiom,
% 5.68/6.01 ! [F: nat > real,Mm: nat] :
% 5.68/6.01 ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.68/6.01 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_bounds_lt_plus1
% 5.68/6.01 thf(fact_7411_pi__series,axiom,
% 5.68/6.01 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = ( suminf_real
% 5.68/6.01 @ ^ [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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_series
% 5.68/6.01 thf(fact_7412_sumr__cos__zero__one,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sumr_cos_zero_one
% 5.68/6.01 thf(fact_7413_summable__arctan__series,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_arctan_series
% 5.68/6.01 thf(fact_7414_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.68/6.01 ( ( ord_le2646555220125990790_nat_o
% 5.68/6.01 @ ^ [X2: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le3146513528884898305at_nat @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7415_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.68/6.01 ( ( ord_le6741204236512500942_int_o
% 5.68/6.01 @ ^ [X2: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le2843351958646193337nt_int @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7416_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr8056137968301705908nteger,S3: set_Pr8056137968301705908nteger] :
% 5.68/6.01 ( ( ord_le3636971675376928563eger_o
% 5.68/6.01 @ ^ [X2: code_integer > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: code_integer > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le3216752416896350996nteger @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7417_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1281608226676607948nteger,S3: set_Pr1281608226676607948nteger] :
% 5.68/6.01 ( ( ord_le4340812435750786203eger_o
% 5.68/6.01 @ ^ [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le653643898420964396nteger @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7418_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr9222295170931077689nt_int,S3: set_Pr9222295170931077689nt_int] :
% 5.68/6.01 ( ( ord_le5643404153117327598_int_o
% 5.68/6.01 @ ^ [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le8725513860283290265nt_int @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7419_pred__subset__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1872883991513573699nt_int,S3: set_Pr1872883991513573699nt_int] :
% 5.68/6.01 ( ( ord_le2124322318746777828_int_o
% 5.68/6.01 @ ^ [X2: int > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y ) @ R )
% 5.68/6.01 @ ^ [X2: int > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y ) @ S3 ) )
% 5.68/6.01 = ( ord_le135402666524580259nt_int @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq2
% 5.68/6.01 thf(fact_7420_summable__iff__shift,axiom,
% 5.68/6.01 ! [F: nat > real,K: nat] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.68/6.01 = ( summable_real @ F ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_iff_shift
% 5.68/6.01 thf(fact_7421_summable__cmult__iff,axiom,
% 5.68/6.01 ! [C: complex,F: nat > complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.68/6.01 = ( ( C = zero_zero_complex )
% 5.68/6.01 | ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_cmult_iff
% 5.68/6.01 thf(fact_7422_summable__cmult__iff,axiom,
% 5.68/6.01 ! [C: real,F: nat > real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.68/6.01 = ( ( C = zero_zero_real )
% 5.68/6.01 | ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_cmult_iff
% 5.68/6.01 thf(fact_7423_summable__divide__iff,axiom,
% 5.68/6.01 ! [F: nat > complex,C: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.68/6.01 = ( ( C = zero_zero_complex )
% 5.68/6.01 | ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_divide_iff
% 5.68/6.01 thf(fact_7424_summable__divide__iff,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.68/6.01 = ( ( C = zero_zero_real )
% 5.68/6.01 | ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_divide_iff
% 5.68/6.01 thf(fact_7425_summable__geometric__iff,axiom,
% 5.68/6.01 ! [C: real] :
% 5.68/6.01 ( ( summable_real @ ( power_power_real @ C ) )
% 5.68/6.01 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_geometric_iff
% 5.68/6.01 thf(fact_7426_summable__geometric__iff,axiom,
% 5.68/6.01 ! [C: complex] :
% 5.68/6.01 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.68/6.01 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_geometric_iff
% 5.68/6.01 thf(fact_7427_summable__comparison__test_H,axiom,
% 5.68/6.01 ! [G: nat > real,N5: nat,F: nat > real] :
% 5.68/6.01 ( ( summable_real @ G )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_comparison_test'
% 5.68/6.01 thf(fact_7428_summable__comparison__test_H,axiom,
% 5.68/6.01 ! [G: nat > real,N5: nat,F: nat > complex] :
% 5.68/6.01 ( ( summable_real @ G )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_comparison_test'
% 5.68/6.01 thf(fact_7429_summable__comparison__test,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real] :
% 5.68/6.01 ( ? [N8: nat] :
% 5.68/6.01 ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_comparison_test
% 5.68/6.01 thf(fact_7430_summable__comparison__test,axiom,
% 5.68/6.01 ! [F: nat > complex,G: nat > real] :
% 5.68/6.01 ( ? [N8: nat] :
% 5.68/6.01 ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_comparison_test
% 5.68/6.01 thf(fact_7431_summable__mult2,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_mult2
% 5.68/6.01 thf(fact_7432_summable__mult,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_mult
% 5.68/6.01 thf(fact_7433_summable__divide,axiom,
% 5.68/6.01 ! [F: nat > complex,C: complex] :
% 5.68/6.01 ( ( summable_complex @ F )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_divide
% 5.68/6.01 thf(fact_7434_summable__divide,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_divide
% 5.68/6.01 thf(fact_7435_summable__Suc__iff,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.68/6.01 = ( summable_real @ F ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_Suc_iff
% 5.68/6.01 thf(fact_7436_summable__ignore__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > real,K: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_ignore_initial_segment
% 5.68/6.01 thf(fact_7437_summable__add,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_add
% 5.68/6.01 thf(fact_7438_summable__add,axiom,
% 5.68/6.01 ! [F: nat > nat,G: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ( summable_nat @ G )
% 5.68/6.01 => ( summable_nat
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_add
% 5.68/6.01 thf(fact_7439_summable__add,axiom,
% 5.68/6.01 ! [F: nat > int,G: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ( summable_int @ G )
% 5.68/6.01 => ( summable_int
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_add
% 5.68/6.01 thf(fact_7440_suminf__le,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( summable_real @ F )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le
% 5.68/6.01 thf(fact_7441_suminf__le,axiom,
% 5.68/6.01 ! [F: nat > nat,G: nat > nat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( summable_nat @ F )
% 5.68/6.01 => ( ( summable_nat @ G )
% 5.68/6.01 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le
% 5.68/6.01 thf(fact_7442_suminf__le,axiom,
% 5.68/6.01 ! [F: nat > int,G: nat > int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( summable_int @ F )
% 5.68/6.01 => ( ( summable_int @ G )
% 5.68/6.01 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le
% 5.68/6.01 thf(fact_7443_summable__mult__D,axiom,
% 5.68/6.01 ! [C: complex,F: nat > complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.68/6.01 => ( ( C != zero_zero_complex )
% 5.68/6.01 => ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_mult_D
% 5.68/6.01 thf(fact_7444_summable__mult__D,axiom,
% 5.68/6.01 ! [C: real,F: nat > real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.68/6.01 => ( ( C != zero_zero_real )
% 5.68/6.01 => ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_mult_D
% 5.68/6.01 thf(fact_7445_summable__zero__power,axiom,
% 5.68/6.01 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power
% 5.68/6.01 thf(fact_7446_summable__zero__power,axiom,
% 5.68/6.01 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power
% 5.68/6.01 thf(fact_7447_summable__zero__power,axiom,
% 5.68/6.01 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power
% 5.68/6.01 thf(fact_7448_suminf__mult,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.68/6.01 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_mult
% 5.68/6.01 thf(fact_7449_suminf__mult2,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.68/6.01 = ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_mult2
% 5.68/6.01 thf(fact_7450_suminf__add,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.68/6.01 = ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_add
% 5.68/6.01 thf(fact_7451_suminf__add,axiom,
% 5.68/6.01 ! [F: nat > nat,G: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ( summable_nat @ G )
% 5.68/6.01 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.68/6.01 = ( suminf_nat
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_add
% 5.68/6.01 thf(fact_7452_suminf__add,axiom,
% 5.68/6.01 ! [F: nat > int,G: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ( summable_int @ G )
% 5.68/6.01 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.68/6.01 = ( suminf_int
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_add
% 5.68/6.01 thf(fact_7453_suminf__divide,axiom,
% 5.68/6.01 ! [F: nat > complex,C: complex] :
% 5.68/6.01 ( ( summable_complex @ F )
% 5.68/6.01 => ( ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_divide
% 5.68/6.01 thf(fact_7454_suminf__divide,axiom,
% 5.68/6.01 ! [F: nat > real,C: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.68/6.01 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_divide
% 5.68/6.01 thf(fact_7455_powser__insidea,axiom,
% 5.68/6.01 ! [F: nat > real,X: real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_insidea
% 5.68/6.01 thf(fact_7456_powser__insidea,axiom,
% 5.68/6.01 ! [F: nat > complex,X: complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_insidea
% 5.68/6.01 thf(fact_7457_suminf__nonneg,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_nonneg
% 5.68/6.01 thf(fact_7458_suminf__nonneg,axiom,
% 5.68/6.01 ! [F: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_nonneg
% 5.68/6.01 thf(fact_7459_suminf__nonneg,axiom,
% 5.68/6.01 ! [F: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_nonneg
% 5.68/6.01 thf(fact_7460_suminf__eq__zero__iff,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ( suminf_real @ F )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ! [N2: nat] :
% 5.68/6.01 ( ( F @ N2 )
% 5.68/6.01 = zero_zero_real ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_eq_zero_iff
% 5.68/6.01 thf(fact_7461_suminf__eq__zero__iff,axiom,
% 5.68/6.01 ! [F: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ( suminf_nat @ F )
% 5.68/6.01 = zero_zero_nat )
% 5.68/6.01 = ( ! [N2: nat] :
% 5.68/6.01 ( ( F @ N2 )
% 5.68/6.01 = zero_zero_nat ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_eq_zero_iff
% 5.68/6.01 thf(fact_7462_suminf__eq__zero__iff,axiom,
% 5.68/6.01 ! [F: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ( suminf_int @ F )
% 5.68/6.01 = zero_zero_int )
% 5.68/6.01 = ( ! [N2: nat] :
% 5.68/6.01 ( ( F @ N2 )
% 5.68/6.01 = zero_zero_int ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_eq_zero_iff
% 5.68/6.01 thf(fact_7463_suminf__pos,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos
% 5.68/6.01 thf(fact_7464_suminf__pos,axiom,
% 5.68/6.01 ! [F: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos
% 5.68/6.01 thf(fact_7465_suminf__pos,axiom,
% 5.68/6.01 ! [F: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos
% 5.68/6.01 thf(fact_7466_summable__zero__power_H,axiom,
% 5.68/6.01 ! [F: nat > complex] :
% 5.68/6.01 ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power'
% 5.68/6.01 thf(fact_7467_summable__zero__power_H,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power'
% 5.68/6.01 thf(fact_7468_summable__zero__power_H,axiom,
% 5.68/6.01 ! [F: nat > int] :
% 5.68/6.01 ( summable_int
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_zero_power'
% 5.68/6.01 thf(fact_7469_summable__0__powser,axiom,
% 5.68/6.01 ! [F: nat > complex] :
% 5.68/6.01 ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_0_powser
% 5.68/6.01 thf(fact_7470_summable__0__powser,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_0_powser
% 5.68/6.01 thf(fact_7471_powser__split__head_I3_J,axiom,
% 5.68/6.01 ! [F: nat > complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(3)
% 5.68/6.01 thf(fact_7472_powser__split__head_I3_J,axiom,
% 5.68/6.01 ! [F: nat > real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(3)
% 5.68/6.01 thf(fact_7473_summable__powser__split__head,axiom,
% 5.68/6.01 ! [F: nat > complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 = ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_powser_split_head
% 5.68/6.01 thf(fact_7474_summable__powser__split__head,axiom,
% 5.68/6.01 ! [F: nat > real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 = ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_powser_split_head
% 5.68/6.01 thf(fact_7475_summable__powser__ignore__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > complex,M: nat,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 = ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_powser_ignore_initial_segment
% 5.68/6.01 thf(fact_7476_summable__powser__ignore__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > real,M: nat,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 = ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_powser_ignore_initial_segment
% 5.68/6.01 thf(fact_7477_pi__ge__zero,axiom,
% 5.68/6.01 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.68/6.01
% 5.68/6.01 % pi_ge_zero
% 5.68/6.01 thf(fact_7478_summable__norm__comparison__test,axiom,
% 5.68/6.01 ! [F: nat > complex,G: nat > real] :
% 5.68/6.01 ( ? [N8: nat] :
% 5.68/6.01 ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_norm_comparison_test
% 5.68/6.01 thf(fact_7479_summable__rabs__comparison__test,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real] :
% 5.68/6.01 ( ? [N8: nat] :
% 5.68/6.01 ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.68/6.01 => ( ( summable_real @ G )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_rabs_comparison_test
% 5.68/6.01 thf(fact_7480_summable__rabs,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_rabs
% 5.68/6.01 thf(fact_7481_suminf__pos2,axiom,
% 5.68/6.01 ! [F: nat > real,I2: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos2
% 5.68/6.01 thf(fact_7482_suminf__pos2,axiom,
% 5.68/6.01 ! [F: nat > nat,I2: nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos2
% 5.68/6.01 thf(fact_7483_suminf__pos2,axiom,
% 5.68/6.01 ! [F: nat > int,I2: nat] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos2
% 5.68/6.01 thf(fact_7484_suminf__pos__iff,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.68/6.01 = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos_iff
% 5.68/6.01 thf(fact_7485_suminf__pos__iff,axiom,
% 5.68/6.01 ! [F: nat > nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.68/6.01 = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos_iff
% 5.68/6.01 thf(fact_7486_suminf__pos__iff,axiom,
% 5.68/6.01 ! [F: nat > int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.68/6.01 = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_pos_iff
% 5.68/6.01 thf(fact_7487_suminf__le__const,axiom,
% 5.68/6.01 ! [F: nat > int,X: int] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le_const
% 5.68/6.01 thf(fact_7488_suminf__le__const,axiom,
% 5.68/6.01 ! [F: nat > nat,X: nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le_const
% 5.68/6.01 thf(fact_7489_suminf__le__const,axiom,
% 5.68/6.01 ! [F: nat > real,X: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_le_const
% 5.68/6.01 thf(fact_7490_summableI__nonneg__bounded,axiom,
% 5.68/6.01 ! [F: nat > int,X: int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( summable_int @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summableI_nonneg_bounded
% 5.68/6.01 thf(fact_7491_summableI__nonneg__bounded,axiom,
% 5.68/6.01 ! [F: nat > nat,X: nat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( summable_nat @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summableI_nonneg_bounded
% 5.68/6.01 thf(fact_7492_summableI__nonneg__bounded,axiom,
% 5.68/6.01 ! [F: nat > real,X: real] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.68/6.01 => ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summableI_nonneg_bounded
% 5.68/6.01 thf(fact_7493_summable__geometric,axiom,
% 5.68/6.01 ! [C: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.68/6.01 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_geometric
% 5.68/6.01 thf(fact_7494_summable__geometric,axiom,
% 5.68/6.01 ! [C: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.68/6.01 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_geometric
% 5.68/6.01 thf(fact_7495_complete__algebra__summable__geometric,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.68/6.01 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complete_algebra_summable_geometric
% 5.68/6.01 thf(fact_7496_complete__algebra__summable__geometric,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.68/6.01 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complete_algebra_summable_geometric
% 5.68/6.01 thf(fact_7497_suminf__split__head,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.68/6.01 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_split_head
% 5.68/6.01 thf(fact_7498_summable__norm,axiom,
% 5.68/6.01 ! [F: nat > real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_norm
% 5.68/6.01 thf(fact_7499_summable__norm,axiom,
% 5.68/6.01 ! [F: nat > complex] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_norm
% 5.68/6.01 thf(fact_7500_sum__le__suminf,axiom,
% 5.68/6.01 ! [F: nat > int,I5: set_nat] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ( finite_finite_nat @ I5 )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.68/6.01 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.68/6.01 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_le_suminf
% 5.68/6.01 thf(fact_7501_sum__le__suminf,axiom,
% 5.68/6.01 ! [F: nat > nat,I5: set_nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ( finite_finite_nat @ I5 )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.68/6.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.68/6.01 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_le_suminf
% 5.68/6.01 thf(fact_7502_sum__le__suminf,axiom,
% 5.68/6.01 ! [F: nat > real,I5: set_nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( finite_finite_nat @ I5 )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_le_suminf
% 5.68/6.01 thf(fact_7503_suminf__split__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > real,K: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( suminf_real @ F )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.68/6.01 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_split_initial_segment
% 5.68/6.01 thf(fact_7504_suminf__minus__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > real,K: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.68/6.01 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_minus_initial_segment
% 5.68/6.01 thf(fact_7505_powser__inside,axiom,
% 5.68/6.01 ! [F: nat > real,X: real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_inside
% 5.68/6.01 thf(fact_7506_powser__inside,axiom,
% 5.68/6.01 ! [F: nat > complex,X: complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_inside
% 5.68/6.01 thf(fact_7507_sum__less__suminf,axiom,
% 5.68/6.01 ! [F: nat > int,N: nat] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf
% 5.68/6.01 thf(fact_7508_sum__less__suminf,axiom,
% 5.68/6.01 ! [F: nat > nat,N: nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf
% 5.68/6.01 thf(fact_7509_sum__less__suminf,axiom,
% 5.68/6.01 ! [F: nat > real,N: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf
% 5.68/6.01 thf(fact_7510_pi__less__4,axiom,
% 5.68/6.01 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_less_4
% 5.68/6.01 thf(fact_7511_pi__ge__two,axiom,
% 5.68/6.01 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.68/6.01
% 5.68/6.01 % pi_ge_two
% 5.68/6.01 thf(fact_7512_pi__half__neq__two,axiom,
% 5.68/6.01 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_neq_two
% 5.68/6.01 thf(fact_7513_powser__split__head_I1_J,axiom,
% 5.68/6.01 ! [F: nat > complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 => ( ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.68/6.01 @ ( times_times_complex
% 5.68/6.01 @ ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 @ Z ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(1)
% 5.68/6.01 thf(fact_7514_powser__split__head_I1_J,axiom,
% 5.68/6.01 ! [F: nat > real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 => ( ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.68/6.01 @ ( times_times_real
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 @ Z ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(1)
% 5.68/6.01 thf(fact_7515_powser__split__head_I2_J,axiom,
% 5.68/6.01 ! [F: nat > complex,Z: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 => ( ( times_times_complex
% 5.68/6.01 @ ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 @ Z )
% 5.68/6.01 = ( minus_minus_complex
% 5.68/6.01 @ ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.68/6.01 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(2)
% 5.68/6.01 thf(fact_7516_powser__split__head_I2_J,axiom,
% 5.68/6.01 ! [F: nat > real,Z: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 => ( ( times_times_real
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 @ Z )
% 5.68/6.01 = ( minus_minus_real
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.68/6.01 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_split_head(2)
% 5.68/6.01 thf(fact_7517_summable__partial__sum__bound,axiom,
% 5.68/6.01 ! [F: nat > complex,E: real] :
% 5.68/6.01 ( ( summable_complex @ F )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.01 => ~ ! [N9: nat] :
% 5.68/6.01 ~ ! [M2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.68/6.01 => ! [N7: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_partial_sum_bound
% 5.68/6.01 thf(fact_7518_summable__partial__sum__bound,axiom,
% 5.68/6.01 ! [F: nat > real,E: real] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.01 => ~ ! [N9: nat] :
% 5.68/6.01 ~ ! [M2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N9 @ M2 )
% 5.68/6.01 => ! [N7: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_partial_sum_bound
% 5.68/6.01 thf(fact_7519_suminf__exist__split,axiom,
% 5.68/6.01 ! [R2: real,F: nat > real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.68/6.01 => ( ( summable_real @ F )
% 5.68/6.01 => ? [N9: nat] :
% 5.68/6.01 ! [N7: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.68/6.01 => ( ord_less_real
% 5.68/6.01 @ ( real_V7735802525324610683m_real
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N7 ) ) ) )
% 5.68/6.01 @ R2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_exist_split
% 5.68/6.01 thf(fact_7520_suminf__exist__split,axiom,
% 5.68/6.01 ! [R2: real,F: nat > complex] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.68/6.01 => ( ( summable_complex @ F )
% 5.68/6.01 => ? [N9: nat] :
% 5.68/6.01 ! [N7: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.68/6.01 => ( ord_less_real
% 5.68/6.01 @ ( real_V1022390504157884413omplex
% 5.68/6.01 @ ( suminf_complex
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N7 ) ) ) )
% 5.68/6.01 @ R2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % suminf_exist_split
% 5.68/6.01 thf(fact_7521_summable__power__series,axiom,
% 5.68/6.01 ! [F: nat > real,Z: real] :
% 5.68/6.01 ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 5.68/6.01 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.68/6.01 => ( ( ord_less_real @ Z @ one_one_real )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_power_series
% 5.68/6.01 thf(fact_7522_Abel__lemma,axiom,
% 5.68/6.01 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.68/6.01 => ( ( ord_less_real @ R2 @ R0 )
% 5.68/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R2 @ N2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Abel_lemma
% 5.68/6.01 thf(fact_7523_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.68/6.01 ( ( ( ^ [X2: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7524_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.68/6.01 ( ( ( ^ [X2: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7525_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr8056137968301705908nteger,S3: set_Pr8056137968301705908nteger] :
% 5.68/6.01 ( ( ( ^ [X2: code_integer > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: code_integer > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7526_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1281608226676607948nteger,S3: set_Pr1281608226676607948nteger] :
% 5.68/6.01 ( ( ( ^ [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7527_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr9222295170931077689nt_int,S3: set_Pr9222295170931077689nt_int] :
% 5.68/6.01 ( ( ( ^ [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7528_pred__equals__eq2,axiom,
% 5.68/6.01 ! [R: set_Pr1872883991513573699nt_int,S3: set_Pr1872883991513573699nt_int] :
% 5.68/6.01 ( ( ( ^ [X2: int > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y ) @ R ) )
% 5.68/6.01 = ( ^ [X2: int > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y ) @ S3 ) ) )
% 5.68/6.01 = ( R = S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_equals_eq2
% 5.68/6.01 thf(fact_7529_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bot_nat_nat_o
% 5.68/6.01 = ( ^ [X2: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7530_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bot_int_int_o
% 5.68/6.01 = ( ^ [X2: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7531_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bo5358457235160185703eger_o
% 5.68/6.01 = ( ^ [X2: code_integer > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X2 @ Y ) @ bot_bo3145834390647256904nteger ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7532_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bo3000040243691356879eger_o
% 5.68/6.01 = ( ^ [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y ) @ bot_bo5443222936135328352nteger ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7533_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bo8662317086119403298_int_o
% 5.68/6.01 = ( ^ [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7534_bot__empty__eq2,axiom,
% 5.68/6.01 ( bot_bo1403522918969695512_int_o
% 5.68/6.01 = ( ^ [X2: int > option6357759511663192854e_term,Y: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % bot_empty_eq2
% 5.68/6.01 thf(fact_7535_summable__ratio__test,axiom,
% 5.68/6.01 ! [C: real,N5: nat,F: nat > real] :
% 5.68/6.01 ( ( ord_less_real @ C @ one_one_real )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.68/6.01 => ( summable_real @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_ratio_test
% 5.68/6.01 thf(fact_7536_summable__ratio__test,axiom,
% 5.68/6.01 ! [C: real,N5: nat,F: nat > complex] :
% 5.68/6.01 ( ( ord_less_real @ C @ one_one_real )
% 5.68/6.01 => ( ! [N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.68/6.01 => ( summable_complex @ F ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % summable_ratio_test
% 5.68/6.01 thf(fact_7537_sum__less__suminf2,axiom,
% 5.68/6.01 ! [F: nat > int,N: nat,I2: nat] :
% 5.68/6.01 ( ( summable_int @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.68/6.01 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf2
% 5.68/6.01 thf(fact_7538_sum__less__suminf2,axiom,
% 5.68/6.01 ! [F: nat > nat,N: nat,I2: nat] :
% 5.68/6.01 ( ( summable_nat @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf2
% 5.68/6.01 thf(fact_7539_sum__less__suminf2,axiom,
% 5.68/6.01 ! [F: nat > real,N: nat,I2: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [M5: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M5 )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.68/6.01 => ( ( ord_less_eq_nat @ N @ I2 )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.68/6.01 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_less_suminf2
% 5.68/6.01 thf(fact_7540_pi__half__neq__zero,axiom,
% 5.68/6.01 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 != zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_neq_zero
% 5.68/6.01 thf(fact_7541_pi__half__less__two,axiom,
% 5.68/6.01 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_less_two
% 5.68/6.01 thf(fact_7542_pi__half__le__two,axiom,
% 5.68/6.01 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_le_two
% 5.68/6.01 thf(fact_7543_pi__half__gt__zero,axiom,
% 5.68/6.01 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_gt_zero
% 5.68/6.01 thf(fact_7544_pi__half__ge__zero,axiom,
% 5.68/6.01 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % pi_half_ge_zero
% 5.68/6.01 thf(fact_7545_m2pi__less__pi,axiom,
% 5.68/6.01 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.68/6.01
% 5.68/6.01 % m2pi_less_pi
% 5.68/6.01 thf(fact_7546_arctan__ubound,axiom,
% 5.68/6.01 ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_ubound
% 5.68/6.01 thf(fact_7547_arctan__one,axiom,
% 5.68/6.01 ( ( arctan @ one_one_real )
% 5.68/6.01 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_one
% 5.68/6.01 thf(fact_7548_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.68/6.01 ( ! [X3: nat,Y3: nat] :
% 5.68/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7549_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 5.68/6.01 ( ! [X3: int,Y3: int] :
% 5.68/6.01 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7550_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr8056137968301705908nteger,S2: set_Pr8056137968301705908nteger] :
% 5.68/6.01 ( ! [X3: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.01 ( ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member3068662437193594005nteger @ ( produc6137756002093451184nteger @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le3216752416896350996nteger @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7551_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr1281608226676607948nteger,S2: set_Pr1281608226676607948nteger] :
% 5.68/6.01 ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.68/6.01 ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le653643898420964396nteger @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7552_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 5.68/6.01 ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/6.01 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le8725513860283290265nt_int @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7553_subrelI,axiom,
% 5.68/6.01 ! [R2: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 5.68/6.01 ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.68/6.01 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R2 )
% 5.68/6.01 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 5.68/6.01 => ( ord_le135402666524580259nt_int @ R2 @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % subrelI
% 5.68/6.01 thf(fact_7554_minus__pi__half__less__zero,axiom,
% 5.68/6.01 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.68/6.01
% 5.68/6.01 % minus_pi_half_less_zero
% 5.68/6.01 thf(fact_7555_arctan__lbound,axiom,
% 5.68/6.01 ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_lbound
% 5.68/6.01 thf(fact_7556_arctan__bounded,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.68/6.01 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_bounded
% 5.68/6.01 thf(fact_7557_pred__subset__eq,axiom,
% 5.68/6.01 ! [R: set_nat,S3: set_nat] :
% 5.68/6.01 ( ( ord_less_eq_nat_o
% 5.68/6.01 @ ^ [X2: nat] : ( member_nat @ X2 @ R )
% 5.68/6.01 @ ^ [X2: nat] : ( member_nat @ X2 @ S3 ) )
% 5.68/6.01 = ( ord_less_eq_set_nat @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq
% 5.68/6.01 thf(fact_7558_pred__subset__eq,axiom,
% 5.68/6.01 ! [R: set_real,S3: set_real] :
% 5.68/6.01 ( ( ord_less_eq_real_o
% 5.68/6.01 @ ^ [X2: real] : ( member_real @ X2 @ R )
% 5.68/6.01 @ ^ [X2: real] : ( member_real @ X2 @ S3 ) )
% 5.68/6.01 = ( ord_less_eq_set_real @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq
% 5.68/6.01 thf(fact_7559_pred__subset__eq,axiom,
% 5.68/6.01 ! [R: set_complex,S3: set_complex] :
% 5.68/6.01 ( ( ord_le4573692005234683329plex_o
% 5.68/6.01 @ ^ [X2: complex] : ( member_complex @ X2 @ R )
% 5.68/6.01 @ ^ [X2: complex] : ( member_complex @ X2 @ S3 ) )
% 5.68/6.01 = ( ord_le211207098394363844omplex @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq
% 5.68/6.01 thf(fact_7560_pred__subset__eq,axiom,
% 5.68/6.01 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.68/6.01 ( ( ord_le704812498762024988_nat_o
% 5.68/6.01 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ R )
% 5.68/6.01 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ S3 ) )
% 5.68/6.01 = ( ord_le3146513528884898305at_nat @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq
% 5.68/6.01 thf(fact_7561_pred__subset__eq,axiom,
% 5.68/6.01 ! [R: set_int,S3: set_int] :
% 5.68/6.01 ( ( ord_less_eq_int_o
% 5.68/6.01 @ ^ [X2: int] : ( member_int @ X2 @ R )
% 5.68/6.01 @ ^ [X2: int] : ( member_int @ X2 @ S3 ) )
% 5.68/6.01 = ( ord_less_eq_set_int @ R @ S3 ) ) ).
% 5.68/6.01
% 5.68/6.01 % pred_subset_eq
% 5.68/6.01 thf(fact_7562_sum__pos__lt__pair,axiom,
% 5.68/6.01 ! [F: nat > real,K: nat] :
% 5.68/6.01 ( ( summable_real @ F )
% 5.68/6.01 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_pos_lt_pair
% 5.68/6.01 thf(fact_7563_machin__Euler,axiom,
% 5.68/6.01 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % machin_Euler
% 5.68/6.01 thf(fact_7564_machin,axiom,
% 5.68/6.01 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % machin
% 5.68/6.01 thf(fact_7565_sin__cos__npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_npi
% 5.68/6.01 thf(fact_7566_cos__pi__eq__zero,axiom,
% 5.68/6.01 ! [M: nat] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_pi_eq_zero
% 5.68/6.01 thf(fact_7567_accp__subset,axiom,
% 5.68/6.01 ! [R1: product_prod_num_num > product_prod_num_num > $o,R22: product_prod_num_num > product_prod_num_num > $o] :
% 5.68/6.01 ( ( ord_le2556027599737686990_num_o @ R1 @ R22 )
% 5.68/6.01 => ( ord_le2239182809043710856_num_o @ ( accp_P3113834385874906142um_num @ R22 ) @ ( accp_P3113834385874906142um_num @ R1 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset
% 5.68/6.01 thf(fact_7568_accp__subset,axiom,
% 5.68/6.01 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.68/6.01 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 5.68/6.01 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset
% 5.68/6.01 thf(fact_7569_accp__subset,axiom,
% 5.68/6.01 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 5.68/6.01 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 5.68/6.01 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset
% 5.68/6.01 thf(fact_7570_accp__subset,axiom,
% 5.68/6.01 ! [R1: list_nat > list_nat > $o,R22: list_nat > list_nat > $o] :
% 5.68/6.01 ( ( ord_le6558929396352911974_nat_o @ R1 @ R22 )
% 5.68/6.01 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R22 ) @ ( accp_list_nat @ R1 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset
% 5.68/6.01 thf(fact_7571_accp__subset,axiom,
% 5.68/6.01 ! [R1: nat > nat > $o,R22: nat > nat > $o] :
% 5.68/6.01 ( ( ord_le2646555220125990790_nat_o @ R1 @ R22 )
% 5.68/6.01 => ( ord_less_eq_nat_o @ ( accp_nat @ R22 ) @ ( accp_nat @ R1 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset
% 5.68/6.01 thf(fact_7572_geometric__deriv__sums,axiom,
% 5.68/6.01 ! [Z: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 5.68/6.01 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % geometric_deriv_sums
% 5.68/6.01 thf(fact_7573_geometric__deriv__sums,axiom,
% 5.68/6.01 ! [Z: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.68/6.01 => ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 5.68/6.01 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % geometric_deriv_sums
% 5.68/6.01 thf(fact_7574_monoseq__def,axiom,
% 5.68/6.01 ( topolo6980174941875973593q_real
% 5.68/6.01 = ( ^ [X6: nat > real] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7575_monoseq__def,axiom,
% 5.68/6.01 ( topolo3100542954746470799et_int
% 5.68/6.01 = ( ^ [X6: nat > set_int] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_set_int @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_set_int @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7576_monoseq__def,axiom,
% 5.68/6.01 ( topolo4267028734544971653eq_rat
% 5.68/6.01 = ( ^ [X6: nat > rat] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_rat @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_rat @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7577_monoseq__def,axiom,
% 5.68/6.01 ( topolo1459490580787246023eq_num
% 5.68/6.01 = ( ^ [X6: nat > num] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_num @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_num @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7578_monoseq__def,axiom,
% 5.68/6.01 ( topolo4902158794631467389eq_nat
% 5.68/6.01 = ( ^ [X6: nat > nat] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_nat @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_nat @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7579_monoseq__def,axiom,
% 5.68/6.01 ( topolo4899668324122417113eq_int
% 5.68/6.01 = ( ^ [X6: nat > int] :
% 5.68/6.01 ( ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_int @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) )
% 5.68/6.01 | ! [M6: nat,N2: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.68/6.01 => ( ord_less_eq_int @ ( X6 @ N2 ) @ ( X6 @ M6 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_def
% 5.68/6.01 thf(fact_7580_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > real] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7581_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > set_int] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7582_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > rat] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7583_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > num] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7584_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > nat] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7585_monoI2,axiom,
% 5.68/6.01 ! [X8: nat > int] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.68/6.01 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI2
% 5.68/6.01 thf(fact_7586_cos__periodic__pi,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_periodic_pi
% 5.68/6.01 thf(fact_7587_cos__periodic__pi2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_periodic_pi2
% 5.68/6.01 thf(fact_7588_sin__periodic__pi,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_periodic_pi
% 5.68/6.01 thf(fact_7589_sin__periodic__pi2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_periodic_pi2
% 5.68/6.01 thf(fact_7590_sin__cos__squared__add3,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.68/6.01 = one_one_complex ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add3
% 5.68/6.01 thf(fact_7591_sin__cos__squared__add3,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add3
% 5.68/6.01 thf(fact_7592_sin__npi2,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_npi2
% 5.68/6.01 thf(fact_7593_sin__npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_npi
% 5.68/6.01 thf(fact_7594_sin__npi__int,axiom,
% 5.68/6.01 ! [N: int] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_npi_int
% 5.68/6.01 thf(fact_7595_powser__sums__zero__iff,axiom,
% 5.68/6.01 ! [A: nat > complex,X: complex] :
% 5.68/6.01 ( ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.68/6.01 @ X )
% 5.68/6.01 = ( ( A @ zero_zero_nat )
% 5.68/6.01 = X ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_zero_iff
% 5.68/6.01 thf(fact_7596_powser__sums__zero__iff,axiom,
% 5.68/6.01 ! [A: nat > real,X: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.68/6.01 @ X )
% 5.68/6.01 = ( ( A @ zero_zero_nat )
% 5.68/6.01 = X ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_zero_iff
% 5.68/6.01 thf(fact_7597_cos__pi__half,axiom,
% 5.68/6.01 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_pi_half
% 5.68/6.01 thf(fact_7598_sin__two__pi,axiom,
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_two_pi
% 5.68/6.01 thf(fact_7599_sin__pi__half,axiom,
% 5.68/6.01 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_pi_half
% 5.68/6.01 thf(fact_7600_cos__two__pi,axiom,
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_two_pi
% 5.68/6.01 thf(fact_7601_cos__periodic,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.68/6.01 = ( cos_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_periodic
% 5.68/6.01 thf(fact_7602_sin__periodic,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.68/6.01 = ( sin_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_periodic
% 5.68/6.01 thf(fact_7603_cos__2pi__minus,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.68/6.01 = ( cos_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_2pi_minus
% 5.68/6.01 thf(fact_7604_cos__npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.68/6.01 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_npi
% 5.68/6.01 thf(fact_7605_cos__npi2,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.01 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_npi2
% 5.68/6.01 thf(fact_7606_sin__cos__squared__add,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add
% 5.68/6.01 thf(fact_7607_sin__cos__squared__add,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = one_one_complex ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add
% 5.68/6.01 thf(fact_7608_sin__cos__squared__add2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add2
% 5.68/6.01 thf(fact_7609_sin__cos__squared__add2,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( 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 ) ) ) )
% 5.68/6.01 = one_one_complex ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_squared_add2
% 5.68/6.01 thf(fact_7610_sin__2npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_2npi
% 5.68/6.01 thf(fact_7611_cos__2npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_2npi
% 5.68/6.01 thf(fact_7612_sin__2pi__minus,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_2pi_minus
% 5.68/6.01 thf(fact_7613_sin__int__2pin,axiom,
% 5.68/6.01 ! [N: int] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_int_2pin
% 5.68/6.01 thf(fact_7614_cos__int__2pin,axiom,
% 5.68/6.01 ! [N: int] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_int_2pin
% 5.68/6.01 thf(fact_7615_cos__3over2__pi,axiom,
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_3over2_pi
% 5.68/6.01 thf(fact_7616_sin__3over2__pi,axiom,
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.68/6.01 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_3over2_pi
% 5.68/6.01 thf(fact_7617_cos__npi__int,axiom,
% 5.68/6.01 ! [N: int] :
% 5.68/6.01 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.68/6.01 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.68/6.01 = one_one_real ) )
% 5.68/6.01 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.68/6.01 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.68/6.01 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_npi_int
% 5.68/6.01 thf(fact_7618_sums__le,axiom,
% 5.68/6.01 ! [F: nat > real,G: nat > real,S2: real,T: real] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( sums_real @ F @ S2 )
% 5.68/6.01 => ( ( sums_real @ G @ T )
% 5.68/6.01 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_le
% 5.68/6.01 thf(fact_7619_sums__le,axiom,
% 5.68/6.01 ! [F: nat > nat,G: nat > nat,S2: nat,T: nat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( sums_nat @ F @ S2 )
% 5.68/6.01 => ( ( sums_nat @ G @ T )
% 5.68/6.01 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_le
% 5.68/6.01 thf(fact_7620_sums__le,axiom,
% 5.68/6.01 ! [F: nat > int,G: nat > int,S2: int,T: int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.01 => ( ( sums_int @ F @ S2 )
% 5.68/6.01 => ( ( sums_int @ G @ T )
% 5.68/6.01 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_le
% 5.68/6.01 thf(fact_7621_sin__add,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( sin_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.01 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_add
% 5.68/6.01 thf(fact_7622_polar__Ex,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ? [R3: real,A3: real] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( times_times_real @ R3 @ ( cos_real @ A3 ) ) )
% 5.68/6.01 & ( Y2
% 5.68/6.01 = ( times_times_real @ R3 @ ( sin_real @ A3 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % polar_Ex
% 5.68/6.01 thf(fact_7623_sin__diff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( sin_real @ ( minus_minus_real @ X @ Y2 ) )
% 5.68/6.01 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_diff
% 5.68/6.01 thf(fact_7624_sums__mult,axiom,
% 5.68/6.01 ! [F: nat > real,A: real,C: real] :
% 5.68/6.01 ( ( sums_real @ F @ A )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.68/6.01 @ ( times_times_real @ C @ A ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult
% 5.68/6.01 thf(fact_7625_sums__mult2,axiom,
% 5.68/6.01 ! [F: nat > real,A: real,C: real] :
% 5.68/6.01 ( ( sums_real @ F @ A )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.68/6.01 @ ( times_times_real @ A @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult2
% 5.68/6.01 thf(fact_7626_sums__add,axiom,
% 5.68/6.01 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.68/6.01 ( ( sums_real @ F @ A )
% 5.68/6.01 => ( ( sums_real @ G @ B )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.01 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_add
% 5.68/6.01 thf(fact_7627_sums__add,axiom,
% 5.68/6.01 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.68/6.01 ( ( sums_nat @ F @ A )
% 5.68/6.01 => ( ( sums_nat @ G @ B )
% 5.68/6.01 => ( sums_nat
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.01 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_add
% 5.68/6.01 thf(fact_7628_sums__add,axiom,
% 5.68/6.01 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.68/6.01 ( ( sums_int @ F @ A )
% 5.68/6.01 => ( ( sums_int @ G @ B )
% 5.68/6.01 => ( sums_int
% 5.68/6.01 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.01 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_add
% 5.68/6.01 thf(fact_7629_sums__divide,axiom,
% 5.68/6.01 ! [F: nat > complex,A: complex,C: complex] :
% 5.68/6.01 ( ( sums_complex @ F @ A )
% 5.68/6.01 => ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 5.68/6.01 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_divide
% 5.68/6.01 thf(fact_7630_sums__divide,axiom,
% 5.68/6.01 ! [F: nat > real,A: real,C: real] :
% 5.68/6.01 ( ( sums_real @ F @ A )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 5.68/6.01 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_divide
% 5.68/6.01 thf(fact_7631_cos__add,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.01 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_add
% 5.68/6.01 thf(fact_7632_cos__diff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 5.68/6.01 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_diff
% 5.68/6.01 thf(fact_7633_sin__double,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_double
% 5.68/6.01 thf(fact_7634_sin__double,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_double
% 5.68/6.01 thf(fact_7635_sincos__principal__value,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ? [Y3: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.68/6.01 & ( ord_less_eq_real @ Y3 @ pi )
% 5.68/6.01 & ( ( sin_real @ Y3 )
% 5.68/6.01 = ( sin_real @ X ) )
% 5.68/6.01 & ( ( cos_real @ Y3 )
% 5.68/6.01 = ( cos_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sincos_principal_value
% 5.68/6.01 thf(fact_7636_sin__x__le__x,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_x_le_x
% 5.68/6.01 thf(fact_7637_sin__le__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_le_one
% 5.68/6.01 thf(fact_7638_cos__le__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_le_one
% 5.68/6.01 thf(fact_7639_abs__sin__x__le__abs__x,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % abs_sin_x_le_abs_x
% 5.68/6.01 thf(fact_7640_sums__mult__iff,axiom,
% 5.68/6.01 ! [C: complex,F: nat > complex,D: complex] :
% 5.68/6.01 ( ( C != zero_zero_complex )
% 5.68/6.01 => ( ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.68/6.01 @ ( times_times_complex @ C @ D ) )
% 5.68/6.01 = ( sums_complex @ F @ D ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult_iff
% 5.68/6.01 thf(fact_7641_sums__mult__iff,axiom,
% 5.68/6.01 ! [C: real,F: nat > real,D: real] :
% 5.68/6.01 ( ( C != zero_zero_real )
% 5.68/6.01 => ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.68/6.01 @ ( times_times_real @ C @ D ) )
% 5.68/6.01 = ( sums_real @ F @ D ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult_iff
% 5.68/6.01 thf(fact_7642_sums__mult2__iff,axiom,
% 5.68/6.01 ! [C: complex,F: nat > complex,D: complex] :
% 5.68/6.01 ( ( C != zero_zero_complex )
% 5.68/6.01 => ( ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.68/6.01 @ ( times_times_complex @ D @ C ) )
% 5.68/6.01 = ( sums_complex @ F @ D ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult2_iff
% 5.68/6.01 thf(fact_7643_sums__mult2__iff,axiom,
% 5.68/6.01 ! [C: real,F: nat > real,D: real] :
% 5.68/6.01 ( ( C != zero_zero_real )
% 5.68/6.01 => ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.68/6.01 @ ( times_times_real @ D @ C ) )
% 5.68/6.01 = ( sums_real @ F @ D ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult2_iff
% 5.68/6.01 thf(fact_7644_sin__cos__le1,axiom,
% 5.68/6.01 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_le1
% 5.68/6.01 thf(fact_7645_cos__squared__eq,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_squared_eq
% 5.68/6.01 thf(fact_7646_cos__squared__eq,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_squared_eq
% 5.68/6.01 thf(fact_7647_sin__squared__eq,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_squared_eq
% 5.68/6.01 thf(fact_7648_sin__squared__eq,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_squared_eq
% 5.68/6.01 thf(fact_7649_sums__mult__D,axiom,
% 5.68/6.01 ! [C: complex,F: nat > complex,A: complex] :
% 5.68/6.01 ( ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.68/6.01 @ A )
% 5.68/6.01 => ( ( C != zero_zero_complex )
% 5.68/6.01 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult_D
% 5.68/6.01 thf(fact_7650_sums__mult__D,axiom,
% 5.68/6.01 ! [C: real,F: nat > real,A: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.68/6.01 @ A )
% 5.68/6.01 => ( ( C != zero_zero_real )
% 5.68/6.01 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_mult_D
% 5.68/6.01 thf(fact_7651_sums__Suc__imp,axiom,
% 5.68/6.01 ! [F: nat > complex,S2: complex] :
% 5.68/6.01 ( ( ( F @ zero_zero_nat )
% 5.68/6.01 = zero_zero_complex )
% 5.68/6.01 => ( ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc_imp
% 5.68/6.01 thf(fact_7652_sums__Suc__imp,axiom,
% 5.68/6.01 ! [F: nat > real,S2: real] :
% 5.68/6.01 ( ( ( F @ zero_zero_nat )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 => ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 => ( sums_real @ F @ S2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc_imp
% 5.68/6.01 thf(fact_7653_sums__Suc__iff,axiom,
% 5.68/6.01 ! [F: nat > real,S2: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc_iff
% 5.68/6.01 thf(fact_7654_sums__Suc,axiom,
% 5.68/6.01 ! [F: nat > real,L2: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ L2 )
% 5.68/6.01 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc
% 5.68/6.01 thf(fact_7655_sums__Suc,axiom,
% 5.68/6.01 ! [F: nat > nat,L2: nat] :
% 5.68/6.01 ( ( sums_nat
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ L2 )
% 5.68/6.01 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc
% 5.68/6.01 thf(fact_7656_sums__Suc,axiom,
% 5.68/6.01 ! [F: nat > int,L2: int] :
% 5.68/6.01 ( ( sums_int
% 5.68/6.01 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.68/6.01 @ L2 )
% 5.68/6.01 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_Suc
% 5.68/6.01 thf(fact_7657_sin__x__ge__neg__x,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_x_ge_neg_x
% 5.68/6.01 thf(fact_7658_sin__ge__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_ge_zero
% 5.68/6.01 thf(fact_7659_sums__zero__iff__shift,axiom,
% 5.68/6.01 ! [N: nat,F: nat > complex,S2: complex] :
% 5.68/6.01 ( ! [I4: nat] :
% 5.68/6.01 ( ( ord_less_nat @ I4 @ N )
% 5.68/6.01 => ( ( F @ I4 )
% 5.68/6.01 = zero_zero_complex ) )
% 5.68/6.01 => ( ( sums_complex
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_zero_iff_shift
% 5.68/6.01 thf(fact_7660_sums__zero__iff__shift,axiom,
% 5.68/6.01 ! [N: nat,F: nat > real,S2: real] :
% 5.68/6.01 ( ! [I4: nat] :
% 5.68/6.01 ( ( ord_less_nat @ I4 @ N )
% 5.68/6.01 => ( ( F @ I4 )
% 5.68/6.01 = zero_zero_real ) )
% 5.68/6.01 => ( ( sums_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 = ( sums_real @ F @ S2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_zero_iff_shift
% 5.68/6.01 thf(fact_7661_sin__ge__minus__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_ge_minus_one
% 5.68/6.01 thf(fact_7662_cos__inj__pi,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.68/6.01 => ( ( ( cos_real @ X )
% 5.68/6.01 = ( cos_real @ Y2 ) )
% 5.68/6.01 => ( X = Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_inj_pi
% 5.68/6.01 thf(fact_7663_cos__mono__le__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_mono_le_eq
% 5.68/6.01 thf(fact_7664_cos__monotone__0__pi__le,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_monotone_0_pi_le
% 5.68/6.01 thf(fact_7665_cos__ge__minus__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_ge_minus_one
% 5.68/6.01 thf(fact_7666_abs__sin__le__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % abs_sin_le_one
% 5.68/6.01 thf(fact_7667_abs__cos__le__one,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % abs_cos_le_one
% 5.68/6.01 thf(fact_7668_sin__times__sin,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_times_sin
% 5.68/6.01 thf(fact_7669_sin__times__sin,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_times_sin
% 5.68/6.01 thf(fact_7670_sin__times__cos,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_times_cos
% 5.68/6.01 thf(fact_7671_sin__times__cos,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_times_cos
% 5.68/6.01 thf(fact_7672_cos__times__sin,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_times_sin
% 5.68/6.01 thf(fact_7673_cos__times__sin,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_times_sin
% 5.68/6.01 thf(fact_7674_sin__plus__sin,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_plus_sin
% 5.68/6.01 thf(fact_7675_sin__plus__sin,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_plus_sin
% 5.68/6.01 thf(fact_7676_sin__diff__sin,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_diff_sin
% 5.68/6.01 thf(fact_7677_sin__diff__sin,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_diff_sin
% 5.68/6.01 thf(fact_7678_cos__diff__cos,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_diff_cos
% 5.68/6.01 thf(fact_7679_cos__diff__cos,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_diff_cos
% 5.68/6.01 thf(fact_7680_cos__double,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double
% 5.68/6.01 thf(fact_7681_cos__double,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double
% 5.68/6.01 thf(fact_7682_cos__double__sin,axiom,
% 5.68/6.01 ! [W: complex] :
% 5.68/6.01 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.68/6.01 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double_sin
% 5.68/6.01 thf(fact_7683_cos__double__sin,axiom,
% 5.68/6.01 ! [W: real] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double_sin
% 5.68/6.01 thf(fact_7684_powser__sums__if,axiom,
% 5.68/6.01 ! [M: nat,Z: complex] :
% 5.68/6.01 ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 5.68/6.01 @ ( power_power_complex @ Z @ M ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_if
% 5.68/6.01 thf(fact_7685_powser__sums__if,axiom,
% 5.68/6.01 ! [M: nat,Z: real] :
% 5.68/6.01 ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 5.68/6.01 @ ( power_power_real @ Z @ M ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_if
% 5.68/6.01 thf(fact_7686_powser__sums__if,axiom,
% 5.68/6.01 ! [M: nat,Z: int] :
% 5.68/6.01 ( sums_int
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 5.68/6.01 @ ( power_power_int @ Z @ M ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_if
% 5.68/6.01 thf(fact_7687_powser__sums__zero,axiom,
% 5.68/6.01 ! [A: nat > complex] :
% 5.68/6.01 ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.68/6.01 @ ( A @ zero_zero_nat ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_zero
% 5.68/6.01 thf(fact_7688_powser__sums__zero,axiom,
% 5.68/6.01 ! [A: nat > real] :
% 5.68/6.01 ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.68/6.01 @ ( A @ zero_zero_nat ) ) ).
% 5.68/6.01
% 5.68/6.01 % powser_sums_zero
% 5.68/6.01 thf(fact_7689_cos__two__neq__zero,axiom,
% 5.68/6.01 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 != zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_two_neq_zero
% 5.68/6.01 thf(fact_7690_cos__mono__less__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ pi )
% 5.68/6.01 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ Y2 @ X ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_mono_less_eq
% 5.68/6.01 thf(fact_7691_cos__monotone__0__pi,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.01 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_monotone_0_pi
% 5.68/6.01 thf(fact_7692_sums__iff__shift,axiom,
% 5.68/6.01 ! [F: nat > real,N: nat,S2: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.68/6.01 @ S2 )
% 5.68/6.01 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_iff_shift
% 5.68/6.01 thf(fact_7693_sums__iff__shift_H,axiom,
% 5.68/6.01 ! [F: nat > real,N: nat,S2: real] :
% 5.68/6.01 ( ( sums_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.68/6.01 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.68/6.01 = ( sums_real @ F @ S2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_iff_shift'
% 5.68/6.01 thf(fact_7694_sums__split__initial__segment,axiom,
% 5.68/6.01 ! [F: nat > real,S2: real,N: nat] :
% 5.68/6.01 ( ( sums_real @ F @ S2 )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N ) )
% 5.68/6.01 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_split_initial_segment
% 5.68/6.01 thf(fact_7695_cos__monotone__minus__pi__0_H,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.01 => ( ord_less_eq_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_monotone_minus_pi_0'
% 5.68/6.01 thf(fact_7696_sums__If__finite__set_H,axiom,
% 5.68/6.01 ! [G: nat > real,S3: real,A2: set_nat,S5: real,F: nat > real] :
% 5.68/6.01 ( ( sums_real @ G @ S3 )
% 5.68/6.01 => ( ( finite_finite_nat @ A2 )
% 5.68/6.01 => ( ( S5
% 5.68/6.01 = ( plus_plus_real @ S3
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.01 @ A2 ) ) )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A2 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.01 @ S5 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_If_finite_set'
% 5.68/6.01 thf(fact_7697_sin__zero__iff__int2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( sin_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ? [I3: int] :
% 5.68/6.01 ( X
% 5.68/6.01 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_zero_iff_int2
% 5.68/6.01 thf(fact_7698_sincos__total__pi,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_eq_real @ T4 @ pi )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( cos_real @ T4 ) )
% 5.68/6.01 & ( Y2
% 5.68/6.01 = ( sin_real @ T4 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sincos_total_pi
% 5.68/6.01 thf(fact_7699_sin__expansion__lemma,axiom,
% 5.68/6.01 ! [X: real,M: nat] :
% 5.68/6.01 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_expansion_lemma
% 5.68/6.01 thf(fact_7700_cos__expansion__lemma,axiom,
% 5.68/6.01 ! [X: real,M: nat] :
% 5.68/6.01 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_expansion_lemma
% 5.68/6.01 thf(fact_7701_sin__gt__zero__02,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_gt_zero_02
% 5.68/6.01 thf(fact_7702_cos__two__less__zero,axiom,
% 5.68/6.01 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.68/6.01
% 5.68/6.01 % cos_two_less_zero
% 5.68/6.01 thf(fact_7703_cos__is__zero,axiom,
% 5.68/6.01 ? [X3: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.68/6.01 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 & ( ( cos_real @ X3 )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 & ! [Y4: real] :
% 5.68/6.01 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.68/6.01 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 & ( ( cos_real @ Y4 )
% 5.68/6.01 = zero_zero_real ) )
% 5.68/6.01 => ( Y4 = X3 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_is_zero
% 5.68/6.01 thf(fact_7704_cos__two__le__zero,axiom,
% 5.68/6.01 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.68/6.01
% 5.68/6.01 % cos_two_le_zero
% 5.68/6.01 thf(fact_7705_cos__monotone__minus__pi__0,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.01 => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_monotone_minus_pi_0
% 5.68/6.01 thf(fact_7706_cos__total,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ? [X3: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.68/6.01 & ( ord_less_eq_real @ X3 @ pi )
% 5.68/6.01 & ( ( cos_real @ X3 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 & ! [Y4: real] :
% 5.68/6.01 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.68/6.01 & ( ord_less_eq_real @ Y4 @ pi )
% 5.68/6.01 & ( ( cos_real @ Y4 )
% 5.68/6.01 = Y2 ) )
% 5.68/6.01 => ( Y4 = X3 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_total
% 5.68/6.01 thf(fact_7707_sincos__total__pi__half,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_eq_real @ T4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( cos_real @ T4 ) )
% 5.68/6.01 & ( Y2
% 5.68/6.01 = ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sincos_total_pi_half
% 5.68/6.01 thf(fact_7708_sincos__total__2pi__le,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_eq_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( cos_real @ T4 ) )
% 5.68/6.01 & ( Y2
% 5.68/6.01 = ( sin_real @ T4 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sincos_total_2pi_le
% 5.68/6.01 thf(fact_7709_sincos__total__2pi,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 => ~ ! [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.01 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 => ( ( X
% 5.68/6.01 = ( cos_real @ T4 ) )
% 5.68/6.01 => ( Y2
% 5.68/6.01 != ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sincos_total_2pi
% 5.68/6.01 thf(fact_7710_sin__pi__divide__n__ge__0,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_pi_divide_n_ge_0
% 5.68/6.01 thf(fact_7711_cos__times__cos,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_times_cos
% 5.68/6.01 thf(fact_7712_cos__times__cos,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_times_cos
% 5.68/6.01 thf(fact_7713_cos__plus__cos,axiom,
% 5.68/6.01 ! [W: complex,Z: complex] :
% 5.68/6.01 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_plus_cos
% 5.68/6.01 thf(fact_7714_cos__plus__cos,axiom,
% 5.68/6.01 ! [W: real,Z: real] :
% 5.68/6.01 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_plus_cos
% 5.68/6.01 thf(fact_7715_geometric__sums,axiom,
% 5.68/6.01 ! [C: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.68/6.01 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % geometric_sums
% 5.68/6.01 thf(fact_7716_geometric__sums,axiom,
% 5.68/6.01 ! [C: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.68/6.01 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % geometric_sums
% 5.68/6.01 thf(fact_7717_power__half__series,axiom,
% 5.68/6.01 ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.68/6.01 @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % power_half_series
% 5.68/6.01 thf(fact_7718_sin__gt__zero2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_gt_zero2
% 5.68/6.01 thf(fact_7719_sin__lt__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ pi @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_lt_zero
% 5.68/6.01 thf(fact_7720_cos__double__less__one,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.01 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double_less_one
% 5.68/6.01 thf(fact_7721_sin__30,axiom,
% 5.68/6.01 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_30
% 5.68/6.01 thf(fact_7722_cos__gt__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_gt_zero
% 5.68/6.01 thf(fact_7723_sin__inj__pi,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ( sin_real @ X )
% 5.68/6.01 = ( sin_real @ Y2 ) )
% 5.68/6.01 => ( X = Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_inj_pi
% 5.68/6.01 thf(fact_7724_sin__mono__le__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_mono_le_eq
% 5.68/6.01 thf(fact_7725_sin__monotone__2pi__le,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_monotone_2pi_le
% 5.68/6.01 thf(fact_7726_cos__60,axiom,
% 5.68/6.01 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_60
% 5.68/6.01 thf(fact_7727_cos__one__2pi__int,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 = ( ? [X2: int] :
% 5.68/6.01 ( X
% 5.68/6.01 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_one_2pi_int
% 5.68/6.01 thf(fact_7728_cos__double__cos,axiom,
% 5.68/6.01 ! [W: complex] :
% 5.68/6.01 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.68/6.01 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double_cos
% 5.68/6.01 thf(fact_7729_cos__double__cos,axiom,
% 5.68/6.01 ! [W: real] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.68/6.01 = ( 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 ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_double_cos
% 5.68/6.01 thf(fact_7730_cos__treble__cos,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_treble_cos
% 5.68/6.01 thf(fact_7731_cos__treble__cos,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_treble_cos
% 5.68/6.01 thf(fact_7732_sums__if_H,axiom,
% 5.68/6.01 ! [G: nat > real,X: real] :
% 5.68/6.01 ( ( sums_real @ G @ X )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_if'
% 5.68/6.01 thf(fact_7733_sums__if,axiom,
% 5.68/6.01 ! [G: nat > real,X: real,F: nat > real,Y2: real] :
% 5.68/6.01 ( ( sums_real @ G @ X )
% 5.68/6.01 => ( ( sums_real @ F @ Y2 )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sums_if
% 5.68/6.01 thf(fact_7734_sin__le__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ pi @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_le_zero
% 5.68/6.01 thf(fact_7735_sin__less__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.01 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_less_zero
% 5.68/6.01 thf(fact_7736_sin__mono__less__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_mono_less_eq
% 5.68/6.01 thf(fact_7737_sin__monotone__2pi,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_monotone_2pi
% 5.68/6.01 thf(fact_7738_sin__total,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ? [X3: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.68/6.01 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( sin_real @ X3 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 & ! [Y4: real] :
% 5.68/6.01 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.68/6.01 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( sin_real @ Y4 )
% 5.68/6.01 = Y2 ) )
% 5.68/6.01 => ( Y4 = X3 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_total
% 5.68/6.01 thf(fact_7739_cos__gt__zero__pi,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_gt_zero_pi
% 5.68/6.01 thf(fact_7740_cos__ge__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_ge_zero
% 5.68/6.01 thf(fact_7741_cos__one__2pi,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 = ( ? [X2: nat] :
% 5.68/6.01 ( X
% 5.68/6.01 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.68/6.01 | ? [X2: nat] :
% 5.68/6.01 ( X
% 5.68/6.01 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_one_2pi
% 5.68/6.01 thf(fact_7742_accp__subset__induct,axiom,
% 5.68/6.01 ! [D4: product_prod_num_num > $o,R: product_prod_num_num > product_prod_num_num > $o,X: product_prod_num_num,P: product_prod_num_num > $o] :
% 5.68/6.01 ( ( ord_le2239182809043710856_num_o @ D4 @ ( accp_P3113834385874906142um_num @ R ) )
% 5.68/6.01 => ( ! [X3: product_prod_num_num,Z3: product_prod_num_num] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ( R @ Z3 @ X3 )
% 5.68/6.01 => ( D4 @ Z3 ) ) )
% 5.68/6.01 => ( ( D4 @ X )
% 5.68/6.01 => ( ! [X3: product_prod_num_num] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ! [Z4: product_prod_num_num] :
% 5.68/6.01 ( ( R @ Z4 @ X3 )
% 5.68/6.01 => ( P @ Z4 ) )
% 5.68/6.01 => ( P @ X3 ) ) )
% 5.68/6.01 => ( P @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset_induct
% 5.68/6.01 thf(fact_7743_accp__subset__induct,axiom,
% 5.68/6.01 ! [D4: product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.68/6.01 ( ( ord_le704812498762024988_nat_o @ D4 @ ( accp_P4275260045618599050at_nat @ R ) )
% 5.68/6.01 => ( ! [X3: product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ( R @ Z3 @ X3 )
% 5.68/6.01 => ( D4 @ Z3 ) ) )
% 5.68/6.01 => ( ( D4 @ X )
% 5.68/6.01 => ( ! [X3: product_prod_nat_nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ! [Z4: product_prod_nat_nat] :
% 5.68/6.01 ( ( R @ Z4 @ X3 )
% 5.68/6.01 => ( P @ Z4 ) )
% 5.68/6.01 => ( P @ X3 ) ) )
% 5.68/6.01 => ( P @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset_induct
% 5.68/6.01 thf(fact_7744_accp__subset__induct,axiom,
% 5.68/6.01 ! [D4: product_prod_int_int > $o,R: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.68/6.01 ( ( ord_le8369615600986905444_int_o @ D4 @ ( accp_P1096762738010456898nt_int @ R ) )
% 5.68/6.01 => ( ! [X3: product_prod_int_int,Z3: product_prod_int_int] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ( R @ Z3 @ X3 )
% 5.68/6.01 => ( D4 @ Z3 ) ) )
% 5.68/6.01 => ( ( D4 @ X )
% 5.68/6.01 => ( ! [X3: product_prod_int_int] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ! [Z4: product_prod_int_int] :
% 5.68/6.01 ( ( R @ Z4 @ X3 )
% 5.68/6.01 => ( P @ Z4 ) )
% 5.68/6.01 => ( P @ X3 ) ) )
% 5.68/6.01 => ( P @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset_induct
% 5.68/6.01 thf(fact_7745_accp__subset__induct,axiom,
% 5.68/6.01 ! [D4: list_nat > $o,R: list_nat > list_nat > $o,X: list_nat,P: list_nat > $o] :
% 5.68/6.01 ( ( ord_le1520216061033275535_nat_o @ D4 @ ( accp_list_nat @ R ) )
% 5.68/6.01 => ( ! [X3: list_nat,Z3: list_nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ( R @ Z3 @ X3 )
% 5.68/6.01 => ( D4 @ Z3 ) ) )
% 5.68/6.01 => ( ( D4 @ X )
% 5.68/6.01 => ( ! [X3: list_nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ! [Z4: list_nat] :
% 5.68/6.01 ( ( R @ Z4 @ X3 )
% 5.68/6.01 => ( P @ Z4 ) )
% 5.68/6.01 => ( P @ X3 ) ) )
% 5.68/6.01 => ( P @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset_induct
% 5.68/6.01 thf(fact_7746_accp__subset__induct,axiom,
% 5.68/6.01 ! [D4: nat > $o,R: nat > nat > $o,X: nat,P: nat > $o] :
% 5.68/6.01 ( ( ord_less_eq_nat_o @ D4 @ ( accp_nat @ R ) )
% 5.68/6.01 => ( ! [X3: nat,Z3: nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ( R @ Z3 @ X3 )
% 5.68/6.01 => ( D4 @ Z3 ) ) )
% 5.68/6.01 => ( ( D4 @ X )
% 5.68/6.01 => ( ! [X3: nat] :
% 5.68/6.01 ( ( D4 @ X3 )
% 5.68/6.01 => ( ! [Z4: nat] :
% 5.68/6.01 ( ( R @ Z4 @ X3 )
% 5.68/6.01 => ( P @ Z4 ) )
% 5.68/6.01 => ( P @ X3 ) ) )
% 5.68/6.01 => ( P @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % accp_subset_induct
% 5.68/6.01 thf(fact_7747_sin__pi__divide__n__gt__0,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_pi_divide_n_gt_0
% 5.68/6.01 thf(fact_7748_sin__zero__iff__int,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( sin_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ? [I3: int] :
% 5.68/6.01 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_zero_iff_int
% 5.68/6.01 thf(fact_7749_cos__zero__iff__int,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ? [I3: int] :
% 5.68/6.01 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_zero_iff_int
% 5.68/6.01 thf(fact_7750_sin__zero__lemma,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ( sin_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 => ? [N3: nat] :
% 5.68/6.01 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_zero_lemma
% 5.68/6.01 thf(fact_7751_sin__zero__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( sin_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ? [N2: nat] :
% 5.68/6.01 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.01 | ? [N2: nat] :
% 5.68/6.01 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_zero_iff
% 5.68/6.01 thf(fact_7752_cos__zero__lemma,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ( cos_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 => ? [N3: nat] :
% 5.68/6.01 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_zero_lemma
% 5.68/6.01 thf(fact_7753_cos__zero__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( ? [N2: nat] :
% 5.68/6.01 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.01 | ? [N2: nat] :
% 5.68/6.01 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.68/6.01 & ( X
% 5.68/6.01 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_zero_iff
% 5.68/6.01 thf(fact_7754_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > real] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7755_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > set_int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7756_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > rat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7757_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > num] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7758_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > nat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7759_mono__SucI1,axiom,
% 5.68/6.01 ! [X8: nat > int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.68/6.01 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI1
% 5.68/6.01 thf(fact_7760_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > real] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7761_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > set_int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7762_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > rat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7763_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > num] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7764_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > nat] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7765_mono__SucI2,axiom,
% 5.68/6.01 ! [X8: nat > int] :
% 5.68/6.01 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.68/6.01 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % mono_SucI2
% 5.68/6.01 thf(fact_7766_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo6980174941875973593q_real
% 5.68/6.01 = ( ^ [X6: nat > real] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_real @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_real @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7767_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo3100542954746470799et_int
% 5.68/6.01 = ( ^ [X6: nat > set_int] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_set_int @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7768_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo4267028734544971653eq_rat
% 5.68/6.01 = ( ^ [X6: nat > rat] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_rat @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7769_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo1459490580787246023eq_num
% 5.68/6.01 = ( ^ [X6: nat > num] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_num @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_num @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7770_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo4902158794631467389eq_nat
% 5.68/6.01 = ( ^ [X6: nat > nat] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_nat @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7771_monoseq__Suc,axiom,
% 5.68/6.01 ( topolo4899668324122417113eq_int
% 5.68/6.01 = ( ^ [X6: nat > int] :
% 5.68/6.01 ( ! [N2: nat] : ( ord_less_eq_int @ ( X6 @ N2 ) @ ( X6 @ ( suc @ N2 ) ) )
% 5.68/6.01 | ! [N2: nat] : ( ord_less_eq_int @ ( X6 @ ( suc @ N2 ) ) @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoseq_Suc
% 5.68/6.01 thf(fact_7772_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > real] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7773_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > set_int] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_set_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7774_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > rat] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7775_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > num] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7776_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > nat] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7777_monoI1,axiom,
% 5.68/6.01 ! [X8: nat > int] :
% 5.68/6.01 ( ! [M5: nat,N3: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.68/6.01 => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.68/6.01 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.68/6.01
% 5.68/6.01 % monoI1
% 5.68/6.01 thf(fact_7778_vebt__maxt_Opelims,axiom,
% 5.68/6.01 ! [X: vEBT_VEBT,Y2: option_nat] :
% 5.68/6.01 ( ( ( vEBT_vebt_maxt @ X )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.68/6.01 => ( ! [A3: $o,B2: $o] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.68/6.01 => ( ( ( B2
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( some_nat @ one_one_nat ) ) )
% 5.68/6.01 & ( ~ B2
% 5.68/6.01 => ( ( A3
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( some_nat @ zero_zero_nat ) ) )
% 5.68/6.01 & ( ~ A3
% 5.68/6.01 => ( Y2 = none_nat ) ) ) ) )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.68/6.01 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.68/6.01 => ( ( Y2 = none_nat )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) ) ) )
% 5.68/6.01 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.68/6.01 => ( ( Y2
% 5.68/6.01 = ( some_nat @ Ma2 ) )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % vebt_maxt.pelims
% 5.68/6.01 thf(fact_7779_vebt__mint_Opelims,axiom,
% 5.68/6.01 ! [X: vEBT_VEBT,Y2: option_nat] :
% 5.68/6.01 ( ( ( vEBT_vebt_mint @ X )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.68/6.01 => ( ! [A3: $o,B2: $o] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.68/6.01 => ( ( ( A3
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( some_nat @ zero_zero_nat ) ) )
% 5.68/6.01 & ( ~ A3
% 5.68/6.01 => ( ( B2
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( some_nat @ one_one_nat ) ) )
% 5.68/6.01 & ( ~ B2
% 5.68/6.01 => ( Y2 = none_nat ) ) ) ) )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.68/6.01 => ( ! [Uu3: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) )
% 5.68/6.01 => ( ( Y2 = none_nat )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu3 @ Uv2 @ Uw2 ) ) ) )
% 5.68/6.01 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.68/6.01 ( ( X
% 5.68/6.01 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.68/6.01 => ( ( Y2
% 5.68/6.01 = ( some_nat @ Mi2 ) )
% 5.68/6.01 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % vebt_mint.pelims
% 5.68/6.01 thf(fact_7780_Maclaurin__minus__cos__expansion,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_real @ X @ T4 )
% 5.68/6.01 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.68/6.01 & ( ( cos_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_minus_cos_expansion
% 5.68/6.01 thf(fact_7781_Maclaurin__cos__expansion2,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_real @ T4 @ X )
% 5.68/6.01 & ( ( cos_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_cos_expansion2
% 5.68/6.01 thf(fact_7782_fact__Suc__0,axiom,
% 5.68/6.01 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = one_one_complex ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc_0
% 5.68/6.01 thf(fact_7783_fact__Suc__0,axiom,
% 5.68/6.01 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = one_one_rat ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc_0
% 5.68/6.01 thf(fact_7784_fact__Suc__0,axiom,
% 5.68/6.01 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = one_one_int ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc_0
% 5.68/6.01 thf(fact_7785_fact__Suc__0,axiom,
% 5.68/6.01 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc_0
% 5.68/6.01 thf(fact_7786_fact__Suc__0,axiom,
% 5.68/6.01 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = one_one_nat ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc_0
% 5.68/6.01 thf(fact_7787_fact__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.68/6.01 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc
% 5.68/6.01 thf(fact_7788_fact__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.68/6.01 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc
% 5.68/6.01 thf(fact_7789_fact__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc
% 5.68/6.01 thf(fact_7790_fact__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.68/6.01 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_Suc
% 5.68/6.01 thf(fact_7791_fact__2,axiom,
% 5.68/6.01 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_2
% 5.68/6.01 thf(fact_7792_fact__2,axiom,
% 5.68/6.01 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_2
% 5.68/6.01 thf(fact_7793_fact__2,axiom,
% 5.68/6.01 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_2
% 5.68/6.01 thf(fact_7794_fact__2,axiom,
% 5.68/6.01 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_2
% 5.68/6.01 thf(fact_7795_fact__2,axiom,
% 5.68/6.01 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_2
% 5.68/6.01 thf(fact_7796_fact__ge__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_zero
% 5.68/6.01 thf(fact_7797_fact__ge__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_zero
% 5.68/6.01 thf(fact_7798_fact__ge__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_zero
% 5.68/6.01 thf(fact_7799_fact__ge__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_zero
% 5.68/6.01 thf(fact_7800_fact__gt__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_gt_zero
% 5.68/6.01 thf(fact_7801_fact__gt__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_gt_zero
% 5.68/6.01 thf(fact_7802_fact__gt__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_gt_zero
% 5.68/6.01 thf(fact_7803_fact__gt__zero,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_gt_zero
% 5.68/6.01 thf(fact_7804_fact__not__neg,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.68/6.01
% 5.68/6.01 % fact_not_neg
% 5.68/6.01 thf(fact_7805_fact__not__neg,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.68/6.01
% 5.68/6.01 % fact_not_neg
% 5.68/6.01 thf(fact_7806_fact__not__neg,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % fact_not_neg
% 5.68/6.01 thf(fact_7807_fact__not__neg,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.68/6.01
% 5.68/6.01 % fact_not_neg
% 5.68/6.01 thf(fact_7808_fact__ge__1,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_1
% 5.68/6.01 thf(fact_7809_fact__ge__1,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_1
% 5.68/6.01 thf(fact_7810_fact__ge__1,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_1
% 5.68/6.01 thf(fact_7811_fact__ge__1,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_1
% 5.68/6.01 thf(fact_7812_fact__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mono
% 5.68/6.01 thf(fact_7813_fact__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mono
% 5.68/6.01 thf(fact_7814_fact__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mono
% 5.68/6.01 thf(fact_7815_fact__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mono
% 5.68/6.01 thf(fact_7816_fact__dvd,axiom,
% 5.68/6.01 ! [N: nat,M: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.01 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_dvd
% 5.68/6.01 thf(fact_7817_fact__dvd,axiom,
% 5.68/6.01 ! [N: nat,M: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.01 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_dvd
% 5.68/6.01 thf(fact_7818_fact__dvd,axiom,
% 5.68/6.01 ! [N: nat,M: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.01 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_dvd
% 5.68/6.01 thf(fact_7819_fact__dvd,axiom,
% 5.68/6.01 ! [N: nat,M: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.01 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_dvd
% 5.68/6.01 thf(fact_7820_fact__less__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.01 => ( ( ord_less_nat @ M @ N )
% 5.68/6.01 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_less_mono
% 5.68/6.01 thf(fact_7821_fact__less__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.01 => ( ( ord_less_nat @ M @ N )
% 5.68/6.01 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_less_mono
% 5.68/6.01 thf(fact_7822_fact__less__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.01 => ( ( ord_less_nat @ M @ N )
% 5.68/6.01 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_less_mono
% 5.68/6.01 thf(fact_7823_fact__less__mono,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.01 => ( ( ord_less_nat @ M @ N )
% 5.68/6.01 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_less_mono
% 5.68/6.01 thf(fact_7824_fact__mod,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.68/6.01 = zero_zero_int ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mod
% 5.68/6.01 thf(fact_7825_fact__mod,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.68/6.01 = zero_z3403309356797280102nteger ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mod
% 5.68/6.01 thf(fact_7826_fact__mod,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.68/6.01 = zero_zero_nat ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mod
% 5.68/6.01 thf(fact_7827_fact__fact__dvd__fact,axiom,
% 5.68/6.01 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_fact_dvd_fact
% 5.68/6.01 thf(fact_7828_fact__fact__dvd__fact,axiom,
% 5.68/6.01 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_fact_dvd_fact
% 5.68/6.01 thf(fact_7829_fact__fact__dvd__fact,axiom,
% 5.68/6.01 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_fact_dvd_fact
% 5.68/6.01 thf(fact_7830_fact__fact__dvd__fact,axiom,
% 5.68/6.01 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_fact_dvd_fact
% 5.68/6.01 thf(fact_7831_fact__fact__dvd__fact,axiom,
% 5.68/6.01 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_fact_dvd_fact
% 5.68/6.01 thf(fact_7832_fact__le__power,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_le_power
% 5.68/6.01 thf(fact_7833_fact__le__power,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_le_power
% 5.68/6.01 thf(fact_7834_fact__le__power,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_le_power
% 5.68/6.01 thf(fact_7835_fact__le__power,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_le_power
% 5.68/6.01 thf(fact_7836_choose__dvd,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_dvd
% 5.68/6.01 thf(fact_7837_choose__dvd,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_dvd
% 5.68/6.01 thf(fact_7838_choose__dvd,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_dvd
% 5.68/6.01 thf(fact_7839_choose__dvd,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_dvd
% 5.68/6.01 thf(fact_7840_choose__dvd,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_dvd
% 5.68/6.01 thf(fact_7841_fact__numeral,axiom,
% 5.68/6.01 ! [K: num] :
% 5.68/6.01 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.68/6.01 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_numeral
% 5.68/6.01 thf(fact_7842_fact__numeral,axiom,
% 5.68/6.01 ! [K: num] :
% 5.68/6.01 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.68/6.01 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_numeral
% 5.68/6.01 thf(fact_7843_fact__numeral,axiom,
% 5.68/6.01 ! [K: num] :
% 5.68/6.01 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.68/6.01 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_numeral
% 5.68/6.01 thf(fact_7844_fact__numeral,axiom,
% 5.68/6.01 ! [K: num] :
% 5.68/6.01 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.68/6.01 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_numeral
% 5.68/6.01 thf(fact_7845_fact__numeral,axiom,
% 5.68/6.01 ! [K: num] :
% 5.68/6.01 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.68/6.01 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_numeral
% 5.68/6.01 thf(fact_7846_square__fact__le__2__fact,axiom,
% 5.68/6.01 ! [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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % square_fact_le_2_fact
% 5.68/6.01 thf(fact_7847_fact__num__eq__if,axiom,
% 5.68/6.01 ( semiri5044797733671781792omplex
% 5.68/6.01 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_num_eq_if
% 5.68/6.01 thf(fact_7848_fact__num__eq__if,axiom,
% 5.68/6.01 ( semiri1406184849735516958ct_int
% 5.68/6.01 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_num_eq_if
% 5.68/6.01 thf(fact_7849_fact__num__eq__if,axiom,
% 5.68/6.01 ( semiri773545260158071498ct_rat
% 5.68/6.01 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_num_eq_if
% 5.68/6.01 thf(fact_7850_fact__num__eq__if,axiom,
% 5.68/6.01 ( semiri2265585572941072030t_real
% 5.68/6.01 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_num_eq_if
% 5.68/6.01 thf(fact_7851_fact__num__eq__if,axiom,
% 5.68/6.01 ( semiri1408675320244567234ct_nat
% 5.68/6.01 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_num_eq_if
% 5.68/6.01 thf(fact_7852_fact__reduce,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( semiri1406184849735516958ct_int @ N )
% 5.68/6.01 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_reduce
% 5.68/6.01 thf(fact_7853_fact__reduce,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( semiri773545260158071498ct_rat @ N )
% 5.68/6.01 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_reduce
% 5.68/6.01 thf(fact_7854_fact__reduce,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( semiri2265585572941072030t_real @ N )
% 5.68/6.01 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_reduce
% 5.68/6.01 thf(fact_7855_fact__reduce,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.68/6.01 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_reduce
% 5.68/6.01 thf(fact_7856_Maclaurin__zero,axiom,
% 5.68/6.01 ! [X: real,N: nat,Diff: nat > complex > real] :
% 5.68/6.01 ( ( X = zero_zero_real )
% 5.68/6.01 => ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_zero
% 5.68/6.01 thf(fact_7857_Maclaurin__zero,axiom,
% 5.68/6.01 ! [X: real,N: nat,Diff: nat > real > real] :
% 5.68/6.01 ( ( X = zero_zero_real )
% 5.68/6.01 => ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_zero
% 5.68/6.01 thf(fact_7858_Maclaurin__zero,axiom,
% 5.68/6.01 ! [X: real,N: nat,Diff: nat > rat > real] :
% 5.68/6.01 ( ( X = zero_zero_real )
% 5.68/6.01 => ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_zero
% 5.68/6.01 thf(fact_7859_Maclaurin__zero,axiom,
% 5.68/6.01 ! [X: real,N: nat,Diff: nat > nat > real] :
% 5.68/6.01 ( ( X = zero_zero_real )
% 5.68/6.01 => ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_zero
% 5.68/6.01 thf(fact_7860_Maclaurin__zero,axiom,
% 5.68/6.01 ! [X: real,N: nat,Diff: nat > int > real] :
% 5.68/6.01 ( ( X = zero_zero_real )
% 5.68/6.01 => ( ( N != zero_zero_nat )
% 5.68/6.01 => ( ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_zero
% 5.68/6.01 thf(fact_7861_Maclaurin__lemma,axiom,
% 5.68/6.01 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.68/6.01 => ? [B8: real] :
% 5.68/6.01 ( ( F @ H2 )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_lemma
% 5.68/6.01 thf(fact_7862_cos__paired,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.01 @ ( cos_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_paired
% 5.68/6.01 thf(fact_7863_cos__coeff__def,axiom,
% 5.68/6.01 ( cos_coeff
% 5.68/6.01 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_coeff_def
% 5.68/6.01 thf(fact_7864_sin__paired,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.68/6.01 @ ( sin_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_paired
% 5.68/6.01 thf(fact_7865_Maclaurin__cos__expansion,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.01 & ( ( cos_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_cos_expansion
% 5.68/6.01 thf(fact_7866_Maclaurin__sin__expansion3,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_real @ T4 @ X )
% 5.68/6.01 & ( ( sin_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_sin_expansion3
% 5.68/6.01 thf(fact_7867_Maclaurin__sin__expansion4,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.68/6.01 & ( ord_less_eq_real @ T4 @ X )
% 5.68/6.01 & ( ( sin_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_sin_expansion4
% 5.68/6.01 thf(fact_7868_Maclaurin__sin__expansion2,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.01 & ( ( sin_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_sin_expansion2
% 5.68/6.01 thf(fact_7869_Maclaurin__sin__expansion,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ? [T4: real] :
% 5.68/6.01 ( ( sin_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_sin_expansion
% 5.68/6.01 thf(fact_7870_sin__coeff__def,axiom,
% 5.68/6.01 ( sin_coeff
% 5.68/6.01 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_coeff_def
% 5.68/6.01 thf(fact_7871_fact__ge__self,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_self
% 5.68/6.01 thf(fact_7872_fact__mono__nat,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_mono_nat
% 5.68/6.01 thf(fact_7873_fact__less__mono__nat,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.01 => ( ( ord_less_nat @ M @ N )
% 5.68/6.01 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_less_mono_nat
% 5.68/6.01 thf(fact_7874_fact__ge__Suc__0__nat,axiom,
% 5.68/6.01 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_ge_Suc_0_nat
% 5.68/6.01 thf(fact_7875_dvd__fact,axiom,
% 5.68/6.01 ! [M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.68/6.01 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % dvd_fact
% 5.68/6.01 thf(fact_7876_fact__diff__Suc,axiom,
% 5.68/6.01 ! [N: nat,M: nat] :
% 5.68/6.01 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.68/6.01 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.68/6.01 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_diff_Suc
% 5.68/6.01 thf(fact_7877_fact__div__fact__le__pow,axiom,
% 5.68/6.01 ! [R2: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ R2 @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_div_fact_le_pow
% 5.68/6.01 thf(fact_7878_sin__coeff__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( sin_coeff @ ( suc @ N ) )
% 5.68/6.01 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_coeff_Suc
% 5.68/6.01 thf(fact_7879_cos__coeff__Suc,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( cos_coeff @ ( suc @ N ) )
% 5.68/6.01 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_coeff_Suc
% 5.68/6.01 thf(fact_7880_fold__atLeastAtMost__nat_Opsimps,axiom,
% 5.68/6.01 ! [F: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 5.68/6.01 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 5.68/6.01 => ( ( ( ord_less_nat @ B @ A )
% 5.68/6.01 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 5.68/6.01 = Acc ) )
% 5.68/6.01 & ( ~ ( ord_less_nat @ B @ A )
% 5.68/6.01 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 5.68/6.01 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fold_atLeastAtMost_nat.psimps
% 5.68/6.01 thf(fact_7881_fold__atLeastAtMost__nat_Opelims,axiom,
% 5.68/6.01 ! [X: nat > nat > nat,Xa2: nat,Xb2: nat,Xc: nat,Y2: nat] :
% 5.68/6.01 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb2 @ Xc )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb2 @ Xc ) ) ) )
% 5.68/6.01 => ~ ( ( ( ( ord_less_nat @ Xb2 @ Xa2 )
% 5.68/6.01 => ( Y2 = Xc ) )
% 5.68/6.01 & ( ~ ( ord_less_nat @ Xb2 @ Xa2 )
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb2 @ ( X @ Xa2 @ Xc ) ) ) ) )
% 5.68/6.01 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb2 @ Xc ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fold_atLeastAtMost_nat.pelims
% 5.68/6.01 thf(fact_7882_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.68/6.01 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb2: option4927543243414619207at_nat,Y2: option4927543243414619207at_nat] :
% 5.68/6.01 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb2 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ Xa2 @ Xb2 ) ) )
% 5.68/6.01 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.68/6.01 => ( ( Y2 = none_P5556105721700978146at_nat )
% 5.68/6.01 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Xb2 ) ) ) ) )
% 5.68/6.01 => ( ! [V2: product_prod_nat_nat] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.68/6.01 => ( ( Xb2 = none_P5556105721700978146at_nat )
% 5.68/6.01 => ( ( Y2 = none_P5556105721700978146at_nat )
% 5.68/6.01 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) ) ) ) )
% 5.68/6.01 => ~ ! [A3: product_prod_nat_nat] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.68/6.01 => ! [B2: product_prod_nat_nat] :
% 5.68/6.01 ( ( Xb2
% 5.68/6.01 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.68/6.01 => ( ( Y2
% 5.68/6.01 = ( some_P7363390416028606310at_nat @ ( X @ A3 @ B2 ) ) )
% 5.68/6.01 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % VEBT_internal.option_shift.pelims
% 5.68/6.01 thf(fact_7883_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.68/6.01 ! [X: num > num > num,Xa2: option_num,Xb2: option_num,Y2: option_num] :
% 5.68/6.01 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb2 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ Xa2 @ Xb2 ) ) )
% 5.68/6.01 => ( ( ( Xa2 = none_num )
% 5.68/6.01 => ( ( Y2 = none_num )
% 5.68/6.01 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ none_num @ Xb2 ) ) ) ) )
% 5.68/6.01 => ( ! [V2: num] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_num @ V2 ) )
% 5.68/6.01 => ( ( Xb2 = none_num )
% 5.68/6.01 => ( ( Y2 = none_num )
% 5.68/6.01 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) ) ) ) )
% 5.68/6.01 => ~ ! [A3: num] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_num @ A3 ) )
% 5.68/6.01 => ! [B2: num] :
% 5.68/6.01 ( ( Xb2
% 5.68/6.01 = ( some_num @ B2 ) )
% 5.68/6.01 => ( ( Y2
% 5.68/6.01 = ( some_num @ ( X @ A3 @ B2 ) ) )
% 5.68/6.01 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % VEBT_internal.option_shift.pelims
% 5.68/6.01 thf(fact_7884_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.68/6.01 ! [X: nat > nat > nat,Xa2: option_nat,Xb2: option_nat,Y2: option_nat] :
% 5.68/6.01 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb2 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ Xa2 @ Xb2 ) ) )
% 5.68/6.01 => ( ( ( Xa2 = none_nat )
% 5.68/6.01 => ( ( Y2 = none_nat )
% 5.68/6.01 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ none_nat @ Xb2 ) ) ) ) )
% 5.68/6.01 => ( ! [V2: nat] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_nat @ V2 ) )
% 5.68/6.01 => ( ( Xb2 = none_nat )
% 5.68/6.01 => ( ( Y2 = none_nat )
% 5.68/6.01 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) ) ) ) )
% 5.68/6.01 => ~ ! [A3: nat] :
% 5.68/6.01 ( ( Xa2
% 5.68/6.01 = ( some_nat @ A3 ) )
% 5.68/6.01 => ! [B2: nat] :
% 5.68/6.01 ( ( Xb2
% 5.68/6.01 = ( some_nat @ B2 ) )
% 5.68/6.01 => ( ( Y2
% 5.68/6.01 = ( some_nat @ ( X @ A3 @ B2 ) ) )
% 5.68/6.01 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % VEBT_internal.option_shift.pelims
% 5.68/6.01 thf(fact_7885_diffs__equiv,axiom,
% 5.68/6.01 ! [C: nat > complex,X: complex] :
% 5.68/6.01 ( ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) )
% 5.68/6.01 => ( sums_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.68/6.01 @ ( suminf_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % diffs_equiv
% 5.68/6.01 thf(fact_7886_diffs__equiv,axiom,
% 5.68/6.01 ! [C: nat > real,X: real] :
% 5.68/6.01 ( ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) )
% 5.68/6.01 => ( sums_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.68/6.01 @ ( suminf_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % diffs_equiv
% 5.68/6.01 thf(fact_7887_tan__double,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( ( cos_complex @ X )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_double
% 5.68/6.01 thf(fact_7888_tan__double,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.68/6.01 = ( 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 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_double
% 5.68/6.01 thf(fact_7889_tan__periodic__pi,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.68/6.01 = ( tan_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_periodic_pi
% 5.68/6.01 thf(fact_7890_tan__npi,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % tan_npi
% 5.68/6.01 thf(fact_7891_tan__periodic__n,axiom,
% 5.68/6.01 ! [X: real,N: num] :
% 5.68/6.01 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.68/6.01 = ( tan_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_periodic_n
% 5.68/6.01 thf(fact_7892_tan__periodic__nat,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.68/6.01 = ( tan_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_periodic_nat
% 5.68/6.01 thf(fact_7893_tan__periodic__int,axiom,
% 5.68/6.01 ! [X: real,I2: int] :
% 5.68/6.01 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.68/6.01 = ( tan_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_periodic_int
% 5.68/6.01 thf(fact_7894_tan__periodic,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.68/6.01 = ( tan_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_periodic
% 5.68/6.01 thf(fact_7895_tan__def,axiom,
% 5.68/6.01 ( tan_complex
% 5.68/6.01 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_def
% 5.68/6.01 thf(fact_7896_tan__def,axiom,
% 5.68/6.01 ( tan_real
% 5.68/6.01 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_def
% 5.68/6.01 thf(fact_7897_diffs__def,axiom,
% 5.68/6.01 ( diffs_int
% 5.68/6.01 = ( ^ [C3: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % diffs_def
% 5.68/6.01 thf(fact_7898_diffs__def,axiom,
% 5.68/6.01 ( diffs_real
% 5.68/6.01 = ( ^ [C3: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % diffs_def
% 5.68/6.01 thf(fact_7899_diffs__def,axiom,
% 5.68/6.01 ( diffs_rat
% 5.68/6.01 = ( ^ [C3: nat > rat,N2: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( C3 @ ( suc @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % diffs_def
% 5.68/6.01 thf(fact_7900_termdiff__converges__all,axiom,
% 5.68/6.01 ! [C: nat > complex,X: complex] :
% 5.68/6.01 ( ! [X3: complex] :
% 5.68/6.01 ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % termdiff_converges_all
% 5.68/6.01 thf(fact_7901_termdiff__converges__all,axiom,
% 5.68/6.01 ! [C: nat > real,X: real] :
% 5.68/6.01 ( ! [X3: real] :
% 5.68/6.01 ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % termdiff_converges_all
% 5.68/6.01 thf(fact_7902_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.68/6.01 ! [X: nat > nat > nat,Xa2: nat,Xb2: nat,Xc: nat,Y2: nat] :
% 5.68/6.01 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb2 @ Xc )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( ( ord_less_nat @ Xb2 @ Xa2 )
% 5.68/6.01 => ( Y2 = Xc ) )
% 5.68/6.01 & ( ~ ( ord_less_nat @ Xb2 @ Xa2 )
% 5.68/6.01 => ( Y2
% 5.68/6.01 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb2 @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fold_atLeastAtMost_nat.elims
% 5.68/6.01 thf(fact_7903_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.68/6.01 ( set_fo2584398358068434914at_nat
% 5.68/6.01 = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fold_atLeastAtMost_nat.simps
% 5.68/6.01 thf(fact_7904_tan__45,axiom,
% 5.68/6.01 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % tan_45
% 5.68/6.01 thf(fact_7905_tan__gt__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_gt_zero
% 5.68/6.01 thf(fact_7906_lemma__tan__total,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ? [X3: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.68/6.01 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ord_less_real @ Y2 @ ( tan_real @ X3 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_tan_total
% 5.68/6.01 thf(fact_7907_tan__total,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ? [X3: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.68/6.01 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( tan_real @ X3 )
% 5.68/6.01 = Y2 )
% 5.68/6.01 & ! [Y4: real] :
% 5.68/6.01 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.68/6.01 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( tan_real @ Y4 )
% 5.68/6.01 = Y2 ) )
% 5.68/6.01 => ( Y4 = X3 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_total
% 5.68/6.01 thf(fact_7908_tan__monotone,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_monotone
% 5.68/6.01 thf(fact_7909_tan__monotone_H,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ X )
% 5.68/6.01 = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_monotone'
% 5.68/6.01 thf(fact_7910_tan__mono__lt__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_mono_lt_eq
% 5.68/6.01 thf(fact_7911_lemma__tan__total1,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ? [X3: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.68/6.01 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( tan_real @ X3 )
% 5.68/6.01 = Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_tan_total1
% 5.68/6.01 thf(fact_7912_tan__minus__45,axiom,
% 5.68/6.01 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.01 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_minus_45
% 5.68/6.01 thf(fact_7913_tan__inverse,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 5.68/6.01 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_inverse
% 5.68/6.01 thf(fact_7914_sum__atLeastAtMost__code,axiom,
% 5.68/6.01 ! [F: nat > complex,A: nat,B: nat] :
% 5.68/6.01 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.01 = ( set_fo1517530859248394432omplex
% 5.68/6.01 @ ^ [A4: nat] : ( plus_plus_complex @ ( F @ A4 ) )
% 5.68/6.01 @ A
% 5.68/6.01 @ B
% 5.68/6.01 @ zero_zero_complex ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_atLeastAtMost_code
% 5.68/6.01 thf(fact_7915_sum__atLeastAtMost__code,axiom,
% 5.68/6.01 ! [F: nat > rat,A: nat,B: nat] :
% 5.68/6.01 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.01 = ( set_fo1949268297981939178at_rat
% 5.68/6.01 @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 5.68/6.01 @ A
% 5.68/6.01 @ B
% 5.68/6.01 @ zero_zero_rat ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_atLeastAtMost_code
% 5.68/6.01 thf(fact_7916_sum__atLeastAtMost__code,axiom,
% 5.68/6.01 ! [F: nat > int,A: nat,B: nat] :
% 5.68/6.01 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.01 = ( set_fo2581907887559384638at_int
% 5.68/6.01 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.68/6.01 @ A
% 5.68/6.01 @ B
% 5.68/6.01 @ zero_zero_int ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_atLeastAtMost_code
% 5.68/6.01 thf(fact_7917_sum__atLeastAtMost__code,axiom,
% 5.68/6.01 ! [F: nat > nat,A: nat,B: nat] :
% 5.68/6.01 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.01 = ( set_fo2584398358068434914at_nat
% 5.68/6.01 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.68/6.01 @ A
% 5.68/6.01 @ B
% 5.68/6.01 @ zero_zero_nat ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_atLeastAtMost_code
% 5.68/6.01 thf(fact_7918_sum__atLeastAtMost__code,axiom,
% 5.68/6.01 ! [F: nat > real,A: nat,B: nat] :
% 5.68/6.01 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.01 = ( set_fo3111899725591712190t_real
% 5.68/6.01 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.68/6.01 @ A
% 5.68/6.01 @ B
% 5.68/6.01 @ zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % sum_atLeastAtMost_code
% 5.68/6.01 thf(fact_7919_add__tan__eq,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( ( cos_complex @ X )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ Y2 )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % add_tan_eq
% 5.68/6.01 thf(fact_7920_add__tan__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ Y2 )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 5.68/6.01 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % add_tan_eq
% 5.68/6.01 thf(fact_7921_termdiff__converges,axiom,
% 5.68/6.01 ! [X: real,K5: real,C: nat > real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 5.68/6.01 => ( ! [X3: real] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.68/6.01 => ( summable_real
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % termdiff_converges
% 5.68/6.01 thf(fact_7922_termdiff__converges,axiom,
% 5.68/6.01 ! [X: complex,K5: real,C: nat > complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 5.68/6.01 => ( ! [X3: complex] :
% 5.68/6.01 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X3 @ N2 ) ) ) )
% 5.68/6.01 => ( summable_complex
% 5.68/6.01 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % termdiff_converges
% 5.68/6.01 thf(fact_7923_tan__pos__pi2__le,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_pos_pi2_le
% 5.68/6.01 thf(fact_7924_tan__total__pos,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ? [X3: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.68/6.01 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( tan_real @ X3 )
% 5.68/6.01 = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_total_pos
% 5.68/6.01 thf(fact_7925_tan__less__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.01 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_less_zero
% 5.68/6.01 thf(fact_7926_tan__mono__le__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_mono_le_eq
% 5.68/6.01 thf(fact_7927_tan__mono__le,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_mono_le
% 5.68/6.01 thf(fact_7928_tan__bound__pi2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_bound_pi2
% 5.68/6.01 thf(fact_7929_arctan__unique,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ( tan_real @ X )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( ( arctan @ Y2 )
% 5.68/6.01 = X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_unique
% 5.68/6.01 thf(fact_7930_arctan__tan,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( arctan @ ( tan_real @ X ) )
% 5.68/6.01 = X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_tan
% 5.68/6.01 thf(fact_7931_arctan,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 5.68/6.01 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 & ( ( tan_real @ ( arctan @ Y2 ) )
% 5.68/6.01 = Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan
% 5.68/6.01 thf(fact_7932_tan__add,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( ( cos_complex @ X )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ Y2 )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_add
% 5.68/6.01 thf(fact_7933_tan__add,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ Y2 )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( tan_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.01 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_add
% 5.68/6.01 thf(fact_7934_tan__diff,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( ( cos_complex @ X )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ Y2 )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_diff
% 5.68/6.01 thf(fact_7935_tan__diff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ Y2 )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y2 ) )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( tan_real @ ( minus_minus_real @ X @ Y2 ) )
% 5.68/6.01 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_diff
% 5.68/6.01 thf(fact_7936_lemma__tan__add1,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( ( cos_complex @ X )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( ( cos_complex @ Y2 )
% 5.68/6.01 != zero_zero_complex )
% 5.68/6.01 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y2 ) ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_tan_add1
% 5.68/6.01 thf(fact_7937_lemma__tan__add1,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( cos_real @ X )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( ( cos_real @ Y2 )
% 5.68/6.01 != zero_zero_real )
% 5.68/6.01 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) )
% 5.68/6.01 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_tan_add1
% 5.68/6.01 thf(fact_7938_tan__total__pi4,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 => ? [Z3: real] :
% 5.68/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 5.68/6.01 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 & ( ( tan_real @ Z3 )
% 5.68/6.01 = X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_total_pi4
% 5.68/6.01 thf(fact_7939_fact__code,axiom,
% 5.68/6.01 ( semiri1406184849735516958ct_int
% 5.68/6.01 = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_code
% 5.68/6.01 thf(fact_7940_fact__code,axiom,
% 5.68/6.01 ( semiri773545260158071498ct_rat
% 5.68/6.01 = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_code
% 5.68/6.01 thf(fact_7941_fact__code,axiom,
% 5.68/6.01 ( semiri2265585572941072030t_real
% 5.68/6.01 = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_code
% 5.68/6.01 thf(fact_7942_fact__code,axiom,
% 5.68/6.01 ( semiri1408675320244567234ct_nat
% 5.68/6.01 = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % fact_code
% 5.68/6.01 thf(fact_7943_tan__half,axiom,
% 5.68/6.01 ( tan_complex
% 5.68/6.01 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_half
% 5.68/6.01 thf(fact_7944_tan__half,axiom,
% 5.68/6.01 ( tan_real
% 5.68/6.01 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_half
% 5.68/6.01 thf(fact_7945_in__measure,axiom,
% 5.68/6.01 ! [X: nat,Y2: nat,F: nat > nat] :
% 5.68/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ ( measure_nat @ F ) )
% 5.68/6.01 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % in_measure
% 5.68/6.01 thf(fact_7946_in__measure,axiom,
% 5.68/6.01 ! [X: int,Y2: int,F: int > nat] :
% 5.68/6.01 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y2 ) @ ( measure_int @ F ) )
% 5.68/6.01 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % in_measure
% 5.68/6.01 thf(fact_7947_complex__unimodular__polar,axiom,
% 5.68/6.01 ! [Z: complex] :
% 5.68/6.01 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 => ~ ! [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.01 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.01 => ( Z
% 5.68/6.01 != ( complex2 @ ( cos_real @ T4 ) @ ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complex_unimodular_polar
% 5.68/6.01 thf(fact_7948_Maclaurin__exp__lt,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( X != zero_zero_real )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ? [T4: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.68/6.01 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.01 & ( ( exp_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_exp_lt
% 5.68/6.01 thf(fact_7949_in__finite__psubset,axiom,
% 5.68/6.01 ! [A2: set_nat,B4: set_nat] :
% 5.68/6.01 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A2 @ B4 ) @ finite_psubset_nat )
% 5.68/6.01 = ( ( ord_less_set_nat @ A2 @ B4 )
% 5.68/6.01 & ( finite_finite_nat @ B4 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % in_finite_psubset
% 5.68/6.01 thf(fact_7950_in__finite__psubset,axiom,
% 5.68/6.01 ! [A2: set_int,B4: set_int] :
% 5.68/6.01 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A2 @ B4 ) @ finite_psubset_int )
% 5.68/6.01 = ( ( ord_less_set_int @ A2 @ B4 )
% 5.68/6.01 & ( finite_finite_int @ B4 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % in_finite_psubset
% 5.68/6.01 thf(fact_7951_in__finite__psubset,axiom,
% 5.68/6.01 ! [A2: set_complex,B4: set_complex] :
% 5.68/6.01 ( ( member351165363924911826omplex @ ( produc3790773574474814305omplex @ A2 @ B4 ) @ finite8643634255014194347omplex )
% 5.68/6.01 = ( ( ord_less_set_complex @ A2 @ B4 )
% 5.68/6.01 & ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % in_finite_psubset
% 5.68/6.01 thf(fact_7952_sin__tan,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( sin_real @ X )
% 5.68/6.01 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_tan
% 5.68/6.01 thf(fact_7953_real__sqrt__eq__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( sqrt @ X )
% 5.68/6.01 = ( sqrt @ Y2 ) )
% 5.68/6.01 = ( X = Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_eq_iff
% 5.68/6.01 thf(fact_7954_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( sqrt @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 = ( X = zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_eq_zero_cancel_iff
% 5.68/6.01 thf(fact_7955_real__sqrt__zero,axiom,
% 5.68/6.01 ( ( sqrt @ zero_zero_real )
% 5.68/6.01 = zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_zero
% 5.68/6.01 thf(fact_7956_real__sqrt__less__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ X @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_less_iff
% 5.68/6.01 thf(fact_7957_real__sqrt__le__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_le_iff
% 5.68/6.01 thf(fact_7958_real__sqrt__eq__1__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( sqrt @ X )
% 5.68/6.01 = one_one_real )
% 5.68/6.01 = ( X = one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_eq_1_iff
% 5.68/6.01 thf(fact_7959_real__sqrt__one,axiom,
% 5.68/6.01 ( ( sqrt @ one_one_real )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_one
% 5.68/6.01 thf(fact_7960_exp__le__cancel__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_le_cancel_iff
% 5.68/6.01 thf(fact_7961_real__sqrt__lt__0__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.68/6.01 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_lt_0_iff
% 5.68/6.01 thf(fact_7962_real__sqrt__gt__0__iff,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_gt_0_iff
% 5.68/6.01 thf(fact_7963_real__sqrt__ge__0__iff,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_0_iff
% 5.68/6.01 thf(fact_7964_real__sqrt__le__0__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.68/6.01 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_le_0_iff
% 5.68/6.01 thf(fact_7965_real__sqrt__lt__1__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.68/6.01 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_lt_1_iff
% 5.68/6.01 thf(fact_7966_real__sqrt__gt__1__iff,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_gt_1_iff
% 5.68/6.01 thf(fact_7967_real__sqrt__ge__1__iff,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_1_iff
% 5.68/6.01 thf(fact_7968_real__sqrt__le__1__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.68/6.01 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_le_1_iff
% 5.68/6.01 thf(fact_7969_real__sqrt__abs2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.68/6.01 = ( abs_abs_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_abs2
% 5.68/6.01 thf(fact_7970_real__sqrt__mult__self,axiom,
% 5.68/6.01 ! [A: real] :
% 5.68/6.01 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.68/6.01 = ( abs_abs_real @ A ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_mult_self
% 5.68/6.01 thf(fact_7971_real__sqrt__four,axiom,
% 5.68/6.01 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_four
% 5.68/6.01 thf(fact_7972_exp__le__one__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.68/6.01 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_le_one_iff
% 5.68/6.01 thf(fact_7973_one__le__exp__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.68/6.01 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % one_le_exp_iff
% 5.68/6.01 thf(fact_7974_real__sqrt__abs,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 = ( abs_abs_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_abs
% 5.68/6.01 thf(fact_7975_real__sqrt__pow2__iff,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = X )
% 5.68/6.01 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_pow2_iff
% 5.68/6.01 thf(fact_7976_real__sqrt__pow2,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = X ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_pow2
% 5.68/6.01 thf(fact_7977_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.68/6.01 ! [X: real,Y2: real,Xa2: real,Ya: real] :
% 5.68/6.01 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_mult_squared_eq
% 5.68/6.01 thf(fact_7978_real__sqrt__divide,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( sqrt @ ( divide_divide_real @ X @ Y2 ) )
% 5.68/6.01 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_divide
% 5.68/6.01 thf(fact_7979_real__sqrt__mult,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( sqrt @ ( times_times_real @ X @ Y2 ) )
% 5.68/6.01 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_mult
% 5.68/6.01 thf(fact_7980_real__sqrt__power,axiom,
% 5.68/6.01 ! [X: real,K: nat] :
% 5.68/6.01 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.68/6.01 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_power
% 5.68/6.01 thf(fact_7981_real__sqrt__minus,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_minus
% 5.68/6.01 thf(fact_7982_norm__exp,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % norm_exp
% 5.68/6.01 thf(fact_7983_norm__exp,axiom,
% 5.68/6.01 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % norm_exp
% 5.68/6.01 thf(fact_7984_real__sqrt__le__mono,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_le_mono
% 5.68/6.01 thf(fact_7985_real__sqrt__less__mono,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ X @ Y2 )
% 5.68/6.01 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_less_mono
% 5.68/6.01 thf(fact_7986_exp__times__arg__commute,axiom,
% 5.68/6.01 ! [A2: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.68/6.01 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_times_arg_commute
% 5.68/6.01 thf(fact_7987_exp__times__arg__commute,axiom,
% 5.68/6.01 ! [A2: real] :
% 5.68/6.01 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.68/6.01 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_times_arg_commute
% 5.68/6.01 thf(fact_7988_real__sqrt__gt__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_gt_zero
% 5.68/6.01 thf(fact_7989_real__sqrt__eq__zero__cancel,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ( sqrt @ X )
% 5.68/6.01 = zero_zero_real )
% 5.68/6.01 => ( X = zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_eq_zero_cancel
% 5.68/6.01 thf(fact_7990_real__sqrt__ge__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_zero
% 5.68/6.01 thf(fact_7991_not__exp__le__zero,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.68/6.01
% 5.68/6.01 % not_exp_le_zero
% 5.68/6.01 thf(fact_7992_exp__ge__zero,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_ge_zero
% 5.68/6.01 thf(fact_7993_real__sqrt__ge__one,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.01 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_one
% 5.68/6.01 thf(fact_7994_exp__add__commuting,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( ( times_times_complex @ X @ Y2 )
% 5.68/6.01 = ( times_times_complex @ Y2 @ X ) )
% 5.68/6.01 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.01 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_add_commuting
% 5.68/6.01 thf(fact_7995_exp__add__commuting,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( times_times_real @ X @ Y2 )
% 5.68/6.01 = ( times_times_real @ Y2 @ X ) )
% 5.68/6.01 => ( ( exp_real @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.01 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_add_commuting
% 5.68/6.01 thf(fact_7996_mult__exp__exp,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) )
% 5.68/6.01 = ( exp_complex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % mult_exp_exp
% 5.68/6.01 thf(fact_7997_mult__exp__exp,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 5.68/6.01 = ( exp_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % mult_exp_exp
% 5.68/6.01 thf(fact_7998_exp__diff,axiom,
% 5.68/6.01 ! [X: complex,Y2: complex] :
% 5.68/6.01 ( ( exp_complex @ ( minus_minus_complex @ X @ Y2 ) )
% 5.68/6.01 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_diff
% 5.68/6.01 thf(fact_7999_exp__diff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( exp_real @ ( minus_minus_real @ X @ Y2 ) )
% 5.68/6.01 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_diff
% 5.68/6.01 thf(fact_8000_Complex__eq__numeral,axiom,
% 5.68/6.01 ! [A: real,B: real,W: num] :
% 5.68/6.01 ( ( ( complex2 @ A @ B )
% 5.68/6.01 = ( numera6690914467698888265omplex @ W ) )
% 5.68/6.01 = ( ( A
% 5.68/6.01 = ( numeral_numeral_real @ W ) )
% 5.68/6.01 & ( B = zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Complex_eq_numeral
% 5.68/6.01 thf(fact_8001_complex__add,axiom,
% 5.68/6.01 ! [A: real,B: real,C: real,D: real] :
% 5.68/6.01 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.68/6.01 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complex_add
% 5.68/6.01 thf(fact_8002_complex__norm,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y2 ) )
% 5.68/6.01 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complex_norm
% 5.68/6.01 thf(fact_8003_real__div__sqrt,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.68/6.01 = ( sqrt @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_div_sqrt
% 5.68/6.01 thf(fact_8004_sqrt__add__le__add__sqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_add_le_add_sqrt
% 5.68/6.01 thf(fact_8005_exp__ge__add__one__self,axiom,
% 5.68/6.01 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_ge_add_one_self
% 5.68/6.01 thf(fact_8006_le__real__sqrt__sumsq,axiom,
% 5.68/6.01 ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % le_real_sqrt_sumsq
% 5.68/6.01 thf(fact_8007_exp__minus__inverse,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.68/6.01 = one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % exp_minus_inverse
% 5.68/6.01 thf(fact_8008_exp__minus__inverse,axiom,
% 5.68/6.01 ! [X: complex] :
% 5.68/6.01 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.68/6.01 = one_one_complex ) ).
% 5.68/6.01
% 5.68/6.01 % exp_minus_inverse
% 5.68/6.01 thf(fact_8009_exp__of__nat__mult,axiom,
% 5.68/6.01 ! [N: nat,X: complex] :
% 5.68/6.01 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 5.68/6.01 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_of_nat_mult
% 5.68/6.01 thf(fact_8010_exp__of__nat__mult,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 5.68/6.01 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_of_nat_mult
% 5.68/6.01 thf(fact_8011_exp__of__nat2__mult,axiom,
% 5.68/6.01 ! [X: complex,N: nat] :
% 5.68/6.01 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.68/6.01 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_of_nat2_mult
% 5.68/6.01 thf(fact_8012_exp__of__nat2__mult,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.01 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_of_nat2_mult
% 5.68/6.01 thf(fact_8013_Complex__eq__neg__numeral,axiom,
% 5.68/6.01 ! [A: real,B: real,W: num] :
% 5.68/6.01 ( ( ( complex2 @ A @ B )
% 5.68/6.01 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.01 = ( ( A
% 5.68/6.01 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.68/6.01 & ( B = zero_zero_real ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Complex_eq_neg_numeral
% 5.68/6.01 thf(fact_8014_complex__mult,axiom,
% 5.68/6.01 ! [A: real,B: real,C: real,D: real] :
% 5.68/6.01 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.68/6.01 = ( 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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % complex_mult
% 5.68/6.01 thf(fact_8015_sqrt2__less__2,axiom,
% 5.68/6.01 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt2_less_2
% 5.68/6.01 thf(fact_8016_exp__ge__add__one__self__aux,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_ge_add_one_self_aux
% 5.68/6.01 thf(fact_8017_lemma__exp__total,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ one_one_real @ Y2 )
% 5.68/6.01 => ? [X3: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.68/6.01 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y2 @ one_one_real ) )
% 5.68/6.01 & ( ( exp_real @ X3 )
% 5.68/6.01 = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_exp_total
% 5.68/6.01 thf(fact_8018_ln__ge__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X ) )
% 5.68/6.01 = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % ln_ge_iff
% 5.68/6.01 thf(fact_8019_ln__x__over__x__mono,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y2 ) @ Y2 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % ln_x_over_x_mono
% 5.68/6.01 thf(fact_8020_real__less__rsqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.68/6.01 => ( ord_less_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_less_rsqrt
% 5.68/6.01 thf(fact_8021_real__le__rsqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_le_rsqrt
% 5.68/6.01 thf(fact_8022_sqrt__le__D,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_le_D
% 5.68/6.01 thf(fact_8023_exp__le,axiom,
% 5.68/6.01 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_le
% 5.68/6.01 thf(fact_8024_tan__60,axiom,
% 5.68/6.01 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.68/6.01 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_60
% 5.68/6.01 thf(fact_8025_exp__divide__power__eq,axiom,
% 5.68/6.01 ! [N: nat,X: complex] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.68/6.01 = ( exp_complex @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_divide_power_eq
% 5.68/6.01 thf(fact_8026_exp__divide__power__eq,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.68/6.01 = ( exp_real @ X ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_divide_power_eq
% 5.68/6.01 thf(fact_8027_tanh__altdef,axiom,
% 5.68/6.01 ( tanh_real
% 5.68/6.01 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tanh_altdef
% 5.68/6.01 thf(fact_8028_tanh__altdef,axiom,
% 5.68/6.01 ( tanh_complex
% 5.68/6.01 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tanh_altdef
% 5.68/6.01 thf(fact_8029_real__sqrt__unique,axiom,
% 5.68/6.01 ! [Y2: real,X: real] :
% 5.68/6.01 ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.01 = X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( sqrt @ X )
% 5.68/6.01 = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_unique
% 5.68/6.01 thf(fact_8030_real__le__lsqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_le_lsqrt
% 5.68/6.01 thf(fact_8031_lemma__real__divide__sqrt__less,axiom,
% 5.68/6.01 ! [U: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ U )
% 5.68/6.01 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.68/6.01
% 5.68/6.01 % lemma_real_divide_sqrt_less
% 5.68/6.01 thf(fact_8032_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = Y2 )
% 5.68/6.01 => ( X = zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_eq_cancel2
% 5.68/6.01 thf(fact_8033_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = X )
% 5.68/6.01 => ( Y2 = zero_zero_real ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_eq_cancel
% 5.68/6.01 thf(fact_8034_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_triangle_ineq
% 5.68/6.01 thf(fact_8035_real__sqrt__sum__squares__ge2,axiom,
% 5.68/6.01 ! [Y2: real,X: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_ge2
% 5.68/6.01 thf(fact_8036_real__sqrt__sum__squares__ge1,axiom,
% 5.68/6.01 ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_ge1
% 5.68/6.01 thf(fact_8037_exp__half__le2,axiom,
% 5.68/6.01 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_half_le2
% 5.68/6.01 thf(fact_8038_sqrt__ge__absD,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y2 ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_ge_absD
% 5.68/6.01 thf(fact_8039_cos__45,axiom,
% 5.68/6.01 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_45
% 5.68/6.01 thf(fact_8040_sin__45,axiom,
% 5.68/6.01 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_45
% 5.68/6.01 thf(fact_8041_exp__double,axiom,
% 5.68/6.01 ! [Z: complex] :
% 5.68/6.01 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.68/6.01 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_double
% 5.68/6.01 thf(fact_8042_exp__double,axiom,
% 5.68/6.01 ! [Z: real] :
% 5.68/6.01 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.68/6.01 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_double
% 5.68/6.01 thf(fact_8043_real__less__lsqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ( ord_less_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_less_lsqrt
% 5.68/6.01 thf(fact_8044_sqrt__sum__squares__le__sum,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_sum_squares_le_sum
% 5.68/6.01 thf(fact_8045_tan__30,axiom,
% 5.68/6.01 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tan_30
% 5.68/6.01 thf(fact_8046_sqrt__even__pow2,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.01 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.01 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_even_pow2
% 5.68/6.01 thf(fact_8047_sqrt__sum__squares__le__sum__abs,axiom,
% 5.68/6.01 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_sum_squares_le_sum_abs
% 5.68/6.01 thf(fact_8048_real__sqrt__ge__abs2,axiom,
% 5.68/6.01 ! [Y2: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_abs2
% 5.68/6.01 thf(fact_8049_real__sqrt__ge__abs1,axiom,
% 5.68/6.01 ! [X: real,Y2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_ge_abs1
% 5.68/6.01 thf(fact_8050_ln__sqrt,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.68/6.01 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % ln_sqrt
% 5.68/6.01 thf(fact_8051_cos__30,axiom,
% 5.68/6.01 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_30
% 5.68/6.01 thf(fact_8052_sin__60,axiom,
% 5.68/6.01 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.68/6.01 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_60
% 5.68/6.01 thf(fact_8053_exp__bound__half,axiom,
% 5.68/6.01 ! [Z: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_bound_half
% 5.68/6.01 thf(fact_8054_exp__bound__half,axiom,
% 5.68/6.01 ! [Z: complex] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_bound_half
% 5.68/6.01 thf(fact_8055_arsinh__real__aux,axiom,
% 5.68/6.01 ! [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 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arsinh_real_aux
% 5.68/6.01 thf(fact_8056_exp__bound,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.01 => ( 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 ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_bound
% 5.68/6.01 thf(fact_8057_real__sqrt__power__even,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 5.68/6.01 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_power_even
% 5.68/6.01 thf(fact_8058_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.68/6.01 ! [X: real,Y2: real,Xa2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_mult_ge_zero
% 5.68/6.01 thf(fact_8059_arith__geo__mean__sqrt,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arith_geo_mean_sqrt
% 5.68/6.01 thf(fact_8060_real__exp__bound__lemma,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_exp_bound_lemma
% 5.68/6.01 thf(fact_8061_cos__x__y__le__one,axiom,
% 5.68/6.01 ! [X: real,Y2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.68/6.01
% 5.68/6.01 % cos_x_y_le_one
% 5.68/6.01 thf(fact_8062_real__sqrt__sum__squares__less,axiom,
% 5.68/6.01 ! [X: real,U: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.01 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % real_sqrt_sum_squares_less
% 5.68/6.01 thf(fact_8063_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.68/6.01 ! [N: nat,X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_ge_one_plus_x_over_n_power_n
% 5.68/6.01 thf(fact_8064_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_ge_one_minus_x_over_n_power_n
% 5.68/6.01 thf(fact_8065_cos__arctan,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( cos_real @ ( arctan @ X ) )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_arctan
% 5.68/6.01 thf(fact_8066_sin__arctan,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( sin_real @ ( arctan @ X ) )
% 5.68/6.01 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_arctan
% 5.68/6.01 thf(fact_8067_exp__bound__lemma,axiom,
% 5.68/6.01 ! [Z: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_bound_lemma
% 5.68/6.01 thf(fact_8068_exp__bound__lemma,axiom,
% 5.68/6.01 ! [Z: complex] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_bound_lemma
% 5.68/6.01 thf(fact_8069_Maclaurin__exp__le,axiom,
% 5.68/6.01 ! [X: real,N: nat] :
% 5.68/6.01 ? [T4: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.01 & ( ( exp_real @ X )
% 5.68/6.01 = ( plus_plus_real
% 5.68/6.01 @ ( groups6591440286371151544t_real
% 5.68/6.01 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.68/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.01 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Maclaurin_exp_le
% 5.68/6.01 thf(fact_8070_sqrt__sum__squares__half__less,axiom,
% 5.68/6.01 ! [X: real,U: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.01 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sqrt_sum_squares_half_less
% 5.68/6.01 thf(fact_8071_exp__lower__Taylor__quadratic,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.01 => ( 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 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % exp_lower_Taylor_quadratic
% 5.68/6.01 thf(fact_8072_sin__cos__sqrt,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.68/6.01 => ( ( sin_real @ X )
% 5.68/6.01 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_cos_sqrt
% 5.68/6.01 thf(fact_8073_arctan__half,axiom,
% 5.68/6.01 ( arctan
% 5.68/6.01 = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arctan_half
% 5.68/6.01 thf(fact_8074_tanh__real__altdef,axiom,
% 5.68/6.01 ( tanh_real
% 5.68/6.01 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % tanh_real_altdef
% 5.68/6.01 thf(fact_8075_cos__tan,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.01 => ( ( cos_real @ X )
% 5.68/6.01 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_tan
% 5.68/6.01 thf(fact_8076_arcosh__real__def,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.01 => ( ( arcosh_real @ X )
% 5.68/6.01 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcosh_real_def
% 5.68/6.01 thf(fact_8077_arsinh__real__def,axiom,
% 5.68/6.01 ( arsinh_real
% 5.68/6.01 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arsinh_real_def
% 5.68/6.01 thf(fact_8078_binomial__code,axiom,
% 5.68/6.01 ( binomial
% 5.68/6.01 = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_code
% 5.68/6.01 thf(fact_8079_cos__arcsin,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.01 => ( ( cos_real @ ( arcsin @ X ) )
% 5.68/6.01 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_arcsin
% 5.68/6.01 thf(fact_8080_sin__arccos__abs,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.01 => ( ( sin_real @ ( arccos @ Y2 ) )
% 5.68/6.01 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_arccos_abs
% 5.68/6.01 thf(fact_8081_binomial__Suc__n,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( binomial @ ( suc @ N ) @ N )
% 5.68/6.01 = ( suc @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_Suc_n
% 5.68/6.01 thf(fact_8082_binomial__1,axiom,
% 5.68/6.01 ! [N: nat] :
% 5.68/6.01 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.01 = N ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_1
% 5.68/6.01 thf(fact_8083_binomial__0__Suc,axiom,
% 5.68/6.01 ! [K: nat] :
% 5.68/6.01 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.68/6.01 = zero_zero_nat ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_0_Suc
% 5.68/6.01 thf(fact_8084_binomial__eq__0__iff,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( ( binomial @ N @ K )
% 5.68/6.01 = zero_zero_nat )
% 5.68/6.01 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_eq_0_iff
% 5.68/6.01 thf(fact_8085_binomial__Suc__Suc,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.68/6.01 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_Suc_Suc
% 5.68/6.01 thf(fact_8086_zero__less__binomial__iff,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.68/6.01 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % zero_less_binomial_iff
% 5.68/6.01 thf(fact_8087_cos__arccos,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ( cos_real @ ( arccos @ Y2 ) )
% 5.68/6.01 = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % cos_arccos
% 5.68/6.01 thf(fact_8088_sin__arcsin,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.68/6.01 = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % sin_arcsin
% 5.68/6.01 thf(fact_8089_arccos__0,axiom,
% 5.68/6.01 ( ( arccos @ zero_zero_real )
% 5.68/6.01 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_0
% 5.68/6.01 thf(fact_8090_arcsin__1,axiom,
% 5.68/6.01 ( ( arcsin @ one_one_real )
% 5.68/6.01 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_1
% 5.68/6.01 thf(fact_8091_arcsin__minus__1,axiom,
% 5.68/6.01 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_minus_1
% 5.68/6.01 thf(fact_8092_binomial__eq__0,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( ord_less_nat @ N @ K )
% 5.68/6.01 => ( ( binomial @ N @ K )
% 5.68/6.01 = zero_zero_nat ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_eq_0
% 5.68/6.01 thf(fact_8093_Suc__times__binomial__eq,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.68/6.01 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Suc_times_binomial_eq
% 5.68/6.01 thf(fact_8094_Suc__times__binomial,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.68/6.01 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Suc_times_binomial
% 5.68/6.01 thf(fact_8095_binomial__symmetric,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( ( binomial @ N @ K )
% 5.68/6.01 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_symmetric
% 5.68/6.01 thf(fact_8096_choose__mult__lemma,axiom,
% 5.68/6.01 ! [M: nat,R2: nat,K: nat] :
% 5.68/6.01 ( ( 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 ) )
% 5.68/6.01 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_mult_lemma
% 5.68/6.01 thf(fact_8097_binomial__le__pow,axiom,
% 5.68/6.01 ! [R2: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ R2 @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_le_pow
% 5.68/6.01 thf(fact_8098_zero__less__binomial,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % zero_less_binomial
% 5.68/6.01 thf(fact_8099_Suc__times__binomial__add,axiom,
% 5.68/6.01 ! [A: nat,B: nat] :
% 5.68/6.01 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.68/6.01 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % Suc_times_binomial_add
% 5.68/6.01 thf(fact_8100_binomial__Suc__Suc__eq__times,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.68/6.01 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_Suc_Suc_eq_times
% 5.68/6.01 thf(fact_8101_choose__mult,axiom,
% 5.68/6.01 ! [K: nat,M: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ M )
% 5.68/6.01 => ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.01 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.68/6.01 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_mult
% 5.68/6.01 thf(fact_8102_binomial__absorb__comp,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.68/6.01 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_absorb_comp
% 5.68/6.01 thf(fact_8103_arccos__le__arccos,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_le_arccos
% 5.68/6.01 thf(fact_8104_arccos__le__mono,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_le_mono
% 5.68/6.01 thf(fact_8105_arccos__eq__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 & ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real ) )
% 5.68/6.01 => ( ( ( arccos @ X )
% 5.68/6.01 = ( arccos @ Y2 ) )
% 5.68/6.01 = ( X = Y2 ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_eq_iff
% 5.68/6.01 thf(fact_8106_arcsin__le__arcsin,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_le_arcsin
% 5.68/6.01 thf(fact_8107_arcsin__minus,axiom,
% 5.68/6.01 ! [X: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.01 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.68/6.01 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_minus
% 5.68/6.01 thf(fact_8108_arcsin__le__mono,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 5.68/6.01 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_le_mono
% 5.68/6.01 thf(fact_8109_arcsin__eq__iff,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.01 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.01 => ( ( ( arcsin @ X )
% 5.68/6.01 = ( arcsin @ Y2 ) )
% 5.68/6.01 = ( X = Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arcsin_eq_iff
% 5.68/6.01 thf(fact_8110_binomial__absorption,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.68/6.01 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_absorption
% 5.68/6.01 thf(fact_8111_binomial__fact__lemma,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.68/6.01 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_fact_lemma
% 5.68/6.01 thf(fact_8112_binomial__ge__n__over__k__pow__k,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_ge_n_over_k_pow_k
% 5.68/6.01 thf(fact_8113_binomial__ge__n__over__k__pow__k,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.01 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_ge_n_over_k_pow_k
% 5.68/6.01 thf(fact_8114_binomial__mono,axiom,
% 5.68/6.01 ! [K: nat,K6: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ K6 )
% 5.68/6.01 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_mono
% 5.68/6.01 thf(fact_8115_binomial__maximum_H,axiom,
% 5.68/6.01 ! [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 ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_maximum'
% 5.68/6.01 thf(fact_8116_binomial__maximum,axiom,
% 5.68/6.01 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_maximum
% 5.68/6.01 thf(fact_8117_binomial__antimono,axiom,
% 5.68/6.01 ! [K: nat,K6: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_eq_nat @ K @ K6 )
% 5.68/6.01 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.68/6.01 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.68/6.01 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_antimono
% 5.68/6.01 thf(fact_8118_binomial__le__pow2,axiom,
% 5.68/6.01 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.01
% 5.68/6.01 % binomial_le_pow2
% 5.68/6.01 thf(fact_8119_arccos__lbound,axiom,
% 5.68/6.01 ! [Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_lbound
% 5.68/6.01 thf(fact_8120_arccos__less__arccos,axiom,
% 5.68/6.01 ! [X: real,Y2: real] :
% 5.68/6.01 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.01 => ( ( ord_less_real @ X @ Y2 )
% 5.68/6.01 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.01 => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % arccos_less_arccos
% 5.68/6.01 thf(fact_8121_choose__reduce__nat,axiom,
% 5.68/6.01 ! [N: nat,K: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.01 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.01 => ( ( binomial @ N @ K )
% 5.68/6.01 = ( 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 ) ) ) ) ) ).
% 5.68/6.01
% 5.68/6.01 % choose_reduce_nat
% 5.68/6.01 thf(fact_8122_times__binomial__minus1__eq,axiom,
% 5.68/6.01 ! [K: nat,N: nat] :
% 5.68/6.01 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.01 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.68/6.01 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % times_binomial_minus1_eq
% 5.68/6.02 thf(fact_8123_arccos__less__mono,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.02 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 5.68/6.02 = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_less_mono
% 5.68/6.02 thf(fact_8124_arccos__ubound,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_ubound
% 5.68/6.02 thf(fact_8125_arccos__cos,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.02 => ( ( arccos @ ( cos_real @ X ) )
% 5.68/6.02 = X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_cos
% 5.68/6.02 thf(fact_8126_arcsin__less__arcsin,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.02 => ( ( ord_less_real @ X @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_less_arcsin
% 5.68/6.02 thf(fact_8127_arcsin__less__mono,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.02 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 5.68/6.02 = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_less_mono
% 5.68/6.02 thf(fact_8128_cos__arccos__abs,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 5.68/6.02 => ( ( cos_real @ ( arccos @ Y2 ) )
% 5.68/6.02 = Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % cos_arccos_abs
% 5.68/6.02 thf(fact_8129_arccos__cos__eq__abs,axiom,
% 5.68/6.02 ! [Theta: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.68/6.02 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.68/6.02 = ( abs_abs_real @ Theta ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_cos_eq_abs
% 5.68/6.02 thf(fact_8130_binomial__altdef__nat,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( binomial @ N @ K )
% 5.68/6.02 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_altdef_nat
% 5.68/6.02 thf(fact_8131_binomial__less__binomial__Suc,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.02 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_less_binomial_Suc
% 5.68/6.02 thf(fact_8132_binomial__strict__mono,axiom,
% 5.68/6.02 ! [K: nat,K6: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K @ K6 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.68/6.02 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_strict_mono
% 5.68/6.02 thf(fact_8133_binomial__strict__antimono,axiom,
% 5.68/6.02 ! [K: nat,K6: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K @ K6 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.68/6.02 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_strict_antimono
% 5.68/6.02 thf(fact_8134_central__binomial__odd,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.02 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.02 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % central_binomial_odd
% 5.68/6.02 thf(fact_8135_binomial__addition__formula,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( binomial @ N @ ( suc @ K ) )
% 5.68/6.02 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_addition_formula
% 5.68/6.02 thf(fact_8136_binomial__fact,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.68/6.02 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_fact
% 5.68/6.02 thf(fact_8137_binomial__fact,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.68/6.02 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_fact
% 5.68/6.02 thf(fact_8138_binomial__fact,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.68/6.02 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_fact
% 5.68/6.02 thf(fact_8139_fact__binomial,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.68/6.02 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_binomial
% 5.68/6.02 thf(fact_8140_fact__binomial,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.68/6.02 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_binomial
% 5.68/6.02 thf(fact_8141_fact__binomial,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.68/6.02 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_binomial
% 5.68/6.02 thf(fact_8142_arccos__bounded,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_bounded
% 5.68/6.02 thf(fact_8143_arccos__cos2,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.68/6.02 => ( ( arccos @ ( cos_real @ X ) )
% 5.68/6.02 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_cos2
% 5.68/6.02 thf(fact_8144_arccos__minus,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.02 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.68/6.02 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_minus
% 5.68/6.02 thf(fact_8145_choose__two,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.02 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_two
% 5.68/6.02 thf(fact_8146_arccos,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi )
% 5.68/6.02 & ( ( cos_real @ ( arccos @ Y2 ) )
% 5.68/6.02 = Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos
% 5.68/6.02 thf(fact_8147_arccos__minus__abs,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.02 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.68/6.02 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_minus_abs
% 5.68/6.02 thf(fact_8148_arccos__le__pi2,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_le_pi2
% 5.68/6.02 thf(fact_8149_arcsin__lt__bounded,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.68/6.02 & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_lt_bounded
% 5.68/6.02 thf(fact_8150_arcsin__lbound,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_lbound
% 5.68/6.02 thf(fact_8151_arcsin__ubound,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_ubound
% 5.68/6.02 thf(fact_8152_arcsin__bounded,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_bounded
% 5.68/6.02 thf(fact_8153_arcsin__sin,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.02 => ( ( arcsin @ ( sin_real @ X ) )
% 5.68/6.02 = X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_sin
% 5.68/6.02 thf(fact_8154_arcsin,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.02 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.68/6.02 = Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin
% 5.68/6.02 thf(fact_8155_arcsin__pi,axiom,
% 5.68/6.02 ! [Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 5.68/6.02 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 5.68/6.02 = Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_pi
% 5.68/6.02 thf(fact_8156_arcsin__le__iff,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y2 )
% 5.68/6.02 = ( ord_less_eq_real @ X @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arcsin_le_iff
% 5.68/6.02 thf(fact_8157_le__arcsin__iff,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.02 => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X ) )
% 5.68/6.02 = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % le_arcsin_iff
% 5.68/6.02 thf(fact_8158_arccos__cos__eq__abs__2pi,axiom,
% 5.68/6.02 ! [Theta: real] :
% 5.68/6.02 ~ ! [K2: int] :
% 5.68/6.02 ( ( arccos @ ( cos_real @ Theta ) )
% 5.68/6.02 != ( 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 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % arccos_cos_eq_abs_2pi
% 5.68/6.02 thf(fact_8159_central__binomial__lower__bound,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( 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 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % central_binomial_lower_bound
% 5.68/6.02 thf(fact_8160_sin__arccos,axiom,
% 5.68/6.02 ! [X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.02 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.02 => ( ( sin_real @ ( arccos @ X ) )
% 5.68/6.02 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sin_arccos
% 5.68/6.02 thf(fact_8161_choose__even__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) @ zero_zero_complex )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_even_sum
% 5.68/6.02 thf(fact_8162_choose__even__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) @ zero_zero_int )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_even_sum
% 5.68/6.02 thf(fact_8163_choose__even__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) @ zero_zero_rat )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_even_sum
% 5.68/6.02 thf(fact_8164_choose__even__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) @ zero_zero_real )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_even_sum
% 5.68/6.02 thf(fact_8165_choose__odd__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] :
% 5.68/6.02 ( if_complex
% 5.68/6.02 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.02 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) )
% 5.68/6.02 @ zero_zero_complex )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_odd_sum
% 5.68/6.02 thf(fact_8166_choose__odd__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] :
% 5.68/6.02 ( if_int
% 5.68/6.02 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.02 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) )
% 5.68/6.02 @ zero_zero_int )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_odd_sum
% 5.68/6.02 thf(fact_8167_choose__odd__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] :
% 5.68/6.02 ( if_rat
% 5.68/6.02 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.02 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) )
% 5.68/6.02 @ zero_zero_rat )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_odd_sum
% 5.68/6.02 thf(fact_8168_choose__odd__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] :
% 5.68/6.02 ( if_real
% 5.68/6.02 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.68/6.02 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) )
% 5.68/6.02 @ zero_zero_real )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_odd_sum
% 5.68/6.02 thf(fact_8169_pochhammer__double,axiom,
% 5.68/6.02 ! [Z: complex,N: nat] :
% 5.68/6.02 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_double
% 5.68/6.02 thf(fact_8170_pochhammer__double,axiom,
% 5.68/6.02 ! [Z: real,N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_double
% 5.68/6.02 thf(fact_8171_pochhammer__double,axiom,
% 5.68/6.02 ! [Z: rat,N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_double
% 5.68/6.02 thf(fact_8172_of__nat__code,axiom,
% 5.68/6.02 ( semiri8010041392384452111omplex
% 5.68/6.02 = ( ^ [N2: nat] :
% 5.68/6.02 ( semiri2816024913162550771omplex
% 5.68/6.02 @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 5.68/6.02 @ N2
% 5.68/6.02 @ zero_zero_complex ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_code
% 5.68/6.02 thf(fact_8173_of__nat__code,axiom,
% 5.68/6.02 ( semiri1314217659103216013at_int
% 5.68/6.02 = ( ^ [N2: nat] :
% 5.68/6.02 ( semiri8420488043553186161ux_int
% 5.68/6.02 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 5.68/6.02 @ N2
% 5.68/6.02 @ zero_zero_int ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_code
% 5.68/6.02 thf(fact_8174_of__nat__code,axiom,
% 5.68/6.02 ( semiri5074537144036343181t_real
% 5.68/6.02 = ( ^ [N2: nat] :
% 5.68/6.02 ( semiri7260567687927622513x_real
% 5.68/6.02 @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 5.68/6.02 @ N2
% 5.68/6.02 @ zero_zero_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_code
% 5.68/6.02 thf(fact_8175_of__nat__code,axiom,
% 5.68/6.02 ( semiri1316708129612266289at_nat
% 5.68/6.02 = ( ^ [N2: nat] :
% 5.68/6.02 ( semiri8422978514062236437ux_nat
% 5.68/6.02 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 5.68/6.02 @ N2
% 5.68/6.02 @ zero_zero_nat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_code
% 5.68/6.02 thf(fact_8176_of__nat__code,axiom,
% 5.68/6.02 ( semiri681578069525770553at_rat
% 5.68/6.02 = ( ^ [N2: nat] :
% 5.68/6.02 ( semiri7787848453975740701ux_rat
% 5.68/6.02 @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 5.68/6.02 @ N2
% 5.68/6.02 @ zero_zero_rat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_code
% 5.68/6.02 thf(fact_8177_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.68/6.02 ! [X: vEBT_VEBT,Y2: $o] :
% 5.68/6.02 ( ( ( vEBT_VEBT_minNull @ X )
% 5.68/6.02 = Y2 )
% 5.68/6.02 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.68/6.02 => ( ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ $false @ $false ) )
% 5.68/6.02 => ( Y2
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.68/6.02 => ( ! [Uv2: $o] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.68/6.02 => ( ~ Y2
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.68/6.02 => ( ! [Uu3: $o] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.68/6.02 => ( ~ Y2
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu3 @ $true ) ) ) )
% 5.68/6.02 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.68/6.02 => ( Y2
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.68/6.02 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.68/6.02 => ( ~ Y2
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % VEBT_internal.minNull.pelims(1)
% 5.68/6.02 thf(fact_8178_atMost__iff,axiom,
% 5.68/6.02 ! [I2: real,K: real] :
% 5.68/6.02 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.68/6.02 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8179_atMost__iff,axiom,
% 5.68/6.02 ! [I2: set_int,K: set_int] :
% 5.68/6.02 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 5.68/6.02 = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8180_atMost__iff,axiom,
% 5.68/6.02 ! [I2: rat,K: rat] :
% 5.68/6.02 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.68/6.02 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8181_atMost__iff,axiom,
% 5.68/6.02 ! [I2: num,K: num] :
% 5.68/6.02 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.68/6.02 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8182_atMost__iff,axiom,
% 5.68/6.02 ! [I2: nat,K: nat] :
% 5.68/6.02 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.68/6.02 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8183_atMost__iff,axiom,
% 5.68/6.02 ! [I2: int,K: int] :
% 5.68/6.02 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.68/6.02 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_iff
% 5.68/6.02 thf(fact_8184_atMost__subset__iff,axiom,
% 5.68/6.02 ! [X: set_int,Y2: set_int] :
% 5.68/6.02 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X ) @ ( set_or58775011639299419et_int @ Y2 ) )
% 5.68/6.02 = ( ord_less_eq_set_int @ X @ Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_subset_iff
% 5.68/6.02 thf(fact_8185_atMost__subset__iff,axiom,
% 5.68/6.02 ! [X: rat,Y2: rat] :
% 5.68/6.02 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y2 ) )
% 5.68/6.02 = ( ord_less_eq_rat @ X @ Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_subset_iff
% 5.68/6.02 thf(fact_8186_atMost__subset__iff,axiom,
% 5.68/6.02 ! [X: num,Y2: num] :
% 5.68/6.02 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y2 ) )
% 5.68/6.02 = ( ord_less_eq_num @ X @ Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_subset_iff
% 5.68/6.02 thf(fact_8187_atMost__subset__iff,axiom,
% 5.68/6.02 ! [X: nat,Y2: nat] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y2 ) )
% 5.68/6.02 = ( ord_less_eq_nat @ X @ Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_subset_iff
% 5.68/6.02 thf(fact_8188_atMost__subset__iff,axiom,
% 5.68/6.02 ! [X: int,Y2: int] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y2 ) )
% 5.68/6.02 = ( ord_less_eq_int @ X @ Y2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_subset_iff
% 5.68/6.02 thf(fact_8189_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: set_int,H2: set_int,H3: set_int] :
% 5.68/6.02 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L2 @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8190_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: rat,H2: rat,H3: rat] :
% 5.68/6.02 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L2 @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8191_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: num,H2: num,H3: num] :
% 5.68/6.02 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8192_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: nat,H2: nat,H3: nat] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8193_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: int,H2: int,H3: int] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8194_Icc__subset__Iic__iff,axiom,
% 5.68/6.02 ! [L2: real,H2: real,H3: real] :
% 5.68/6.02 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.68/6.02 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.68/6.02 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Icc_subset_Iic_iff
% 5.68/6.02 thf(fact_8195_sum_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc
% 5.68/6.02 thf(fact_8196_sum_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc
% 5.68/6.02 thf(fact_8197_sum_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc
% 5.68/6.02 thf(fact_8198_sum_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc
% 5.68/6.02 thf(fact_8199_atMost__def,axiom,
% 5.68/6.02 ( set_ord_atMost_real
% 5.68/6.02 = ( ^ [U2: real] :
% 5.68/6.02 ( collect_real
% 5.68/6.02 @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8200_atMost__def,axiom,
% 5.68/6.02 ( set_or58775011639299419et_int
% 5.68/6.02 = ( ^ [U2: set_int] :
% 5.68/6.02 ( collect_set_int
% 5.68/6.02 @ ^ [X2: set_int] : ( ord_less_eq_set_int @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8201_atMost__def,axiom,
% 5.68/6.02 ( set_ord_atMost_rat
% 5.68/6.02 = ( ^ [U2: rat] :
% 5.68/6.02 ( collect_rat
% 5.68/6.02 @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8202_atMost__def,axiom,
% 5.68/6.02 ( set_ord_atMost_num
% 5.68/6.02 = ( ^ [U2: num] :
% 5.68/6.02 ( collect_num
% 5.68/6.02 @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8203_atMost__def,axiom,
% 5.68/6.02 ( set_ord_atMost_nat
% 5.68/6.02 = ( ^ [U2: nat] :
% 5.68/6.02 ( collect_nat
% 5.68/6.02 @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8204_atMost__def,axiom,
% 5.68/6.02 ( set_ord_atMost_int
% 5.68/6.02 = ( ^ [U2: int] :
% 5.68/6.02 ( collect_int
% 5.68/6.02 @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % atMost_def
% 5.68/6.02 thf(fact_8205_lessThan__Suc__atMost,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.68/6.02 = ( set_ord_atMost_nat @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % lessThan_Suc_atMost
% 5.68/6.02 thf(fact_8206_pochhammer__pos,axiom,
% 5.68/6.02 ! [X: real,N: nat] :
% 5.68/6.02 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.02 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_pos
% 5.68/6.02 thf(fact_8207_pochhammer__pos,axiom,
% 5.68/6.02 ! [X: rat,N: nat] :
% 5.68/6.02 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.68/6.02 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_pos
% 5.68/6.02 thf(fact_8208_pochhammer__pos,axiom,
% 5.68/6.02 ! [X: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.02 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_pos
% 5.68/6.02 thf(fact_8209_pochhammer__pos,axiom,
% 5.68/6.02 ! [X: int,N: nat] :
% 5.68/6.02 ( ( ord_less_int @ zero_zero_int @ X )
% 5.68/6.02 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_pos
% 5.68/6.02 thf(fact_8210_pochhammer__eq__0__mono,axiom,
% 5.68/6.02 ! [A: complex,N: nat,M: nat] :
% 5.68/6.02 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.68/6.02 = zero_zero_complex )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.68/6.02 = zero_zero_complex ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_mono
% 5.68/6.02 thf(fact_8211_pochhammer__eq__0__mono,axiom,
% 5.68/6.02 ! [A: real,N: nat,M: nat] :
% 5.68/6.02 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.68/6.02 = zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.68/6.02 = zero_zero_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_mono
% 5.68/6.02 thf(fact_8212_pochhammer__eq__0__mono,axiom,
% 5.68/6.02 ! [A: rat,N: nat,M: nat] :
% 5.68/6.02 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.68/6.02 = zero_zero_rat )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.68/6.02 = zero_zero_rat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_mono
% 5.68/6.02 thf(fact_8213_pochhammer__neq__0__mono,axiom,
% 5.68/6.02 ! [A: complex,M: nat,N: nat] :
% 5.68/6.02 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.68/6.02 != zero_zero_complex )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.68/6.02 != zero_zero_complex ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_neq_0_mono
% 5.68/6.02 thf(fact_8214_pochhammer__neq__0__mono,axiom,
% 5.68/6.02 ! [A: real,M: nat,N: nat] :
% 5.68/6.02 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.68/6.02 != zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.68/6.02 != zero_zero_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_neq_0_mono
% 5.68/6.02 thf(fact_8215_pochhammer__neq__0__mono,axiom,
% 5.68/6.02 ! [A: rat,M: nat,N: nat] :
% 5.68/6.02 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.68/6.02 != zero_zero_rat )
% 5.68/6.02 => ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.02 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.68/6.02 != zero_zero_rat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_neq_0_mono
% 5.68/6.02 thf(fact_8216_not__Iic__le__Icc,axiom,
% 5.68/6.02 ! [H2: int,L3: int,H3: int] :
% 5.68/6.02 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.68/6.02
% 5.68/6.02 % not_Iic_le_Icc
% 5.68/6.02 thf(fact_8217_not__Iic__le__Icc,axiom,
% 5.68/6.02 ! [H2: real,L3: real,H3: real] :
% 5.68/6.02 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.68/6.02
% 5.68/6.02 % not_Iic_le_Icc
% 5.68/6.02 thf(fact_8218_finite__nat__iff__bounded__le,axiom,
% 5.68/6.02 ( finite_finite_nat
% 5.68/6.02 = ( ^ [S4: set_nat] :
% 5.68/6.02 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % finite_nat_iff_bounded_le
% 5.68/6.02 thf(fact_8219_pochhammer__nonneg,axiom,
% 5.68/6.02 ! [X: real,N: nat] :
% 5.68/6.02 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.02 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_nonneg
% 5.68/6.02 thf(fact_8220_pochhammer__nonneg,axiom,
% 5.68/6.02 ! [X: rat,N: nat] :
% 5.68/6.02 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.68/6.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_nonneg
% 5.68/6.02 thf(fact_8221_pochhammer__nonneg,axiom,
% 5.68/6.02 ! [X: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.68/6.02 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_nonneg
% 5.68/6.02 thf(fact_8222_pochhammer__nonneg,axiom,
% 5.68/6.02 ! [X: int,N: nat] :
% 5.68/6.02 ( ( ord_less_int @ zero_zero_int @ X )
% 5.68/6.02 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_nonneg
% 5.68/6.02 thf(fact_8223_pochhammer__binomial__sum,axiom,
% 5.68/6.02 ! [A: int,B: int,N: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.68/6.02 = ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_binomial_sum
% 5.68/6.02 thf(fact_8224_pochhammer__binomial__sum,axiom,
% 5.68/6.02 ! [A: rat,B: rat,N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.68/6.02 = ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_binomial_sum
% 5.68/6.02 thf(fact_8225_pochhammer__binomial__sum,axiom,
% 5.68/6.02 ! [A: real,B: real,N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_binomial_sum
% 5.68/6.02 thf(fact_8226_Iic__subset__Iio__iff,axiom,
% 5.68/6.02 ! [A: rat,B: rat] :
% 5.68/6.02 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.68/6.02 = ( ord_less_rat @ A @ B ) ) ).
% 5.68/6.02
% 5.68/6.02 % Iic_subset_Iio_iff
% 5.68/6.02 thf(fact_8227_Iic__subset__Iio__iff,axiom,
% 5.68/6.02 ! [A: num,B: num] :
% 5.68/6.02 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.68/6.02 = ( ord_less_num @ A @ B ) ) ).
% 5.68/6.02
% 5.68/6.02 % Iic_subset_Iio_iff
% 5.68/6.02 thf(fact_8228_Iic__subset__Iio__iff,axiom,
% 5.68/6.02 ! [A: nat,B: nat] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.68/6.02 = ( ord_less_nat @ A @ B ) ) ).
% 5.68/6.02
% 5.68/6.02 % Iic_subset_Iio_iff
% 5.68/6.02 thf(fact_8229_Iic__subset__Iio__iff,axiom,
% 5.68/6.02 ! [A: int,B: int] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.68/6.02 = ( ord_less_int @ A @ B ) ) ).
% 5.68/6.02
% 5.68/6.02 % Iic_subset_Iio_iff
% 5.68/6.02 thf(fact_8230_Iic__subset__Iio__iff,axiom,
% 5.68/6.02 ! [A: real,B: real] :
% 5.68/6.02 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.68/6.02 = ( ord_less_real @ A @ B ) ) ).
% 5.68/6.02
% 5.68/6.02 % Iic_subset_Iio_iff
% 5.68/6.02 thf(fact_8231_sum__choose__upper,axiom,
% 5.68/6.02 ! [M: nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_choose_upper
% 5.68/6.02 thf(fact_8232_pochhammer__rec,axiom,
% 5.68/6.02 ! [A: complex,N: nat] :
% 5.68/6.02 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec
% 5.68/6.02 thf(fact_8233_pochhammer__rec,axiom,
% 5.68/6.02 ! [A: real,N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec
% 5.68/6.02 thf(fact_8234_pochhammer__rec,axiom,
% 5.68/6.02 ! [A: rat,N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec
% 5.68/6.02 thf(fact_8235_pochhammer__rec,axiom,
% 5.68/6.02 ! [A: nat,N: nat] :
% 5.68/6.02 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec
% 5.68/6.02 thf(fact_8236_pochhammer__rec,axiom,
% 5.68/6.02 ! [A: int,N: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec
% 5.68/6.02 thf(fact_8237_pochhammer__rec_H,axiom,
% 5.68/6.02 ! [Z: int,N: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec'
% 5.68/6.02 thf(fact_8238_pochhammer__rec_H,axiom,
% 5.68/6.02 ! [Z: real,N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec'
% 5.68/6.02 thf(fact_8239_pochhammer__rec_H,axiom,
% 5.68/6.02 ! [Z: nat,N: nat] :
% 5.68/6.02 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec'
% 5.68/6.02 thf(fact_8240_pochhammer__rec_H,axiom,
% 5.68/6.02 ! [Z: rat,N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_rec'
% 5.68/6.02 thf(fact_8241_pochhammer__Suc,axiom,
% 5.68/6.02 ! [A: int,N: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_Suc
% 5.68/6.02 thf(fact_8242_pochhammer__Suc,axiom,
% 5.68/6.02 ! [A: real,N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_Suc
% 5.68/6.02 thf(fact_8243_pochhammer__Suc,axiom,
% 5.68/6.02 ! [A: nat,N: nat] :
% 5.68/6.02 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_Suc
% 5.68/6.02 thf(fact_8244_pochhammer__Suc,axiom,
% 5.68/6.02 ! [A: rat,N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.68/6.02 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_Suc
% 5.68/6.02 thf(fact_8245_pochhammer__eq__0__iff,axiom,
% 5.68/6.02 ! [A: complex,N: nat] :
% 5.68/6.02 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.68/6.02 = zero_zero_complex )
% 5.68/6.02 = ( ? [K3: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K3 @ N )
% 5.68/6.02 & ( A
% 5.68/6.02 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_iff
% 5.68/6.02 thf(fact_8246_pochhammer__eq__0__iff,axiom,
% 5.68/6.02 ! [A: real,N: nat] :
% 5.68/6.02 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.68/6.02 = zero_zero_real )
% 5.68/6.02 = ( ? [K3: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K3 @ N )
% 5.68/6.02 & ( A
% 5.68/6.02 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_iff
% 5.68/6.02 thf(fact_8247_pochhammer__eq__0__iff,axiom,
% 5.68/6.02 ! [A: rat,N: nat] :
% 5.68/6.02 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.68/6.02 = zero_zero_rat )
% 5.68/6.02 = ( ? [K3: nat] :
% 5.68/6.02 ( ( ord_less_nat @ K3 @ N )
% 5.68/6.02 & ( A
% 5.68/6.02 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_eq_0_iff
% 5.68/6.02 thf(fact_8248_pochhammer__of__nat__eq__0__iff,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.68/6.02 = zero_zero_complex )
% 5.68/6.02 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_iff
% 5.68/6.02 thf(fact_8249_pochhammer__of__nat__eq__0__iff,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.68/6.02 = zero_z3403309356797280102nteger )
% 5.68/6.02 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_iff
% 5.68/6.02 thf(fact_8250_pochhammer__of__nat__eq__0__iff,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.68/6.02 = zero_zero_int )
% 5.68/6.02 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_iff
% 5.68/6.02 thf(fact_8251_pochhammer__of__nat__eq__0__iff,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.68/6.02 = zero_zero_real )
% 5.68/6.02 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_iff
% 5.68/6.02 thf(fact_8252_pochhammer__of__nat__eq__0__iff,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.68/6.02 = zero_zero_rat )
% 5.68/6.02 = ( ord_less_nat @ N @ K ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_iff
% 5.68/6.02 thf(fact_8253_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ K )
% 5.68/6.02 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.68/6.02 = zero_zero_complex ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma
% 5.68/6.02 thf(fact_8254_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ K )
% 5.68/6.02 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.68/6.02 = zero_z3403309356797280102nteger ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma
% 5.68/6.02 thf(fact_8255_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ K )
% 5.68/6.02 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.68/6.02 = zero_zero_int ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma
% 5.68/6.02 thf(fact_8256_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ K )
% 5.68/6.02 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.68/6.02 = zero_zero_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma
% 5.68/6.02 thf(fact_8257_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.68/6.02 ! [N: nat,K: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ K )
% 5.68/6.02 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.68/6.02 = zero_zero_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma
% 5.68/6.02 thf(fact_8258_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.68/6.02 != zero_zero_complex ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma'
% 5.68/6.02 thf(fact_8259_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.68/6.02 != zero_z3403309356797280102nteger ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma'
% 5.68/6.02 thf(fact_8260_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.68/6.02 != zero_zero_int ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma'
% 5.68/6.02 thf(fact_8261_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.68/6.02 != zero_zero_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma'
% 5.68/6.02 thf(fact_8262_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.68/6.02 != zero_zero_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_of_nat_eq_0_lemma'
% 5.68/6.02 thf(fact_8263_sum_OatMost__Suc__shift,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc_shift
% 5.68/6.02 thf(fact_8264_sum_OatMost__Suc__shift,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc_shift
% 5.68/6.02 thf(fact_8265_sum_OatMost__Suc__shift,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc_shift
% 5.68/6.02 thf(fact_8266_sum_OatMost__Suc__shift,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_Suc_shift
% 5.68/6.02 thf(fact_8267_sum__telescope,axiom,
% 5.68/6.02 ! [F: nat > rat,I2: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ I2 ) )
% 5.68/6.02 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_telescope
% 5.68/6.02 thf(fact_8268_sum__telescope,axiom,
% 5.68/6.02 ! [F: nat > int,I2: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ I2 ) )
% 5.68/6.02 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_telescope
% 5.68/6.02 thf(fact_8269_sum__telescope,axiom,
% 5.68/6.02 ! [F: nat > real,I2: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ I2 ) )
% 5.68/6.02 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_telescope
% 5.68/6.02 thf(fact_8270_pochhammer__product_H,axiom,
% 5.68/6.02 ! [Z: int,N: nat,M: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.68/6.02 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product'
% 5.68/6.02 thf(fact_8271_pochhammer__product_H,axiom,
% 5.68/6.02 ! [Z: real,N: nat,M: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.68/6.02 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product'
% 5.68/6.02 thf(fact_8272_pochhammer__product_H,axiom,
% 5.68/6.02 ! [Z: nat,N: nat,M: nat] :
% 5.68/6.02 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.68/6.02 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product'
% 5.68/6.02 thf(fact_8273_pochhammer__product_H,axiom,
% 5.68/6.02 ! [Z: rat,N: nat,M: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.68/6.02 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product'
% 5.68/6.02 thf(fact_8274_polyfun__eq__coeffs,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat,D: nat > complex] :
% 5.68/6.02 ( ( ! [X2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.68/6.02 = ( ! [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 => ( ( C @ I3 )
% 5.68/6.02 = ( D @ I3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_coeffs
% 5.68/6.02 thf(fact_8275_polyfun__eq__coeffs,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat,D: nat > real] :
% 5.68/6.02 ( ( ! [X2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) )
% 5.68/6.02 = ( ! [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 => ( ( C @ I3 )
% 5.68/6.02 = ( D @ I3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_coeffs
% 5.68/6.02 thf(fact_8276_bounded__imp__summable,axiom,
% 5.68/6.02 ! [A: nat > int,B4: int] :
% 5.68/6.02 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 5.68/6.02 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B4 )
% 5.68/6.02 => ( summable_int @ A ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % bounded_imp_summable
% 5.68/6.02 thf(fact_8277_bounded__imp__summable,axiom,
% 5.68/6.02 ! [A: nat > nat,B4: nat] :
% 5.68/6.02 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 5.68/6.02 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B4 )
% 5.68/6.02 => ( summable_nat @ A ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % bounded_imp_summable
% 5.68/6.02 thf(fact_8278_bounded__imp__summable,axiom,
% 5.68/6.02 ! [A: nat > real,B4: real] :
% 5.68/6.02 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.02 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B4 )
% 5.68/6.02 => ( summable_real @ A ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % bounded_imp_summable
% 5.68/6.02 thf(fact_8279_sum_Onested__swap_H,axiom,
% 5.68/6.02 ! [A: nat > nat > nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.nested_swap'
% 5.68/6.02 thf(fact_8280_sum_Onested__swap_H,axiom,
% 5.68/6.02 ! [A: nat > nat > real,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.nested_swap'
% 5.68/6.02 thf(fact_8281_sum__choose__lower,axiom,
% 5.68/6.02 ! [R2: nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_choose_lower
% 5.68/6.02 thf(fact_8282_choose__rising__sum_I1_J,axiom,
% 5.68/6.02 ! [N: nat,M: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_rising_sum(1)
% 5.68/6.02 thf(fact_8283_choose__rising__sum_I2_J,axiom,
% 5.68/6.02 ! [N: nat,M: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_rising_sum(2)
% 5.68/6.02 thf(fact_8284_zero__polynom__imp__zero__coeffs,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat,K: nat] :
% 5.68/6.02 ( ! [W2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( C @ K )
% 5.68/6.02 = zero_zero_complex ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % zero_polynom_imp_zero_coeffs
% 5.68/6.02 thf(fact_8285_zero__polynom__imp__zero__coeffs,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat,K: nat] :
% 5.68/6.02 ( ! [W2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( C @ K )
% 5.68/6.02 = zero_zero_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % zero_polynom_imp_zero_coeffs
% 5.68/6.02 thf(fact_8286_polyfun__eq__0,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat] :
% 5.68/6.02 ( ( ! [X2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) )
% 5.68/6.02 = ( ! [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 => ( ( C @ I3 )
% 5.68/6.02 = zero_zero_complex ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_0
% 5.68/6.02 thf(fact_8287_polyfun__eq__0,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat] :
% 5.68/6.02 ( ( ! [X2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) )
% 5.68/6.02 = ( ! [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 => ( ( C @ I3 )
% 5.68/6.02 = zero_zero_real ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_0
% 5.68/6.02 thf(fact_8288_sum_OatMost__shift,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_shift
% 5.68/6.02 thf(fact_8289_sum_OatMost__shift,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_shift
% 5.68/6.02 thf(fact_8290_sum_OatMost__shift,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_shift
% 5.68/6.02 thf(fact_8291_sum_OatMost__shift,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.atMost_shift
% 5.68/6.02 thf(fact_8292_sum__up__index__split,axiom,
% 5.68/6.02 ! [F: nat > rat,M: nat,N: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.02 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_up_index_split
% 5.68/6.02 thf(fact_8293_sum__up__index__split,axiom,
% 5.68/6.02 ! [F: nat > int,M: nat,N: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.02 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_up_index_split
% 5.68/6.02 thf(fact_8294_sum__up__index__split,axiom,
% 5.68/6.02 ! [F: nat > nat,M: nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.02 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_up_index_split
% 5.68/6.02 thf(fact_8295_sum__up__index__split,axiom,
% 5.68/6.02 ! [F: nat > real,M: nat,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) )
% 5.68/6.02 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_up_index_split
% 5.68/6.02 thf(fact_8296_pochhammer__product,axiom,
% 5.68/6.02 ! [M: nat,N: nat,Z: int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.68/6.02 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product
% 5.68/6.02 thf(fact_8297_pochhammer__product,axiom,
% 5.68/6.02 ! [M: nat,N: nat,Z: real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.68/6.02 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product
% 5.68/6.02 thf(fact_8298_pochhammer__product,axiom,
% 5.68/6.02 ! [M: nat,N: nat,Z: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.68/6.02 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product
% 5.68/6.02 thf(fact_8299_pochhammer__product,axiom,
% 5.68/6.02 ! [M: nat,N: nat,Z: rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.68/6.02 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_product
% 5.68/6.02 thf(fact_8300_sum_Otriangle__reindex__eq,axiom,
% 5.68/6.02 ! [G: nat > nat > nat,N: nat] :
% 5.68/6.02 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.68/6.02 @ ( collec3392354462482085612at_nat
% 5.68/6.02 @ ( produc6081775807080527818_nat_o
% 5.68/6.02 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.triangle_reindex_eq
% 5.68/6.02 thf(fact_8301_sum_Otriangle__reindex__eq,axiom,
% 5.68/6.02 ! [G: nat > nat > real,N: nat] :
% 5.68/6.02 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.68/6.02 @ ( collec3392354462482085612at_nat
% 5.68/6.02 @ ( produc6081775807080527818_nat_o
% 5.68/6.02 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.triangle_reindex_eq
% 5.68/6.02 thf(fact_8302_sum__choose__diagonal,axiom,
% 5.68/6.02 ! [M: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_choose_diagonal
% 5.68/6.02 thf(fact_8303_vandermonde,axiom,
% 5.68/6.02 ! [M: nat,N: nat,R2: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R2 ) )
% 5.68/6.02 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % vandermonde
% 5.68/6.02 thf(fact_8304_sum__gp__basic,axiom,
% 5.68/6.02 ! [X: complex,N: nat] :
% 5.68/6.02 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp_basic
% 5.68/6.02 thf(fact_8305_sum__gp__basic,axiom,
% 5.68/6.02 ! [X: rat,N: nat] :
% 5.68/6.02 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp_basic
% 5.68/6.02 thf(fact_8306_sum__gp__basic,axiom,
% 5.68/6.02 ! [X: int,N: nat] :
% 5.68/6.02 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp_basic
% 5.68/6.02 thf(fact_8307_sum__gp__basic,axiom,
% 5.68/6.02 ! [X: real,N: nat] :
% 5.68/6.02 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp_basic
% 5.68/6.02 thf(fact_8308_polyfun__roots__finite,axiom,
% 5.68/6.02 ! [C: nat > complex,K: nat,N: nat] :
% 5.68/6.02 ( ( ( C @ K )
% 5.68/6.02 != zero_zero_complex )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( finite3207457112153483333omplex
% 5.68/6.02 @ ( collect_complex
% 5.68/6.02 @ ^ [Z2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_roots_finite
% 5.68/6.02 thf(fact_8309_polyfun__roots__finite,axiom,
% 5.68/6.02 ! [C: nat > real,K: nat,N: nat] :
% 5.68/6.02 ( ( ( C @ K )
% 5.68/6.02 != zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( finite_finite_real
% 5.68/6.02 @ ( collect_real
% 5.68/6.02 @ ^ [Z2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_roots_finite
% 5.68/6.02 thf(fact_8310_polyfun__finite__roots,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex
% 5.68/6.02 @ ( collect_complex
% 5.68/6.02 @ ^ [X2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) ) )
% 5.68/6.02 = ( ? [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 & ( ( C @ I3 )
% 5.68/6.02 != zero_zero_complex ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_finite_roots
% 5.68/6.02 thf(fact_8311_polyfun__finite__roots,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat] :
% 5.68/6.02 ( ( finite_finite_real
% 5.68/6.02 @ ( collect_real
% 5.68/6.02 @ ^ [X2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) ) )
% 5.68/6.02 = ( ? [I3: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ I3 @ N )
% 5.68/6.02 & ( ( C @ I3 )
% 5.68/6.02 != zero_zero_real ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_finite_roots
% 5.68/6.02 thf(fact_8312_polyfun__linear__factor__root,axiom,
% 5.68/6.02 ! [C: nat > complex,A: complex,N: nat] :
% 5.68/6.02 ( ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex )
% 5.68/6.02 => ~ ! [B2: nat > complex] :
% 5.68/6.02 ~ ! [Z4: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( B2 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor_root
% 5.68/6.02 thf(fact_8313_polyfun__linear__factor__root,axiom,
% 5.68/6.02 ! [C: nat > rat,A: rat,N: nat] :
% 5.68/6.02 ( ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_rat )
% 5.68/6.02 => ~ ! [B2: nat > rat] :
% 5.68/6.02 ~ ! [Z4: rat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( B2 @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor_root
% 5.68/6.02 thf(fact_8314_polyfun__linear__factor__root,axiom,
% 5.68/6.02 ! [C: nat > int,A: int,N: nat] :
% 5.68/6.02 ( ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_int )
% 5.68/6.02 => ~ ! [B2: nat > int] :
% 5.68/6.02 ~ ! [Z4: int] :
% 5.68/6.02 ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( B2 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor_root
% 5.68/6.02 thf(fact_8315_polyfun__linear__factor__root,axiom,
% 5.68/6.02 ! [C: nat > real,A: real,N: nat] :
% 5.68/6.02 ( ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real )
% 5.68/6.02 => ~ ! [B2: nat > real] :
% 5.68/6.02 ~ ! [Z4: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( B2 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor_root
% 5.68/6.02 thf(fact_8316_polyfun__linear__factor,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat,A: complex] :
% 5.68/6.02 ? [B2: nat > complex] :
% 5.68/6.02 ! [Z4: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_complex
% 5.68/6.02 @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( B2 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor
% 5.68/6.02 thf(fact_8317_polyfun__linear__factor,axiom,
% 5.68/6.02 ! [C: nat > rat,N: nat,A: rat] :
% 5.68/6.02 ? [B2: nat > rat] :
% 5.68/6.02 ! [Z4: rat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_rat
% 5.68/6.02 @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( B2 @ I3 ) @ ( power_power_rat @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor
% 5.68/6.02 thf(fact_8318_polyfun__linear__factor,axiom,
% 5.68/6.02 ! [C: nat > int,N: nat,A: int] :
% 5.68/6.02 ? [B2: nat > int] :
% 5.68/6.02 ! [Z4: int] :
% 5.68/6.02 ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_int
% 5.68/6.02 @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( B2 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor
% 5.68/6.02 thf(fact_8319_polyfun__linear__factor,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat,A: real] :
% 5.68/6.02 ? [B2: nat > real] :
% 5.68/6.02 ! [Z4: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( plus_plus_real
% 5.68/6.02 @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( B2 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_linear_factor
% 5.68/6.02 thf(fact_8320_sum__power__shift,axiom,
% 5.68/6.02 ! [M: nat,N: nat,X: complex] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.02 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_power_shift
% 5.68/6.02 thf(fact_8321_sum__power__shift,axiom,
% 5.68/6.02 ! [M: nat,N: nat,X: rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.02 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_power_shift
% 5.68/6.02 thf(fact_8322_sum__power__shift,axiom,
% 5.68/6.02 ! [M: nat,N: nat,X: int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.02 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_power_shift
% 5.68/6.02 thf(fact_8323_sum__power__shift,axiom,
% 5.68/6.02 ! [M: nat,N: nat,X: real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.02 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.02 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_power_shift
% 5.68/6.02 thf(fact_8324_pochhammer__absorb__comp,axiom,
% 5.68/6.02 ! [R2: complex,K: nat] :
% 5.68/6.02 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.68/6.02 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_absorb_comp
% 5.68/6.02 thf(fact_8325_pochhammer__absorb__comp,axiom,
% 5.68/6.02 ! [R2: code_integer,K: nat] :
% 5.68/6.02 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.68/6.02 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_absorb_comp
% 5.68/6.02 thf(fact_8326_pochhammer__absorb__comp,axiom,
% 5.68/6.02 ! [R2: int,K: nat] :
% 5.68/6.02 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.68/6.02 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_absorb_comp
% 5.68/6.02 thf(fact_8327_pochhammer__absorb__comp,axiom,
% 5.68/6.02 ! [R2: real,K: nat] :
% 5.68/6.02 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.68/6.02 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_absorb_comp
% 5.68/6.02 thf(fact_8328_pochhammer__absorb__comp,axiom,
% 5.68/6.02 ! [R2: rat,K: nat] :
% 5.68/6.02 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.68/6.02 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_absorb_comp
% 5.68/6.02 thf(fact_8329_pochhammer__same,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.68/6.02 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_same
% 5.68/6.02 thf(fact_8330_pochhammer__same,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.68/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_same
% 5.68/6.02 thf(fact_8331_pochhammer__same,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.68/6.02 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_same
% 5.68/6.02 thf(fact_8332_pochhammer__same,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.68/6.02 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_same
% 5.68/6.02 thf(fact_8333_pochhammer__same,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.68/6.02 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_same
% 5.68/6.02 thf(fact_8334_sum_Otriangle__reindex,axiom,
% 5.68/6.02 ! [G: nat > nat > nat,N: nat] :
% 5.68/6.02 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.68/6.02 @ ( collec3392354462482085612at_nat
% 5.68/6.02 @ ( produc6081775807080527818_nat_o
% 5.68/6.02 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.triangle_reindex
% 5.68/6.02 thf(fact_8335_sum_Otriangle__reindex,axiom,
% 5.68/6.02 ! [G: nat > nat > real,N: nat] :
% 5.68/6.02 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.68/6.02 @ ( collec3392354462482085612at_nat
% 5.68/6.02 @ ( produc6081775807080527818_nat_o
% 5.68/6.02 @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K3 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.triangle_reindex
% 5.68/6.02 thf(fact_8336_summable__Cauchy__product,axiom,
% 5.68/6.02 ! [A: nat > complex,B: nat > complex] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.68/6.02 => ( summable_complex
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % summable_Cauchy_product
% 5.68/6.02 thf(fact_8337_summable__Cauchy__product,axiom,
% 5.68/6.02 ! [A: nat > real,B: nat > real] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.68/6.02 => ( summable_real
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % summable_Cauchy_product
% 5.68/6.02 thf(fact_8338_choose__row__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_row_sum
% 5.68/6.02 thf(fact_8339_Cauchy__product,axiom,
% 5.68/6.02 ! [A: nat > complex,B: nat > complex] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.68/6.02 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.68/6.02 = ( suminf_complex
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Cauchy_product
% 5.68/6.02 thf(fact_8340_Cauchy__product,axiom,
% 5.68/6.02 ! [A: nat > real,B: nat > real] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.68/6.02 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.68/6.02 = ( suminf_real
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Cauchy_product
% 5.68/6.02 thf(fact_8341_binomial,axiom,
% 5.68/6.02 ! [A: nat,B: nat,N: nat] :
% 5.68/6.02 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [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 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial
% 5.68/6.02 thf(fact_8342_sum_Oin__pairs__0,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.02 = ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.in_pairs_0
% 5.68/6.02 thf(fact_8343_sum_Oin__pairs__0,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.02 = ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.in_pairs_0
% 5.68/6.02 thf(fact_8344_sum_Oin__pairs__0,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.in_pairs_0
% 5.68/6.02 thf(fact_8345_sum_Oin__pairs__0,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.in_pairs_0
% 5.68/6.02 thf(fact_8346_polynomial__product,axiom,
% 5.68/6.02 ! [M: nat,A: nat > complex,N: nat,B: nat > complex,X: complex] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( ord_less_nat @ M @ I4 )
% 5.68/6.02 => ( ( A @ I4 )
% 5.68/6.02 = zero_zero_complex ) )
% 5.68/6.02 => ( ! [J2: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ J2 )
% 5.68/6.02 => ( ( B @ J2 )
% 5.68/6.02 = zero_zero_complex ) )
% 5.68/6.02 => ( ( times_times_complex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [R5: nat] :
% 5.68/6.02 ( times_times_complex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R5 ) )
% 5.68/6.02 @ ( power_power_complex @ X @ R5 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polynomial_product
% 5.68/6.02 thf(fact_8347_polynomial__product,axiom,
% 5.68/6.02 ! [M: nat,A: nat > rat,N: nat,B: nat > rat,X: rat] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( ord_less_nat @ M @ I4 )
% 5.68/6.02 => ( ( A @ I4 )
% 5.68/6.02 = zero_zero_rat ) )
% 5.68/6.02 => ( ! [J2: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ J2 )
% 5.68/6.02 => ( ( B @ J2 )
% 5.68/6.02 = zero_zero_rat ) )
% 5.68/6.02 => ( ( times_times_rat
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [R5: nat] :
% 5.68/6.02 ( times_times_rat
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R5 ) )
% 5.68/6.02 @ ( power_power_rat @ X @ R5 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polynomial_product
% 5.68/6.02 thf(fact_8348_polynomial__product,axiom,
% 5.68/6.02 ! [M: nat,A: nat > int,N: nat,B: nat > int,X: int] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( ord_less_nat @ M @ I4 )
% 5.68/6.02 => ( ( A @ I4 )
% 5.68/6.02 = zero_zero_int ) )
% 5.68/6.02 => ( ! [J2: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ J2 )
% 5.68/6.02 => ( ( B @ J2 )
% 5.68/6.02 = zero_zero_int ) )
% 5.68/6.02 => ( ( times_times_int
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [R5: nat] :
% 5.68/6.02 ( times_times_int
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R5 ) )
% 5.68/6.02 @ ( power_power_int @ X @ R5 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polynomial_product
% 5.68/6.02 thf(fact_8349_polynomial__product,axiom,
% 5.68/6.02 ! [M: nat,A: nat > real,N: nat,B: nat > real,X: real] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( ord_less_nat @ M @ I4 )
% 5.68/6.02 => ( ( A @ I4 )
% 5.68/6.02 = zero_zero_real ) )
% 5.68/6.02 => ( ! [J2: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ J2 )
% 5.68/6.02 => ( ( B @ J2 )
% 5.68/6.02 = zero_zero_real ) )
% 5.68/6.02 => ( ( times_times_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [R5: nat] :
% 5.68/6.02 ( times_times_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R5 ) )
% 5.68/6.02 @ ( power_power_real @ X @ R5 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polynomial_product
% 5.68/6.02 thf(fact_8350_polyfun__eq__const,axiom,
% 5.68/6.02 ! [C: nat > complex,N: nat,K: complex] :
% 5.68/6.02 ( ( ! [X2: complex] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = K ) )
% 5.68/6.02 = ( ( ( C @ zero_zero_nat )
% 5.68/6.02 = K )
% 5.68/6.02 & ! [X2: nat] :
% 5.68/6.02 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.68/6.02 => ( ( C @ X2 )
% 5.68/6.02 = zero_zero_complex ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_const
% 5.68/6.02 thf(fact_8351_polyfun__eq__const,axiom,
% 5.68/6.02 ! [C: nat > real,N: nat,K: real] :
% 5.68/6.02 ( ( ! [X2: real] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = K ) )
% 5.68/6.02 = ( ( ( C @ zero_zero_nat )
% 5.68/6.02 = K )
% 5.68/6.02 & ! [X2: nat] :
% 5.68/6.02 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 5.68/6.02 => ( ( C @ X2 )
% 5.68/6.02 = zero_zero_real ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_eq_const
% 5.68/6.02 thf(fact_8352_binomial__ring,axiom,
% 5.68/6.02 ! [A: complex,B: complex,N: nat] :
% 5.68/6.02 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 5.68/6.02 = ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_ring
% 5.68/6.02 thf(fact_8353_binomial__ring,axiom,
% 5.68/6.02 ! [A: int,B: int,N: nat] :
% 5.68/6.02 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.68/6.02 = ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_ring
% 5.68/6.02 thf(fact_8354_binomial__ring,axiom,
% 5.68/6.02 ! [A: rat,B: rat,N: nat] :
% 5.68/6.02 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 5.68/6.02 = ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_ring
% 5.68/6.02 thf(fact_8355_binomial__ring,axiom,
% 5.68/6.02 ! [A: nat,B: nat,N: nat] :
% 5.68/6.02 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [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 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_ring
% 5.68/6.02 thf(fact_8356_binomial__ring,axiom,
% 5.68/6.02 ! [A: real,B: real,N: nat] :
% 5.68/6.02 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_ring
% 5.68/6.02 thf(fact_8357_pochhammer__minus_H,axiom,
% 5.68/6.02 ! [B: complex,K: nat] :
% 5.68/6.02 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.68/6.02 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus'
% 5.68/6.02 thf(fact_8358_pochhammer__minus_H,axiom,
% 5.68/6.02 ! [B: code_integer,K: nat] :
% 5.68/6.02 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.68/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus'
% 5.68/6.02 thf(fact_8359_pochhammer__minus_H,axiom,
% 5.68/6.02 ! [B: int,K: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.68/6.02 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus'
% 5.68/6.02 thf(fact_8360_pochhammer__minus_H,axiom,
% 5.68/6.02 ! [B: real,K: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.68/6.02 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus'
% 5.68/6.02 thf(fact_8361_pochhammer__minus_H,axiom,
% 5.68/6.02 ! [B: rat,K: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.68/6.02 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus'
% 5.68/6.02 thf(fact_8362_pochhammer__minus,axiom,
% 5.68/6.02 ! [B: complex,K: nat] :
% 5.68/6.02 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus
% 5.68/6.02 thf(fact_8363_pochhammer__minus,axiom,
% 5.68/6.02 ! [B: code_integer,K: nat] :
% 5.68/6.02 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.68/6.02 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus
% 5.68/6.02 thf(fact_8364_pochhammer__minus,axiom,
% 5.68/6.02 ! [B: int,K: nat] :
% 5.68/6.02 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus
% 5.68/6.02 thf(fact_8365_pochhammer__minus,axiom,
% 5.68/6.02 ! [B: real,K: nat] :
% 5.68/6.02 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus
% 5.68/6.02 thf(fact_8366_pochhammer__minus,axiom,
% 5.68/6.02 ! [B: rat,K: nat] :
% 5.68/6.02 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_minus
% 5.68/6.02 thf(fact_8367_polynomial__product__nat,axiom,
% 5.68/6.02 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( ord_less_nat @ M @ I4 )
% 5.68/6.02 => ( ( A @ I4 )
% 5.68/6.02 = zero_zero_nat ) )
% 5.68/6.02 => ( ! [J2: nat] :
% 5.68/6.02 ( ( ord_less_nat @ N @ J2 )
% 5.68/6.02 => ( ( B @ J2 )
% 5.68/6.02 = zero_zero_nat ) )
% 5.68/6.02 => ( ( times_times_nat
% 5.68/6.02 @ ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 @ ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [R5: nat] :
% 5.68/6.02 ( times_times_nat
% 5.68/6.02 @ ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ R5 ) )
% 5.68/6.02 @ ( power_power_nat @ X @ R5 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polynomial_product_nat
% 5.68/6.02 thf(fact_8368_choose__square__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_square_sum
% 5.68/6.02 thf(fact_8369_Cauchy__product__sums,axiom,
% 5.68/6.02 ! [A: nat > complex,B: nat > complex] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.68/6.02 => ( sums_complex
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Cauchy_product_sums
% 5.68/6.02 thf(fact_8370_Cauchy__product__sums,axiom,
% 5.68/6.02 ! [A: nat > real,B: nat > real] :
% 5.68/6.02 ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.68/6.02 => ( ( summable_real
% 5.68/6.02 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.68/6.02 => ( sums_real
% 5.68/6.02 @ ^ [K3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( B @ ( minus_minus_nat @ K3 @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ K3 ) )
% 5.68/6.02 @ ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Cauchy_product_sums
% 5.68/6.02 thf(fact_8371_sum_Ozero__middle,axiom,
% 5.68/6.02 ! [P4: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.02 => ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.02 = ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.zero_middle
% 5.68/6.02 thf(fact_8372_sum_Ozero__middle,axiom,
% 5.68/6.02 ! [P4: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.02 = ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.zero_middle
% 5.68/6.02 thf(fact_8373_sum_Ozero__middle,axiom,
% 5.68/6.02 ! [P4: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.02 => ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.02 = ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.zero_middle
% 5.68/6.02 thf(fact_8374_sum_Ozero__middle,axiom,
% 5.68/6.02 ! [P4: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.02 => ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.02 = ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.zero_middle
% 5.68/6.02 thf(fact_8375_sum_Ozero__middle,axiom,
% 5.68/6.02 ! [P4: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.02 => ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.02 = ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum.zero_middle
% 5.68/6.02 thf(fact_8376_root__polyfun,axiom,
% 5.68/6.02 ! [N: nat,Z: int,A: int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( ( power_power_int @ Z @ N )
% 5.68/6.02 = A )
% 5.68/6.02 = ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( if_int @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I3 = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_int ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % root_polyfun
% 5.68/6.02 thf(fact_8377_root__polyfun,axiom,
% 5.68/6.02 ! [N: nat,Z: complex,A: complex] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( ( power_power_complex @ Z @ N )
% 5.68/6.02 = A )
% 5.68/6.02 = ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( if_complex @ ( I3 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I3 = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % root_polyfun
% 5.68/6.02 thf(fact_8378_root__polyfun,axiom,
% 5.68/6.02 ! [N: nat,Z: code_integer,A: code_integer] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( ( power_8256067586552552935nteger @ Z @ N )
% 5.68/6.02 = A )
% 5.68/6.02 = ( ( groups7501900531339628137nteger
% 5.68/6.02 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I3 = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_z3403309356797280102nteger ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % root_polyfun
% 5.68/6.02 thf(fact_8379_root__polyfun,axiom,
% 5.68/6.02 ! [N: nat,Z: rat,A: rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( ( power_power_rat @ Z @ N )
% 5.68/6.02 = A )
% 5.68/6.02 = ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( if_rat @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I3 = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_rat ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % root_polyfun
% 5.68/6.02 thf(fact_8380_root__polyfun,axiom,
% 5.68/6.02 ! [N: nat,Z: real,A: real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( ( power_power_real @ Z @ N )
% 5.68/6.02 = A )
% 5.68/6.02 = ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( if_real @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I3 = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % root_polyfun
% 5.68/6.02 thf(fact_8381_sum__gp0,axiom,
% 5.68/6.02 ! [X: complex,N: nat] :
% 5.68/6.02 ( ( ( X = one_one_complex )
% 5.68/6.02 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.68/6.02 & ( ( X != one_one_complex )
% 5.68/6.02 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp0
% 5.68/6.02 thf(fact_8382_sum__gp0,axiom,
% 5.68/6.02 ! [X: rat,N: nat] :
% 5.68/6.02 ( ( ( X = one_one_rat )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.68/6.02 & ( ( X != one_one_rat )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp0
% 5.68/6.02 thf(fact_8383_sum__gp0,axiom,
% 5.68/6.02 ! [X: real,N: nat] :
% 5.68/6.02 ( ( ( X = one_one_real )
% 5.68/6.02 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 5.68/6.02 & ( ( X != one_one_real )
% 5.68/6.02 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sum_gp0
% 5.68/6.02 thf(fact_8384_choose__alternating__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( N != one_one_nat )
% 5.68/6.02 => ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_linear_sum
% 5.68/6.02 thf(fact_8385_choose__alternating__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( N != one_one_nat )
% 5.68/6.02 => ( ( groups7501900531339628137nteger
% 5.68/6.02 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_z3403309356797280102nteger ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_linear_sum
% 5.68/6.02 thf(fact_8386_choose__alternating__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( N != one_one_nat )
% 5.68/6.02 => ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_int ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_linear_sum
% 5.68/6.02 thf(fact_8387_choose__alternating__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( N != one_one_nat )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_linear_sum
% 5.68/6.02 thf(fact_8388_choose__alternating__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( N != one_one_nat )
% 5.68/6.02 => ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ I3 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_linear_sum
% 5.68/6.02 thf(fact_8389_polyfun__diff__alt,axiom,
% 5.68/6.02 ! [N: nat,A: nat > complex,X: complex,Y2: complex] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_complex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y2 @ K3 ) ) @ ( power_power_complex @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff_alt
% 5.68/6.02 thf(fact_8390_polyfun__diff__alt,axiom,
% 5.68/6.02 ! [N: nat,A: nat > rat,X: rat,Y2: rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_rat
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y2 @ K3 ) ) @ ( power_power_rat @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff_alt
% 5.68/6.02 thf(fact_8391_polyfun__diff__alt,axiom,
% 5.68/6.02 ! [N: nat,A: nat > int,X: int,Y2: int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_int
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y2 @ K3 ) ) @ ( power_power_int @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff_alt
% 5.68/6.02 thf(fact_8392_polyfun__diff__alt,axiom,
% 5.68/6.02 ! [N: nat,A: nat > real,X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y2 @ K3 ) ) @ ( power_power_real @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff_alt
% 5.68/6.02 thf(fact_8393_pochhammer__code,axiom,
% 5.68/6.02 ( comm_s2602460028002588243omplex
% 5.68/6.02 = ( ^ [A4: complex,N2: nat] :
% 5.68/6.02 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.68/6.02 @ ( set_fo1517530859248394432omplex
% 5.68/6.02 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.68/6.02 @ zero_zero_nat
% 5.68/6.02 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.68/6.02 @ one_one_complex ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_code
% 5.68/6.02 thf(fact_8394_pochhammer__code,axiom,
% 5.68/6.02 ( comm_s4660882817536571857er_int
% 5.68/6.02 = ( ^ [A4: int,N2: nat] :
% 5.68/6.02 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.68/6.02 @ ( set_fo2581907887559384638at_int
% 5.68/6.02 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.68/6.02 @ zero_zero_nat
% 5.68/6.02 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.68/6.02 @ one_one_int ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_code
% 5.68/6.02 thf(fact_8395_pochhammer__code,axiom,
% 5.68/6.02 ( comm_s7457072308508201937r_real
% 5.68/6.02 = ( ^ [A4: real,N2: nat] :
% 5.68/6.02 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.68/6.02 @ ( set_fo3111899725591712190t_real
% 5.68/6.02 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.68/6.02 @ zero_zero_nat
% 5.68/6.02 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.68/6.02 @ one_one_real ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_code
% 5.68/6.02 thf(fact_8396_pochhammer__code,axiom,
% 5.68/6.02 ( comm_s4028243227959126397er_rat
% 5.68/6.02 = ( ^ [A4: rat,N2: nat] :
% 5.68/6.02 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.68/6.02 @ ( set_fo1949268297981939178at_rat
% 5.68/6.02 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.68/6.02 @ zero_zero_nat
% 5.68/6.02 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.68/6.02 @ one_one_rat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_code
% 5.68/6.02 thf(fact_8397_pochhammer__code,axiom,
% 5.68/6.02 ( comm_s4663373288045622133er_nat
% 5.68/6.02 = ( ^ [A4: nat,N2: nat] :
% 5.68/6.02 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.68/6.02 @ ( set_fo2584398358068434914at_nat
% 5.68/6.02 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.68/6.02 @ zero_zero_nat
% 5.68/6.02 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.68/6.02 @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_code
% 5.68/6.02 thf(fact_8398_binomial__r__part__sum,axiom,
% 5.68/6.02 ! [M: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % binomial_r_part_sum
% 5.68/6.02 thf(fact_8399_choose__linear__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( groups3542108847815614940at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_linear_sum
% 5.68/6.02 thf(fact_8400_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.68/6.02 ! [X: vEBT_VEBT] :
% 5.68/6.02 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.68/6.02 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.68/6.02 => ( ! [Uv2: $o] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.68/6.02 => ( ! [Uu3: $o] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ Uu3 @ $true ) )
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu3 @ $true ) ) )
% 5.68/6.02 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % VEBT_internal.minNull.pelims(3)
% 5.68/6.02 thf(fact_8401_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.68/6.02 ! [X: vEBT_VEBT] :
% 5.68/6.02 ( ( vEBT_VEBT_minNull @ X )
% 5.68/6.02 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.68/6.02 => ( ( ( X
% 5.68/6.02 = ( vEBT_Leaf @ $false @ $false ) )
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.68/6.02 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.68/6.02 ( ( X
% 5.68/6.02 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.68/6.02 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % VEBT_internal.minNull.pelims(2)
% 5.68/6.02 thf(fact_8402_choose__alternating__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_complex ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_sum
% 5.68/6.02 thf(fact_8403_choose__alternating__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( groups7501900531339628137nteger
% 5.68/6.02 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_z3403309356797280102nteger ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_sum
% 5.68/6.02 thf(fact_8404_choose__alternating__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_int ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_sum
% 5.68/6.02 thf(fact_8405_choose__alternating__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_sum
% 5.68/6.02 thf(fact_8406_choose__alternating__sum,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.02 => ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 = zero_zero_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % choose_alternating_sum
% 5.68/6.02 thf(fact_8407_polyfun__extremal__lemma,axiom,
% 5.68/6.02 ! [E: real,C: nat > complex,N: nat] :
% 5.68/6.02 ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.02 => ? [M8: real] :
% 5.68/6.02 ! [Z4: complex] :
% 5.68/6.02 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 5.68/6.02 => ( ord_less_eq_real
% 5.68/6.02 @ ( real_V1022390504157884413omplex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_extremal_lemma
% 5.68/6.02 thf(fact_8408_polyfun__extremal__lemma,axiom,
% 5.68/6.02 ! [E: real,C: nat > real,N: nat] :
% 5.68/6.02 ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.02 => ? [M8: real] :
% 5.68/6.02 ! [Z4: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 5.68/6.02 => ( ord_less_eq_real
% 5.68/6.02 @ ( real_V7735802525324610683m_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_extremal_lemma
% 5.68/6.02 thf(fact_8409_polyfun__diff,axiom,
% 5.68/6.02 ! [N: nat,A: nat > complex,X: complex,Y2: complex] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_complex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_complex @ ( minus_minus_complex @ X @ Y2 )
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( times_times_complex
% 5.68/6.02 @ ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( power_power_complex @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff
% 5.68/6.02 thf(fact_8410_polyfun__diff,axiom,
% 5.68/6.02 ! [N: nat,A: nat > rat,X: rat,Y2: rat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_rat
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( minus_minus_rat @ X @ Y2 )
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( times_times_rat
% 5.68/6.02 @ ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y2 @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( power_power_rat @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff
% 5.68/6.02 thf(fact_8411_polyfun__diff,axiom,
% 5.68/6.02 ! [N: nat,A: nat > int,X: int,Y2: int] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_int
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( minus_minus_int @ X @ Y2 )
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( times_times_int
% 5.68/6.02 @ ( groups3539618377306564664at_int
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y2 @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( power_power_int @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff
% 5.68/6.02 thf(fact_8412_polyfun__diff,axiom,
% 5.68/6.02 ! [N: nat,A: nat > real,X: real,Y2: real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.68/6.02 => ( ( minus_minus_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y2 @ I3 ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( minus_minus_real @ X @ Y2 )
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [J3: nat] :
% 5.68/6.02 ( times_times_real
% 5.68/6.02 @ ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.02 @ ( power_power_real @ X @ J3 ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % polyfun_diff
% 5.68/6.02 thf(fact_8413_fact__double,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_double
% 5.68/6.02 thf(fact_8414_fact__double,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_double
% 5.68/6.02 thf(fact_8415_fact__double,axiom,
% 5.68/6.02 ! [N: nat] :
% 5.68/6.02 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.02 = ( 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 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % fact_double
% 5.68/6.02 thf(fact_8416_sin__x__sin__y,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( sums_real
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [N2: nat] :
% 5.68/6.02 ( if_real
% 5.68/6.02 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.68/6.02 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.68/6.02 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) )
% 5.68/6.02 @ zero_zero_real )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sin_x_sin_y
% 5.68/6.02 thf(fact_8417_sin__x__sin__y,axiom,
% 5.68/6.02 ! [X: complex,Y2: complex] :
% 5.68/6.02 ( sums_complex
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [N2: nat] :
% 5.68/6.02 ( if_complex
% 5.68/6.02 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.68/6.02 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.68/6.02 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) )
% 5.68/6.02 @ zero_zero_complex )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sin_x_sin_y
% 5.68/6.02 thf(fact_8418_sums__cos__x__plus__y,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( sums_real
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) ) @ zero_zero_real )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( cos_real @ ( plus_plus_real @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sums_cos_x_plus_y
% 5.68/6.02 thf(fact_8419_sums__cos__x__plus__y,axiom,
% 5.68/6.02 ! [X: complex,Y2: complex] :
% 5.68/6.02 ( sums_complex
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [N2: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) ) @ zero_zero_complex )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( cos_complex @ ( plus_plus_complex @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % sums_cos_x_plus_y
% 5.68/6.02 thf(fact_8420_cos__x__cos__y,axiom,
% 5.68/6.02 ! [X: real,Y2: real] :
% 5.68/6.02 ( sums_real
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [N2: nat] :
% 5.68/6.02 ( if_real
% 5.68/6.02 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.68/6.02 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.68/6.02 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) )
% 5.68/6.02 @ zero_zero_real )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % cos_x_cos_y
% 5.68/6.02 thf(fact_8421_cos__x__cos__y,axiom,
% 5.68/6.02 ! [X: complex,Y2: complex] :
% 5.68/6.02 ( sums_complex
% 5.68/6.02 @ ^ [P5: nat] :
% 5.68/6.02 ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [N2: nat] :
% 5.68/6.02 ( if_complex
% 5.68/6.02 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.68/6.02 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.68/6.02 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N2 ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_complex @ Y2 @ ( minus_minus_nat @ P5 @ N2 ) ) )
% 5.68/6.02 @ zero_zero_complex )
% 5.68/6.02 @ ( set_ord_atMost_nat @ P5 ) )
% 5.68/6.02 @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % cos_x_cos_y
% 5.68/6.02 thf(fact_8422_pochhammer__times__pochhammer__half,axiom,
% 5.68/6.02 ! [Z: complex,N: nat] :
% 5.68/6.02 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.68/6.02 = ( groups6464643781859351333omplex
% 5.68/6.02 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_times_pochhammer_half
% 5.68/6.02 thf(fact_8423_pochhammer__times__pochhammer__half,axiom,
% 5.68/6.02 ! [Z: real,N: nat] :
% 5.68/6.02 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.68/6.02 = ( groups129246275422532515t_real
% 5.68/6.02 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_times_pochhammer_half
% 5.68/6.02 thf(fact_8424_pochhammer__times__pochhammer__half,axiom,
% 5.68/6.02 ! [Z: rat,N: nat] :
% 5.68/6.02 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.68/6.02 = ( groups73079841787564623at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % pochhammer_times_pochhammer_half
% 5.68/6.02 thf(fact_8425_gbinomial__partial__row__sum,axiom,
% 5.68/6.02 ! [A: complex,M: nat] :
% 5.68/6.02 ( ( groups2073611262835488442omplex
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_partial_row_sum
% 5.68/6.02 thf(fact_8426_gbinomial__partial__row__sum,axiom,
% 5.68/6.02 ! [A: rat,M: nat] :
% 5.68/6.02 ( ( groups2906978787729119204at_rat
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_partial_row_sum
% 5.68/6.02 thf(fact_8427_gbinomial__partial__row__sum,axiom,
% 5.68/6.02 ! [A: real,M: nat] :
% 5.68/6.02 ( ( groups6591440286371151544t_real
% 5.68/6.02 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.68/6.02 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.02 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_partial_row_sum
% 5.68/6.02 thf(fact_8428_of__nat__id,axiom,
% 5.68/6.02 ( semiri1316708129612266289at_nat
% 5.68/6.02 = ( ^ [N2: nat] : N2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % of_nat_id
% 5.68/6.02 thf(fact_8429_mult__scaleR__right,axiom,
% 5.68/6.02 ! [X: real,A: real,Y2: real] :
% 5.68/6.02 ( ( times_times_real @ X @ ( real_V1485227260804924795R_real @ A @ Y2 ) )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % mult_scaleR_right
% 5.68/6.02 thf(fact_8430_mult__scaleR__right,axiom,
% 5.68/6.02 ! [X: complex,A: real,Y2: complex] :
% 5.68/6.02 ( ( times_times_complex @ X @ ( real_V2046097035970521341omplex @ A @ Y2 ) )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % mult_scaleR_right
% 5.68/6.02 thf(fact_8431_mult__scaleR__left,axiom,
% 5.68/6.02 ! [A: real,X: real,Y2: real] :
% 5.68/6.02 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X ) @ Y2 )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % mult_scaleR_left
% 5.68/6.02 thf(fact_8432_mult__scaleR__left,axiom,
% 5.68/6.02 ! [A: real,X: complex,Y2: complex] :
% 5.68/6.02 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ Y2 )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % mult_scaleR_left
% 5.68/6.02 thf(fact_8433_scaleR__scaleR,axiom,
% 5.68/6.02 ! [A: real,B: real,X: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X ) )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_scaleR
% 5.68/6.02 thf(fact_8434_scaleR__scaleR,axiom,
% 5.68/6.02 ! [A: real,B: real,X: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X ) )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_scaleR
% 5.68/6.02 thf(fact_8435_scaleR__eq__iff,axiom,
% 5.68/6.02 ! [B: real,U: real,A: real] :
% 5.68/6.02 ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.68/6.02 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 5.68/6.02 = ( ( A = B )
% 5.68/6.02 | ( U = one_one_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_eq_iff
% 5.68/6.02 thf(fact_8436_scaleR__eq__iff,axiom,
% 5.68/6.02 ! [B: complex,U: real,A: complex] :
% 5.68/6.02 ( ( ( plus_plus_complex @ B @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.68/6.02 = ( plus_plus_complex @ A @ ( real_V2046097035970521341omplex @ U @ B ) ) )
% 5.68/6.02 = ( ( A = B )
% 5.68/6.02 | ( U = one_one_real ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_eq_iff
% 5.68/6.02 thf(fact_8437_scaleR__power,axiom,
% 5.68/6.02 ! [X: real,Y2: real,N: nat] :
% 5.68/6.02 ( ( power_power_real @ ( real_V1485227260804924795R_real @ X @ Y2 ) @ N )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y2 @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_power
% 5.68/6.02 thf(fact_8438_scaleR__power,axiom,
% 5.68/6.02 ! [X: real,Y2: complex,N: nat] :
% 5.68/6.02 ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X @ Y2 ) @ N )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ ( power_power_real @ X @ N ) @ ( power_power_complex @ Y2 @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_power
% 5.68/6.02 thf(fact_8439_gbinomial__0_I2_J,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.68/6.02 = zero_zero_complex ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_0(2)
% 5.68/6.02 thf(fact_8440_gbinomial__0_I2_J,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.68/6.02 = zero_zero_real ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_0(2)
% 5.68/6.02 thf(fact_8441_gbinomial__0_I2_J,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.68/6.02 = zero_zero_rat ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_0(2)
% 5.68/6.02 thf(fact_8442_gbinomial__0_I2_J,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.68/6.02 = zero_zero_nat ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_0(2)
% 5.68/6.02 thf(fact_8443_gbinomial__0_I2_J,axiom,
% 5.68/6.02 ! [K: nat] :
% 5.68/6.02 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.68/6.02 = zero_zero_int ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_0(2)
% 5.68/6.02 thf(fact_8444_scaleR__collapse,axiom,
% 5.68/6.02 ! [U: real,A: real] :
% 5.68/6.02 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.68/6.02 = A ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_collapse
% 5.68/6.02 thf(fact_8445_scaleR__collapse,axiom,
% 5.68/6.02 ! [U: real,A: complex] :
% 5.68/6.02 ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.68/6.02 = A ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_collapse
% 5.68/6.02 thf(fact_8446_prod_OlessThan__Suc,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.lessThan_Suc
% 5.68/6.02 thf(fact_8447_prod_OlessThan__Suc,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.lessThan_Suc
% 5.68/6.02 thf(fact_8448_prod_OlessThan__Suc,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.lessThan_Suc
% 5.68/6.02 thf(fact_8449_prod_OlessThan__Suc,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.lessThan_Suc
% 5.68/6.02 thf(fact_8450_prod_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atMost_Suc
% 5.68/6.02 thf(fact_8451_prod_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atMost_Suc
% 5.68/6.02 thf(fact_8452_prod_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atMost_Suc
% 5.68/6.02 thf(fact_8453_prod_OatMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atMost_Suc
% 5.68/6.02 thf(fact_8454_norm__scaleR,axiom,
% 5.68/6.02 ! [A: real,X: real] :
% 5.68/6.02 ( ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ A @ X ) )
% 5.68/6.02 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % norm_scaleR
% 5.68/6.02 thf(fact_8455_norm__scaleR,axiom,
% 5.68/6.02 ! [A: real,X: complex] :
% 5.68/6.02 ( ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ A @ X ) )
% 5.68/6.02 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % norm_scaleR
% 5.68/6.02 thf(fact_8456_scaleR__times,axiom,
% 5.68/6.02 ! [U: num,W: num,A: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_times
% 5.68/6.02 thf(fact_8457_scaleR__times,axiom,
% 5.68/6.02 ! [U: num,W: num,A: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_times
% 5.68/6.02 thf(fact_8458_inverse__scaleR__times,axiom,
% 5.68/6.02 ! [V: num,W: num,A: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % inverse_scaleR_times
% 5.68/6.02 thf(fact_8459_inverse__scaleR__times,axiom,
% 5.68/6.02 ! [V: num,W: num,A: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % inverse_scaleR_times
% 5.68/6.02 thf(fact_8460_fraction__scaleR__times,axiom,
% 5.68/6.02 ! [U: num,V: num,W: num,A: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.68/6.02 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % fraction_scaleR_times
% 5.68/6.02 thf(fact_8461_fraction__scaleR__times,axiom,
% 5.68/6.02 ! [U: num,V: num,W: num,A: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.68/6.02 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % fraction_scaleR_times
% 5.68/6.02 thf(fact_8462_prod_Ocl__ivl__Suc,axiom,
% 5.68/6.02 ! [N: nat,M: nat,G: nat > complex] :
% 5.68/6.02 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.cl_ivl_Suc
% 5.68/6.02 thf(fact_8463_prod_Ocl__ivl__Suc,axiom,
% 5.68/6.02 ! [N: nat,M: nat,G: nat > real] :
% 5.68/6.02 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.cl_ivl_Suc
% 5.68/6.02 thf(fact_8464_prod_Ocl__ivl__Suc,axiom,
% 5.68/6.02 ! [N: nat,M: nat,G: nat > rat] :
% 5.68/6.02 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.cl_ivl_Suc
% 5.68/6.02 thf(fact_8465_prod_Ocl__ivl__Suc,axiom,
% 5.68/6.02 ! [N: nat,M: nat,G: nat > nat] :
% 5.68/6.02 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.cl_ivl_Suc
% 5.68/6.02 thf(fact_8466_prod_Ocl__ivl__Suc,axiom,
% 5.68/6.02 ! [N: nat,M: nat,G: nat > int] :
% 5.68/6.02 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.68/6.02 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.cl_ivl_Suc
% 5.68/6.02 thf(fact_8467_scaleR__half__double,axiom,
% 5.68/6.02 ! [A: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.68/6.02 = A ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_half_double
% 5.68/6.02 thf(fact_8468_scaleR__half__double,axiom,
% 5.68/6.02 ! [A: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ A @ A ) )
% 5.68/6.02 = A ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_half_double
% 5.68/6.02 thf(fact_8469_scaleR__right__distrib,axiom,
% 5.68/6.02 ! [A: real,X: real,Y2: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X @ Y2 ) )
% 5.68/6.02 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_right_distrib
% 5.68/6.02 thf(fact_8470_scaleR__right__distrib,axiom,
% 5.68/6.02 ! [A: real,X: complex,Y2: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ A @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.02 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ A @ Y2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_right_distrib
% 5.68/6.02 thf(fact_8471_real__scaleR__def,axiom,
% 5.68/6.02 real_V1485227260804924795R_real = times_times_real ).
% 5.68/6.02
% 5.68/6.02 % real_scaleR_def
% 5.68/6.02 thf(fact_8472_prod_Odistrib,axiom,
% 5.68/6.02 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/6.02 @ A2 )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.distrib
% 5.68/6.02 thf(fact_8473_prod_Odistrib,axiom,
% 5.68/6.02 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/6.02 @ A2 )
% 5.68/6.02 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.distrib
% 5.68/6.02 thf(fact_8474_prod_Odistrib,axiom,
% 5.68/6.02 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.68/6.02 ( ( groups1705073143266064639nt_int
% 5.68/6.02 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.68/6.02 @ A2 )
% 5.68/6.02 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.distrib
% 5.68/6.02 thf(fact_8475_prod__power__distrib,axiom,
% 5.68/6.02 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.68/6.02 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 5.68/6.02 = ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_power_distrib
% 5.68/6.02 thf(fact_8476_prod__power__distrib,axiom,
% 5.68/6.02 ! [F: nat > int,A2: set_nat,N: nat] :
% 5.68/6.02 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 5.68/6.02 = ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_power_distrib
% 5.68/6.02 thf(fact_8477_prod__power__distrib,axiom,
% 5.68/6.02 ! [F: int > int,A2: set_int,N: nat] :
% 5.68/6.02 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 5.68/6.02 = ( groups1705073143266064639nt_int
% 5.68/6.02 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_power_distrib
% 5.68/6.02 thf(fact_8478_mod__prod__eq,axiom,
% 5.68/6.02 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.68/6.02 ( ( modulo_modulo_nat
% 5.68/6.02 @ ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.68/6.02 @ A2 )
% 5.68/6.02 @ A )
% 5.68/6.02 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % mod_prod_eq
% 5.68/6.02 thf(fact_8479_mod__prod__eq,axiom,
% 5.68/6.02 ! [F: nat > int,A: int,A2: set_nat] :
% 5.68/6.02 ( ( modulo_modulo_int
% 5.68/6.02 @ ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.68/6.02 @ A2 )
% 5.68/6.02 @ A )
% 5.68/6.02 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % mod_prod_eq
% 5.68/6.02 thf(fact_8480_mod__prod__eq,axiom,
% 5.68/6.02 ! [F: int > int,A: int,A2: set_int] :
% 5.68/6.02 ( ( modulo_modulo_int
% 5.68/6.02 @ ( groups1705073143266064639nt_int
% 5.68/6.02 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.68/6.02 @ A2 )
% 5.68/6.02 @ A )
% 5.68/6.02 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.68/6.02
% 5.68/6.02 % mod_prod_eq
% 5.68/6.02 thf(fact_8481_prod__nonneg,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > nat] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_nonneg
% 5.68/6.02 thf(fact_8482_prod__nonneg,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > int] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_nonneg
% 5.68/6.02 thf(fact_8483_prod__nonneg,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > int] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_nonneg
% 5.68/6.02 thf(fact_8484_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8485_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > real,G: real > real] :
% 5.68/6.02 ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8486_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > real,G: int > real] :
% 5.68/6.02 ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8487_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.68/6.02 ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8488_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.68/6.02 ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8489_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.68/6.02 ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8490_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.68/6.02 ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8491_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.68/6.02 ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8492_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.68/6.02 ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8493_prod__mono,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.68/6.02 ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.68/6.02 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_mono
% 5.68/6.02 thf(fact_8494_prod__pos,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > nat] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_pos
% 5.68/6.02 thf(fact_8495_prod__pos,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > int] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_pos
% 5.68/6.02 thf(fact_8496_prod__pos,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > int] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_pos
% 5.68/6.02 thf(fact_8497_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > real] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8498_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > real] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8499_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > real] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8500_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > real] :
% 5.68/6.02 ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8501_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > rat] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8502_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > rat] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8503_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > rat] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8504_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > rat] :
% 5.68/6.02 ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8505_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > nat] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8506_prod__ge__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > nat] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_ge_1
% 5.68/6.02 thf(fact_8507_scaleR__left__distrib,axiom,
% 5.68/6.02 ! [A: real,B: real,X: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X )
% 5.68/6.02 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left_distrib
% 5.68/6.02 thf(fact_8508_scaleR__left__distrib,axiom,
% 5.68/6.02 ! [A: real,B: real,X: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ A @ B ) @ X )
% 5.68/6.02 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ B @ X ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left_distrib
% 5.68/6.02 thf(fact_8509_scaleR__left_Oadd,axiom,
% 5.68/6.02 ! [X: real,Y2: real,Xa2: real] :
% 5.68/6.02 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X @ Y2 ) @ Xa2 )
% 5.68/6.02 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X @ Xa2 ) @ ( real_V1485227260804924795R_real @ Y2 @ Xa2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left.add
% 5.68/6.02 thf(fact_8510_scaleR__left_Oadd,axiom,
% 5.68/6.02 ! [X: real,Y2: real,Xa2: complex] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ X @ Y2 ) @ Xa2 )
% 5.68/6.02 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ X @ Xa2 ) @ ( real_V2046097035970521341omplex @ Y2 @ Xa2 ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left.add
% 5.68/6.02 thf(fact_8511_complex__scaleR,axiom,
% 5.68/6.02 ! [R2: real,A: real,B: real] :
% 5.68/6.02 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.68/6.02 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % complex_scaleR
% 5.68/6.02 thf(fact_8512_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.68/6.02 ! [G: nat > nat,M: nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.68/6.02 = ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.shift_bounds_cl_Suc_ivl
% 5.68/6.02 thf(fact_8513_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.68/6.02 ! [G: nat > int,M: nat,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.68/6.02 = ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.shift_bounds_cl_Suc_ivl
% 5.68/6.02 thf(fact_8514_power__sum,axiom,
% 5.68/6.02 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.68/6.02 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.68/6.02 = ( groups129246275422532515t_real
% 5.68/6.02 @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % power_sum
% 5.68/6.02 thf(fact_8515_power__sum,axiom,
% 5.68/6.02 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.68/6.02 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.68/6.02 = ( groups6464643781859351333omplex
% 5.68/6.02 @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % power_sum
% 5.68/6.02 thf(fact_8516_power__sum,axiom,
% 5.68/6.02 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.68/6.02 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.68/6.02 = ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % power_sum
% 5.68/6.02 thf(fact_8517_power__sum,axiom,
% 5.68/6.02 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.68/6.02 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.68/6.02 = ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % power_sum
% 5.68/6.02 thf(fact_8518_power__sum,axiom,
% 5.68/6.02 ! [C: int,F: int > nat,A2: set_int] :
% 5.68/6.02 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.68/6.02 = ( groups1705073143266064639nt_int
% 5.68/6.02 @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.68/6.02 @ A2 ) ) ).
% 5.68/6.02
% 5.68/6.02 % power_sum
% 5.68/6.02 thf(fact_8519_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.68/6.02 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.68/6.02 = ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.shift_bounds_cl_nat_ivl
% 5.68/6.02 thf(fact_8520_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.68/6.02 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.68/6.02 = ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.shift_bounds_cl_nat_ivl
% 5.68/6.02 thf(fact_8521_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > real] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8522_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > real] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8523_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > real] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8524_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > real] :
% 5.68/6.02 ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.68/6.02 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8525_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_nat,F: nat > rat] :
% 5.68/6.02 ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8526_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > rat] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8527_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > rat] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8528_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_complex,F: complex > rat] :
% 5.68/6.02 ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.68/6.02 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8529_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_real,F: real > nat] :
% 5.68/6.02 ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8530_prod__le__1,axiom,
% 5.68/6.02 ! [A2: set_int,F: int > nat] :
% 5.68/6.02 ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ A2 )
% 5.68/6.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.68/6.02 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.68/6.02 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_le_1
% 5.68/6.02 thf(fact_8531_prod_Orelated,axiom,
% 5.68/6.02 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.68/6.02 ( ( R @ one_one_complex @ one_one_complex )
% 5.68/6.02 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_nat @ S3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups6464643781859351333omplex @ H2 @ S3 ) @ ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8532_prod_Orelated,axiom,
% 5.68/6.02 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.68/6.02 ( ( R @ one_one_complex @ one_one_complex )
% 5.68/6.02 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_int @ S3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups7440179247065528705omplex @ H2 @ S3 ) @ ( groups7440179247065528705omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8533_prod_Orelated,axiom,
% 5.68/6.02 ! [R: complex > complex > $o,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.68/6.02 ( ( R @ one_one_complex @ one_one_complex )
% 5.68/6.02 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups3708469109370488835omplex @ H2 @ S3 ) @ ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8534_prod_Orelated,axiom,
% 5.68/6.02 ! [R: real > real > $o,S3: set_nat,H2: nat > real,G: nat > real] :
% 5.68/6.02 ( ( R @ one_one_real @ one_one_real )
% 5.68/6.02 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_nat @ S3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups129246275422532515t_real @ H2 @ S3 ) @ ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8535_prod_Orelated,axiom,
% 5.68/6.02 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.68/6.02 ( ( R @ one_one_real @ one_one_real )
% 5.68/6.02 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_int @ S3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups2316167850115554303t_real @ H2 @ S3 ) @ ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8536_prod_Orelated,axiom,
% 5.68/6.02 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.68/6.02 ( ( R @ one_one_real @ one_one_real )
% 5.68/6.02 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups766887009212190081x_real @ H2 @ S3 ) @ ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8537_prod_Orelated,axiom,
% 5.68/6.02 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.68/6.02 ( ( R @ one_one_rat @ one_one_rat )
% 5.68/6.02 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_nat @ S3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8538_prod_Orelated,axiom,
% 5.68/6.02 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.68/6.02 ( ( R @ one_one_rat @ one_one_rat )
% 5.68/6.02 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_int @ S3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S3 ) @ ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8539_prod_Orelated,axiom,
% 5.68/6.02 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.68/6.02 ( ( R @ one_one_rat @ one_one_rat )
% 5.68/6.02 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ S3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups225925009352817453ex_rat @ H2 @ S3 ) @ ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8540_prod_Orelated,axiom,
% 5.68/6.02 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.68/6.02 ( ( R @ one_one_nat @ one_one_nat )
% 5.68/6.02 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.68/6.02 ( ( ( R @ X15 @ X23 )
% 5.68/6.02 & ( R @ Y15 @ Y23 ) )
% 5.68/6.02 => ( R @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.68/6.02 => ( ( finite_finite_int @ S3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ S3 )
% 5.68/6.02 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.68/6.02 => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S3 ) @ ( groups1707563613775114915nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.related
% 5.68/6.02 thf(fact_8541_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8542_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8543_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,F: nat > code_integer] :
% 5.68/6.02 ( ( finite_finite_nat @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8544_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > code_integer] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups8682486955453173170nteger @ F @ A2 ) @ ( groups8682486955453173170nteger @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8545_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,F: int > nat] :
% 5.68/6.02 ( ( finite_finite_int @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8546_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,F: int > code_integer] :
% 5.68/6.02 ( ( finite_finite_int @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( groups3827104343326376752nteger @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8547_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,F: nat > nat] :
% 5.68/6.02 ( ( finite_finite_nat @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8548_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,F: nat > int] :
% 5.68/6.02 ( ( finite_finite_nat @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8549_prod__dvd__prod__subset,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,F: int > int] :
% 5.68/6.02 ( ( finite_finite_int @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.02 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B4 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset
% 5.68/6.02 thf(fact_8550_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 5.68/6.02 ( ( finite_finite_real @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8551_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8552_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_real,A2: set_real,F: real > int,G: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8553_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8554_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_real,A2: set_real,F: real > code_integer,G: real > code_integer] :
% 5.68/6.02 ( ( finite_finite_real @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups6225526099057966256nteger @ F @ A2 ) @ ( groups6225526099057966256nteger @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8555_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 5.68/6.02 ( ( finite_finite_nat @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: nat] :
% 5.68/6.02 ( ( member_nat @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8556_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,F: complex > code_integer,G: complex > code_integer] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups8682486955453173170nteger @ F @ A2 ) @ ( groups8682486955453173170nteger @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8557_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 5.68/6.02 ( ( finite_finite_int @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: int] :
% 5.68/6.02 ( ( member_int @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8558_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,F: int > code_integer,G: int > code_integer] :
% 5.68/6.02 ( ( finite_finite_int @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: int] :
% 5.68/6.02 ( ( member_int @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_Code_integer @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( groups3827104343326376752nteger @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8559_prod__dvd__prod__subset2,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.68/6.02 ( ( finite_finite_nat @ B4 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.02 => ( ! [A3: nat] :
% 5.68/6.02 ( ( member_nat @ A3 @ A2 )
% 5.68/6.02 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.68/6.02 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod_dvd_prod_subset2
% 5.68/6.02 thf(fact_8560_scaleR__right__mono,axiom,
% 5.68/6.02 ! [A: real,B: real,X: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.02 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_right_mono
% 5.68/6.02 thf(fact_8561_scaleR__right__mono__neg,axiom,
% 5.68/6.02 ! [B: real,A: real,C: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ B @ A )
% 5.68/6.02 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_right_mono_neg
% 5.68/6.02 thf(fact_8562_scaleR__le__cancel__left__pos,axiom,
% 5.68/6.02 ! [C: real,A: real,B: real] :
% 5.68/6.02 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.68/6.02 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_le_cancel_left_pos
% 5.68/6.02 thf(fact_8563_scaleR__le__cancel__left__neg,axiom,
% 5.68/6.02 ! [C: real,A: real,B: real] :
% 5.68/6.02 ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/6.02 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.68/6.02 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_le_cancel_left_neg
% 5.68/6.02 thf(fact_8564_scaleR__le__cancel__left,axiom,
% 5.68/6.02 ! [C: real,A: real,B: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.68/6.02 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/6.02 => ( ord_less_eq_real @ A @ B ) )
% 5.68/6.02 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.68/6.02 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_le_cancel_left
% 5.68/6.02 thf(fact_8565_scaleR__left__mono,axiom,
% 5.68/6.02 ! [X: real,Y2: real,A: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.02 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y2 ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left_mono
% 5.68/6.02 thf(fact_8566_scaleR__left__mono__neg,axiom,
% 5.68/6.02 ! [B: real,A: real,C: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ B @ A )
% 5.68/6.02 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.68/6.02 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % scaleR_left_mono_neg
% 5.68/6.02 thf(fact_8567_gbinomial__Suc__Suc,axiom,
% 5.68/6.02 ! [A: complex,K: nat] :
% 5.68/6.02 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.68/6.02 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc_Suc
% 5.68/6.02 thf(fact_8568_gbinomial__Suc__Suc,axiom,
% 5.68/6.02 ! [A: real,K: nat] :
% 5.68/6.02 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.68/6.02 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc_Suc
% 5.68/6.02 thf(fact_8569_gbinomial__Suc__Suc,axiom,
% 5.68/6.02 ! [A: rat,K: nat] :
% 5.68/6.02 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.68/6.02 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc_Suc
% 5.68/6.02 thf(fact_8570_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.68/6.02 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.68/6.02 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.68/6.02
% 5.68/6.02 % Real_Vector_Spaces.le_add_iff1
% 5.68/6.02 thf(fact_8571_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.68/6.02 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.68/6.02 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.68/6.02 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % Real_Vector_Spaces.le_add_iff2
% 5.68/6.02 thf(fact_8572_gbinomial__of__nat__symmetric,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.68/6.02 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_of_nat_symmetric
% 5.68/6.02 thf(fact_8573_gbinomial__of__nat__symmetric,axiom,
% 5.68/6.02 ! [K: nat,N: nat] :
% 5.68/6.02 ( ( ord_less_eq_nat @ K @ N )
% 5.68/6.02 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.68/6.02 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_of_nat_symmetric
% 5.68/6.02 thf(fact_8574_prod_Onat__diff__reindex,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.02 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.nat_diff_reindex
% 5.68/6.02 thf(fact_8575_prod_Onat__diff__reindex,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 5.68/6.02 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.02 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.nat_diff_reindex
% 5.68/6.02 thf(fact_8576_prod_OatLeastAtMost__rev,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat,M: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.68/6.02 = ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeastAtMost_rev
% 5.68/6.02 thf(fact_8577_prod_OatLeastAtMost__rev,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat,M: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.68/6.02 = ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeastAtMost_rev
% 5.68/6.02 thf(fact_8578_gbinomial__Suc,axiom,
% 5.68/6.02 ! [A: complex,K: nat] :
% 5.68/6.02 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.68/6.02 = ( divide1717551699836669952omplex
% 5.68/6.02 @ ( groups6464643781859351333omplex
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.68/6.02 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc
% 5.68/6.02 thf(fact_8579_gbinomial__Suc,axiom,
% 5.68/6.02 ! [A: rat,K: nat] :
% 5.68/6.02 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.68/6.02 = ( divide_divide_rat
% 5.68/6.02 @ ( groups73079841787564623at_rat
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.68/6.02 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc
% 5.68/6.02 thf(fact_8580_gbinomial__Suc,axiom,
% 5.68/6.02 ! [A: real,K: nat] :
% 5.68/6.02 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.68/6.02 = ( divide_divide_real
% 5.68/6.02 @ ( groups129246275422532515t_real
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.68/6.02 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc
% 5.68/6.02 thf(fact_8581_gbinomial__Suc,axiom,
% 5.68/6.02 ! [A: nat,K: nat] :
% 5.68/6.02 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.68/6.02 = ( divide_divide_nat
% 5.68/6.02 @ ( groups708209901874060359at_nat
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.68/6.02 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc
% 5.68/6.02 thf(fact_8582_gbinomial__Suc,axiom,
% 5.68/6.02 ! [A: int,K: nat] :
% 5.68/6.02 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.68/6.02 = ( divide_divide_int
% 5.68/6.02 @ ( groups705719431365010083at_int
% 5.68/6.02 @ ^ [I3: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 5.68/6.02 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.68/6.02 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % gbinomial_Suc
% 5.68/6.02 thf(fact_8583_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_real,I2: real,F: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( member_real @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8584_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_nat,I2: nat,F: nat > real] :
% 5.68/6.02 ( ( finite_finite_nat @ I5 )
% 5.68/6.02 => ( ( member_nat @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8585_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_int,I2: int,F: int > real] :
% 5.68/6.02 ( ( finite_finite_int @ I5 )
% 5.68/6.02 => ( ( member_int @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8586_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_complex,I2: complex,F: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( member_complex @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8587_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_real,I2: real,F: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( member_real @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8588_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.68/6.02 ( ( finite_finite_nat @ I5 )
% 5.68/6.02 => ( ( member_nat @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8589_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_int,I2: int,F: int > rat] :
% 5.68/6.02 ( ( finite_finite_int @ I5 )
% 5.68/6.02 => ( ( member_int @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8590_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_complex,I2: complex,F: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( member_complex @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8591_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_real,I2: real,F: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( member_real @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8592_less__1__prod2,axiom,
% 5.68/6.02 ! [I5: set_complex,I2: complex,F: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( member_complex @ I2 @ I5 )
% 5.68/6.02 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod2
% 5.68/6.02 thf(fact_8593_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_complex,F: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_complex )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8594_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_nat,F: nat > real] :
% 5.68/6.02 ( ( finite_finite_nat @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_nat )
% 5.68/6.02 => ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8595_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_int,F: int > real] :
% 5.68/6.02 ( ( finite_finite_int @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_int )
% 5.68/6.02 => ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8596_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_real,F: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_real )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8597_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_complex,F: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_complex )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8598_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_nat,F: nat > rat] :
% 5.68/6.02 ( ( finite_finite_nat @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_nat )
% 5.68/6.02 => ( ! [I4: nat] :
% 5.68/6.02 ( ( member_nat @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8599_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_int,F: int > rat] :
% 5.68/6.02 ( ( finite_finite_int @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_int )
% 5.68/6.02 => ( ! [I4: int] :
% 5.68/6.02 ( ( member_int @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8600_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_real,F: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_real )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8601_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_complex,F: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_complex )
% 5.68/6.02 => ( ! [I4: complex] :
% 5.68/6.02 ( ( member_complex @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8602_less__1__prod,axiom,
% 5.68/6.02 ! [I5: set_real,F: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ I5 )
% 5.68/6.02 => ( ( I5 != bot_bot_set_real )
% 5.68/6.02 => ( ! [I4: real] :
% 5.68/6.02 ( ( member_real @ I4 @ I5 )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.68/6.02 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % less_1_prod
% 5.68/6.02 thf(fact_8603_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,G: complex > real] :
% 5.68/6.02 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.68/6.02 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups766887009212190081x_real @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8604_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,G: nat > real] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_nat @ A2 )
% 5.68/6.02 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.68/6.02 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B4 ) ) @ ( groups129246275422532515t_real @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8605_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,G: complex > rat] :
% 5.68/6.02 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.68/6.02 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups225925009352817453ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8606_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,G: nat > rat] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_nat @ A2 )
% 5.68/6.02 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.68/6.02 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A2 @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8607_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,G: complex > nat] :
% 5.68/6.02 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.68/6.02 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups861055069439313189ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8608_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_complex,A2: set_complex,G: complex > int] :
% 5.68/6.02 ( ( ord_le211207098394363844omplex @ B4 @ A2 )
% 5.68/6.02 => ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.68/6.02 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) @ ( groups858564598930262913ex_int @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8609_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,G: int > real] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_int @ A2 )
% 5.68/6.02 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.68/6.02 = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups2316167850115554303t_real @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8610_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,G: int > rat] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_int @ A2 )
% 5.68/6.02 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.68/6.02 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups1072433553688619179nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8611_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_int,A2: set_int,G: int > nat] :
% 5.68/6.02 ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_int @ A2 )
% 5.68/6.02 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.68/6.02 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ B4 ) ) @ ( groups1707563613775114915nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8612_prod_Osubset__diff,axiom,
% 5.68/6.02 ! [B4: set_nat,A2: set_nat,G: nat > nat] :
% 5.68/6.02 ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 5.68/6.02 => ( ( finite_finite_nat @ A2 )
% 5.68/6.02 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A2 @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ B4 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.subset_diff
% 5.68/6.02 thf(fact_8613_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups713298508707869441omplex @ G @ C4 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8614_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > complex,H2: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8615_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups1681761925125756287l_real @ G @ C4 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8616_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups766887009212190081x_real @ G @ C4 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8617_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups4061424788464935467al_rat @ G @ C4 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8618_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups225925009352817453ex_rat @ G @ C4 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8619_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > nat,H2: real > nat] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( ( groups4696554848551431203al_nat @ G @ A2 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups4696554848551431203al_nat @ G @ C4 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8620_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups861055069439313189ex_nat @ G @ C4 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8621_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > int,H2: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( ( groups4694064378042380927al_int @ G @ A2 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups4694064378042380927al_int @ G @ C4 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8622_prod_Osame__carrier,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > int,H2: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ B4 ) )
% 5.68/6.02 = ( ( groups858564598930262913ex_int @ G @ C4 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrier
% 5.68/6.02 thf(fact_8623_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > complex,H2: real > complex] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups713298508707869441omplex @ G @ A2 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8624_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > complex,H2: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8625_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > real,H2: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( ( groups1681761925125756287l_real @ G @ C4 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8626_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8627_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( ( groups4061424788464935467al_rat @ G @ C4 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8628_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( ( groups225925009352817453ex_rat @ G @ C4 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8629_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > nat,H2: real > nat] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( ( groups4696554848551431203al_nat @ G @ C4 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8630_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( ( groups861055069439313189ex_nat @ G @ C4 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8631_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_real,A2: set_real,B4: set_real,G: real > int,H2: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: real] :
% 5.68/6.02 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [B2: real] :
% 5.68/6.02 ( ( member_real @ B2 @ ( minus_minus_set_real @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( ( groups4694064378042380927al_int @ G @ C4 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups4694064378042380927al_int @ G @ A2 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8632_prod_Osame__carrierI,axiom,
% 5.68/6.02 ! [C4: set_complex,A2: set_complex,B4: set_complex,G: complex > int,H2: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ B4 @ C4 )
% 5.68/6.02 => ( ! [A3: complex] :
% 5.68/6.02 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.68/6.02 => ( ( G @ A3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [B2: complex] :
% 5.68/6.02 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C4 @ B4 ) )
% 5.68/6.02 => ( ( H2 @ B2 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( ( groups858564598930262913ex_int @ G @ C4 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ C4 ) )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.same_carrierI
% 5.68/6.02 thf(fact_8633_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8634_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.68/6.02 = ( groups766887009212190081x_real @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8635_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8636_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ S3 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8637_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ S3 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8638_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups6464643781859351333omplex @ G @ S3 )
% 5.68/6.02 = ( groups6464643781859351333omplex @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8639_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > real] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups129246275422532515t_real @ G @ S3 )
% 5.68/6.02 = ( groups129246275422532515t_real @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8640_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( groups73079841787564623at_rat @ G @ S3 )
% 5.68/6.02 = ( groups73079841787564623at_rat @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8641_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.68/6.02 ( ( finite_finite_int @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.68/6.02 = ( groups7440179247065528705omplex @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8642_prod_Omono__neutral__left,axiom,
% 5.68/6.02 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.68/6.02 ( ( finite_finite_int @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.68/6.02 = ( groups2316167850115554303t_real @ G @ T3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_left
% 5.68/6.02 thf(fact_8643_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8644_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ T3 )
% 5.68/6.02 = ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8645_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8646_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8647_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8648_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups6464643781859351333omplex @ G @ T3 )
% 5.68/6.02 = ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8649_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > real] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups129246275422532515t_real @ G @ T3 )
% 5.68/6.02 = ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8650_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.68/6.02 ( ( finite_finite_nat @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: nat] :
% 5.68/6.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ( groups73079841787564623at_rat @ G @ T3 )
% 5.68/6.02 = ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8651_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.68/6.02 ( ( finite_finite_int @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ( groups7440179247065528705omplex @ G @ T3 )
% 5.68/6.02 = ( groups7440179247065528705omplex @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8652_prod_Omono__neutral__right,axiom,
% 5.68/6.02 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.68/6.02 ( ( finite_finite_int @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: int] :
% 5.68/6.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ( groups2316167850115554303t_real @ G @ T3 )
% 5.68/6.02 = ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_right
% 5.68/6.02 thf(fact_8653_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8654_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8655_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8656_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8657_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4061424788464935467al_rat @ G @ S3 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8658_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8659_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,H2: real > nat,G: real > nat] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4696554848551431203al_nat @ G @ S3 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8660_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ S3 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8661_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,H2: real > int,G: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4694064378042380927al_int @ G @ S3 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8662_prod_Omono__neutral__cong__left,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( H2 @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ S3 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_left
% 5.68/6.02 thf(fact_8663_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups713298508707869441omplex @ G @ T3 )
% 5.68/6.02 = ( groups713298508707869441omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8664_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > complex,H2: complex > complex] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_complex ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 5.68/6.02 = ( groups3708469109370488835omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8665_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups1681761925125756287l_real @ G @ T3 )
% 5.68/6.02 = ( groups1681761925125756287l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8666_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_real ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups766887009212190081x_real @ G @ T3 )
% 5.68/6.02 = ( groups766887009212190081x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8667_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4061424788464935467al_rat @ G @ T3 )
% 5.68/6.02 = ( groups4061424788464935467al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8668_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_rat ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups225925009352817453ex_rat @ G @ T3 )
% 5.68/6.02 = ( groups225925009352817453ex_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8669_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,G: real > nat,H2: real > nat] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4696554848551431203al_nat @ G @ T3 )
% 5.68/6.02 = ( groups4696554848551431203al_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8670_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_nat ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 5.68/6.02 = ( groups861055069439313189ex_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8671_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_real,S3: set_real,G: real > int,H2: real > int] :
% 5.68/6.02 ( ( finite_finite_real @ T3 )
% 5.68/6.02 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [X3: real] :
% 5.68/6.02 ( ( member_real @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups4694064378042380927al_int @ G @ T3 )
% 5.68/6.02 = ( groups4694064378042380927al_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8672_prod_Omono__neutral__cong__right,axiom,
% 5.68/6.02 ! [T3: set_complex,S3: set_complex,G: complex > int,H2: complex > int] :
% 5.68/6.02 ( ( finite3207457112153483333omplex @ T3 )
% 5.68/6.02 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = one_one_int ) )
% 5.68/6.02 => ( ! [X3: complex] :
% 5.68/6.02 ( ( member_complex @ X3 @ S3 )
% 5.68/6.02 => ( ( G @ X3 )
% 5.68/6.02 = ( H2 @ X3 ) ) )
% 5.68/6.02 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 5.68/6.02 = ( groups858564598930262913ex_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.mono_neutral_cong_right
% 5.68/6.02 thf(fact_8673_prod_OatLeast0__atMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > real,N: nat] :
% 5.68/6.02 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeast0_atMost_Suc
% 5.68/6.02 thf(fact_8674_prod_OatLeast0__atMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > rat,N: nat] :
% 5.68/6.02 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeast0_atMost_Suc
% 5.68/6.02 thf(fact_8675_prod_OatLeast0__atMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > nat,N: nat] :
% 5.68/6.02 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeast0_atMost_Suc
% 5.68/6.02 thf(fact_8676_prod_OatLeast0__atMost__Suc,axiom,
% 5.68/6.02 ! [G: nat > int,N: nat] :
% 5.68/6.02 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.68/6.02 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.68/6.02
% 5.68/6.02 % prod.atLeast0_atMost_Suc
% 5.68/6.02 thf(fact_8677_prod_OatLeast__Suc__atMost,axiom,
% 5.68/6.02 ! [M: nat,N: nat,G: nat > real] :
% 5.68/6.02 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.03 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast_Suc_atMost
% 5.68/6.03 thf(fact_8678_prod_OatLeast__Suc__atMost,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast_Suc_atMost
% 5.68/6.03 thf(fact_8679_prod_OatLeast__Suc__atMost,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast_Suc_atMost
% 5.68/6.03 thf(fact_8680_prod_OatLeast__Suc__atMost,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.68/6.03 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast_Suc_atMost
% 5.68/6.03 thf(fact_8681_prod_Onat__ivl__Suc_H,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > real] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/6.03 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nat_ivl_Suc'
% 5.68/6.03 thf(fact_8682_prod_Onat__ivl__Suc_H,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/6.03 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nat_ivl_Suc'
% 5.68/6.03 thf(fact_8683_prod_Onat__ivl__Suc_H,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/6.03 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nat_ivl_Suc'
% 5.68/6.03 thf(fact_8684_prod_Onat__ivl__Suc_H,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/6.03 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nat_ivl_Suc'
% 5.68/6.03 thf(fact_8685_scaleR__le__0__iff,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.68/6.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.68/6.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.68/6.03 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.68/6.03 | ( A = zero_zero_real ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_le_0_iff
% 5.68/6.03 thf(fact_8686_zero__le__scaleR__iff,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.68/6.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.68/6.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.68/6.03 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.68/6.03 | ( A = zero_zero_real ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % zero_le_scaleR_iff
% 5.68/6.03 thf(fact_8687_scaleR__nonpos__nonpos,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_nonpos_nonpos
% 5.68/6.03 thf(fact_8688_scaleR__nonpos__nonneg,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_nonpos_nonneg
% 5.68/6.03 thf(fact_8689_scaleR__nonneg__nonpos,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_nonneg_nonpos
% 5.68/6.03 thf(fact_8690_scaleR__nonneg__nonneg,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_nonneg_nonneg
% 5.68/6.03 thf(fact_8691_split__scaleR__pos__le,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.68/6.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/6.03 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % split_scaleR_pos_le
% 5.68/6.03 thf(fact_8692_split__scaleR__neg__le,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 & ( ord_less_eq_real @ X @ zero_zero_real ) )
% 5.68/6.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/6.03 & ( ord_less_eq_real @ zero_zero_real @ X ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % split_scaleR_neg_le
% 5.68/6.03 thf(fact_8693_scaleR__mono_H,axiom,
% 5.68/6.03 ! [A: real,B: real,C: real,D: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.03 => ( ( ord_less_eq_real @ C @ D )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_mono'
% 5.68/6.03 thf(fact_8694_scaleR__mono,axiom,
% 5.68/6.03 ! [A: real,B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ Y2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_mono
% 5.68/6.03 thf(fact_8695_scaleR__left__le__one__le,axiom,
% 5.68/6.03 ! [X: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_left_le_one_le
% 5.68/6.03 thf(fact_8696_scaleR__2,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 = ( plus_plus_real @ X @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_2
% 5.68/6.03 thf(fact_8697_scaleR__2,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 = ( plus_plus_complex @ X @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % scaleR_2
% 5.68/6.03 thf(fact_8698_gbinomial__addition__formula,axiom,
% 5.68/6.03 ! [A: complex,K: nat] :
% 5.68/6.03 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.68/6.03 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_addition_formula
% 5.68/6.03 thf(fact_8699_gbinomial__addition__formula,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.68/6.03 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_addition_formula
% 5.68/6.03 thf(fact_8700_gbinomial__addition__formula,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.68/6.03 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_addition_formula
% 5.68/6.03 thf(fact_8701_gbinomial__absorb__comp,axiom,
% 5.68/6.03 ! [A: complex,K: nat] :
% 5.68/6.03 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.68/6.03 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorb_comp
% 5.68/6.03 thf(fact_8702_gbinomial__absorb__comp,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.68/6.03 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorb_comp
% 5.68/6.03 thf(fact_8703_gbinomial__absorb__comp,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.68/6.03 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorb_comp
% 5.68/6.03 thf(fact_8704_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.68/6.03 ! [K: nat,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.68/6.03 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_ge_n_over_k_pow_k
% 5.68/6.03 thf(fact_8705_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.68/6.03 ! [K: nat,A: rat] :
% 5.68/6.03 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.68/6.03 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_ge_n_over_k_pow_k
% 5.68/6.03 thf(fact_8706_gbinomial__mult__1,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_mult_1
% 5.68/6.03 thf(fact_8707_gbinomial__mult__1,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_mult_1
% 5.68/6.03 thf(fact_8708_gbinomial__mult__1_H,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.68/6.03 = ( 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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_mult_1'
% 5.68/6.03 thf(fact_8709_gbinomial__mult__1_H,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.68/6.03 = ( 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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_mult_1'
% 5.68/6.03 thf(fact_8710_prod_OlessThan__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > real,N: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.lessThan_Suc_shift
% 5.68/6.03 thf(fact_8711_prod_OlessThan__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > rat,N: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.lessThan_Suc_shift
% 5.68/6.03 thf(fact_8712_prod_OlessThan__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.lessThan_Suc_shift
% 5.68/6.03 thf(fact_8713_prod_OlessThan__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.lessThan_Suc_shift
% 5.68/6.03 thf(fact_8714_prod_OSuc__reindex__ivl,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > real] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_real @ ( G @ M )
% 5.68/6.03 @ ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.Suc_reindex_ivl
% 5.68/6.03 thf(fact_8715_prod_OSuc__reindex__ivl,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > rat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ M )
% 5.68/6.03 @ ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.Suc_reindex_ivl
% 5.68/6.03 thf(fact_8716_prod_OSuc__reindex__ivl,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ M )
% 5.68/6.03 @ ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.Suc_reindex_ivl
% 5.68/6.03 thf(fact_8717_prod_OSuc__reindex__ivl,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( G @ M )
% 5.68/6.03 @ ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.Suc_reindex_ivl
% 5.68/6.03 thf(fact_8718_prod_OatMost__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > real,N: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_Suc_shift
% 5.68/6.03 thf(fact_8719_prod_OatMost__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > rat,N: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_Suc_shift
% 5.68/6.03 thf(fact_8720_prod_OatMost__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_Suc_shift
% 5.68/6.03 thf(fact_8721_prod_OatMost__Suc__shift,axiom,
% 5.68/6.03 ! [G: nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_Suc_shift
% 5.68/6.03 thf(fact_8722_prod_OatLeast1__atMost__eq,axiom,
% 5.68/6.03 ! [G: nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast1_atMost_eq
% 5.68/6.03 thf(fact_8723_prod_OatLeast1__atMost__eq,axiom,
% 5.68/6.03 ! [G: nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atLeast1_atMost_eq
% 5.68/6.03 thf(fact_8724_prod_Onested__swap_H,axiom,
% 5.68/6.03 ! [A: nat > nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [J3: nat] :
% 5.68/6.03 ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nested_swap'
% 5.68/6.03 thf(fact_8725_prod_Onested__swap_H,axiom,
% 5.68/6.03 ! [A: nat > nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [J3: nat] :
% 5.68/6.03 ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.nested_swap'
% 5.68/6.03 thf(fact_8726_prod__atLeastAtMost__code,axiom,
% 5.68/6.03 ! [F: nat > complex,A: nat,B: nat] :
% 5.68/6.03 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.03 = ( set_fo1517530859248394432omplex
% 5.68/6.03 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 5.68/6.03 @ A
% 5.68/6.03 @ B
% 5.68/6.03 @ one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_atLeastAtMost_code
% 5.68/6.03 thf(fact_8727_prod__atLeastAtMost__code,axiom,
% 5.68/6.03 ! [F: nat > real,A: nat,B: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.03 = ( set_fo3111899725591712190t_real
% 5.68/6.03 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 5.68/6.03 @ A
% 5.68/6.03 @ B
% 5.68/6.03 @ one_one_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_atLeastAtMost_code
% 5.68/6.03 thf(fact_8728_prod__atLeastAtMost__code,axiom,
% 5.68/6.03 ! [F: nat > rat,A: nat,B: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.03 = ( set_fo1949268297981939178at_rat
% 5.68/6.03 @ ^ [A4: nat] : ( times_times_rat @ ( F @ A4 ) )
% 5.68/6.03 @ A
% 5.68/6.03 @ B
% 5.68/6.03 @ one_one_rat ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_atLeastAtMost_code
% 5.68/6.03 thf(fact_8729_prod__atLeastAtMost__code,axiom,
% 5.68/6.03 ! [F: nat > nat,A: nat,B: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.03 = ( set_fo2584398358068434914at_nat
% 5.68/6.03 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 5.68/6.03 @ A
% 5.68/6.03 @ B
% 5.68/6.03 @ one_one_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_atLeastAtMost_code
% 5.68/6.03 thf(fact_8730_prod__atLeastAtMost__code,axiom,
% 5.68/6.03 ! [F: nat > int,A: nat,B: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.68/6.03 = ( set_fo2581907887559384638at_int
% 5.68/6.03 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 5.68/6.03 @ A
% 5.68/6.03 @ B
% 5.68/6.03 @ one_one_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_atLeastAtMost_code
% 5.68/6.03 thf(fact_8731_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_complex )
% 5.68/6.03 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8732_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_nat )
% 5.68/6.03 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8733_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > real,G: int > real] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_int )
% 5.68/6.03 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8734_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_real,F: real > real,G: real > real] :
% 5.68/6.03 ( ( finite_finite_real @ A2 )
% 5.68/6.03 => ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_real )
% 5.68/6.03 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8735_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_complex )
% 5.68/6.03 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8736_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_nat )
% 5.68/6.03 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8737_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_int )
% 5.68/6.03 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8738_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.68/6.03 ( ( finite_finite_real @ A2 )
% 5.68/6.03 => ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_rat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_real )
% 5.68/6.03 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8739_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_complex )
% 5.68/6.03 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8740_prod__mono__strict,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ A2 )
% 5.68/6.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.68/6.03 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.68/6.03 => ( ( A2 != bot_bot_set_int )
% 5.68/6.03 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono_strict
% 5.68/6.03 thf(fact_8741_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_nat,F: nat > code_integer] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: nat] :
% 5.68/6.03 ( ( member_nat @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8742_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > code_integer] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3827104343326376752nteger @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: int] :
% 5.68/6.03 ( ( member_int @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8743_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > code_integer] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: complex] :
% 5.68/6.03 ( ( member_complex @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8744_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > nat] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: int] :
% 5.68/6.03 ( ( member_int @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8745_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > nat] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: complex] :
% 5.68/6.03 ( ( member_complex @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8746_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_complex,F: complex > int] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: complex] :
% 5.68/6.03 ( ( member_complex @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8747_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_nat,F: nat > nat] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: nat] :
% 5.68/6.03 ( ( member_nat @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8748_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_nat,F: nat > int] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: nat] :
% 5.68/6.03 ( ( member_nat @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8749_even__prod__iff,axiom,
% 5.68/6.03 ! [A2: set_int,F: int > int] :
% 5.68/6.03 ( ( finite_finite_int @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.68/6.03 = ( ? [X2: int] :
% 5.68/6.03 ( ( member_int @ X2 @ A2 )
% 5.68/6.03 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_prod_iff
% 5.68/6.03 thf(fact_8750_prod_Oub__add__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > real,P4: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/6.03 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/6.03 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.ub_add_nat
% 5.68/6.03 thf(fact_8751_prod_Oub__add__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > rat,P4: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/6.03 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/6.03 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.ub_add_nat
% 5.68/6.03 thf(fact_8752_prod_Oub__add__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > nat,P4: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/6.03 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/6.03 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.ub_add_nat
% 5.68/6.03 thf(fact_8753_prod_Oub__add__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat,G: nat > int,P4: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.68/6.03 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.68/6.03 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.ub_add_nat
% 5.68/6.03 thf(fact_8754_sin__converges,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( sums_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) )
% 5.68/6.03 @ ( sin_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_converges
% 5.68/6.03 thf(fact_8755_sin__converges,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( sums_complex
% 5.68/6.03 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) )
% 5.68/6.03 @ ( sin_complex @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_converges
% 5.68/6.03 thf(fact_8756_sin__def,axiom,
% 5.68/6.03 ( sin_real
% 5.68/6.03 = ( ^ [X2: real] :
% 5.68/6.03 ( suminf_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_def
% 5.68/6.03 thf(fact_8757_sin__def,axiom,
% 5.68/6.03 ( sin_complex
% 5.68/6.03 = ( ^ [X2: complex] :
% 5.68/6.03 ( suminf_complex
% 5.68/6.03 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_def
% 5.68/6.03 thf(fact_8758_cos__converges,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( sums_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) )
% 5.68/6.03 @ ( cos_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_converges
% 5.68/6.03 thf(fact_8759_cos__converges,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( sums_complex
% 5.68/6.03 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) )
% 5.68/6.03 @ ( cos_complex @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_converges
% 5.68/6.03 thf(fact_8760_cos__def,axiom,
% 5.68/6.03 ( cos_real
% 5.68/6.03 = ( ^ [X2: real] :
% 5.68/6.03 ( suminf_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_def
% 5.68/6.03 thf(fact_8761_cos__def,axiom,
% 5.68/6.03 ( cos_complex
% 5.68/6.03 = ( ^ [X2: complex] :
% 5.68/6.03 ( suminf_complex
% 5.68/6.03 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_def
% 5.68/6.03 thf(fact_8762_summable__norm__sin,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( summable_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % summable_norm_sin
% 5.68/6.03 thf(fact_8763_summable__norm__sin,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( summable_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % summable_norm_sin
% 5.68/6.03 thf(fact_8764_summable__norm__cos,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( summable_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % summable_norm_cos
% 5.68/6.03 thf(fact_8765_summable__norm__cos,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( summable_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % summable_norm_cos
% 5.68/6.03 thf(fact_8766_Suc__times__gbinomial,axiom,
% 5.68/6.03 ! [K: nat,A: complex] :
% 5.68/6.03 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_times_gbinomial
% 5.68/6.03 thf(fact_8767_Suc__times__gbinomial,axiom,
% 5.68/6.03 ! [K: nat,A: real] :
% 5.68/6.03 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_times_gbinomial
% 5.68/6.03 thf(fact_8768_Suc__times__gbinomial,axiom,
% 5.68/6.03 ! [K: nat,A: rat] :
% 5.68/6.03 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_times_gbinomial
% 5.68/6.03 thf(fact_8769_gbinomial__absorption,axiom,
% 5.68/6.03 ! [K: nat,A: complex] :
% 5.68/6.03 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorption
% 5.68/6.03 thf(fact_8770_gbinomial__absorption,axiom,
% 5.68/6.03 ! [K: nat,A: real] :
% 5.68/6.03 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorption
% 5.68/6.03 thf(fact_8771_gbinomial__absorption,axiom,
% 5.68/6.03 ! [K: nat,A: rat] :
% 5.68/6.03 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.68/6.03 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_absorption
% 5.68/6.03 thf(fact_8772_gbinomial__trinomial__revision,axiom,
% 5.68/6.03 ! [K: nat,M: nat,A: real] :
% 5.68/6.03 ( ( ord_less_eq_nat @ K @ M )
% 5.68/6.03 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.68/6.03 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_trinomial_revision
% 5.68/6.03 thf(fact_8773_gbinomial__trinomial__revision,axiom,
% 5.68/6.03 ! [K: nat,M: nat,A: rat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ K @ M )
% 5.68/6.03 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.68/6.03 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_trinomial_revision
% 5.68/6.03 thf(fact_8774_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_real,Z: real > real,W: real > real] :
% 5.68/6.03 ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I5 ) @ ( groups1681761925125756287l_real @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups8097168146408367636l_real
% 5.68/6.03 @ ^ [I3: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8775_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_int,Z: int > real,W: int > real] :
% 5.68/6.03 ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I5 ) @ ( groups2316167850115554303t_real @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups8778361861064173332t_real
% 5.68/6.03 @ ^ [I3: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8776_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_complex,Z: complex > real,W: complex > real] :
% 5.68/6.03 ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups766887009212190081x_real @ Z @ I5 ) @ ( groups766887009212190081x_real @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups5808333547571424918x_real
% 5.68/6.03 @ ^ [I3: complex] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8777_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > real,W: product_prod_nat_nat > real] :
% 5.68/6.03 ( ! [I4: product_prod_nat_nat] :
% 5.68/6.03 ( ( member8440522571783428010at_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: product_prod_nat_nat] :
% 5.68/6.03 ( ( member8440522571783428010at_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6036352826371341000t_real @ Z @ I5 ) @ ( groups6036352826371341000t_real @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups4567486121110086003t_real
% 5.68/6.03 @ ^ [I3: product_prod_nat_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8778_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_real,Z: real > complex,W: real > complex] :
% 5.68/6.03 ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: real] :
% 5.68/6.03 ( ( member_real @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I5 ) @ ( groups713298508707869441omplex @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups8097168146408367636l_real
% 5.68/6.03 @ ^ [I3: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8779_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_int,Z: int > complex,W: int > complex] :
% 5.68/6.03 ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: int] :
% 5.68/6.03 ( ( member_int @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I5 ) @ ( groups7440179247065528705omplex @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups8778361861064173332t_real
% 5.68/6.03 @ ^ [I3: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8780_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_complex,Z: complex > complex,W: complex > complex] :
% 5.68/6.03 ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: complex] :
% 5.68/6.03 ( ( member_complex @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I5 ) @ ( groups3708469109370488835omplex @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups5808333547571424918x_real
% 5.68/6.03 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8781_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > complex,W: product_prod_nat_nat > complex] :
% 5.68/6.03 ( ! [I4: product_prod_nat_nat] :
% 5.68/6.03 ( ( member8440522571783428010at_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: product_prod_nat_nat] :
% 5.68/6.03 ( ( member8440522571783428010at_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z @ I5 ) @ ( groups8110221916422527690omplex @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups4567486121110086003t_real
% 5.68/6.03 @ ^ [I3: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8782_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_nat,Z: nat > real,W: nat > real] :
% 5.68/6.03 ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I5 ) @ ( groups129246275422532515t_real @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups6591440286371151544t_real
% 5.68/6.03 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8783_norm__prod__diff,axiom,
% 5.68/6.03 ! [I5: set_nat,Z: nat > complex,W: nat > complex] :
% 5.68/6.03 ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ! [I4: nat] :
% 5.68/6.03 ( ( member_nat @ I4 @ I5 )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I5 ) @ ( groups6464643781859351333omplex @ W @ I5 ) ) )
% 5.68/6.03 @ ( groups6591440286371151544t_real
% 5.68/6.03 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I3 ) @ ( W @ I3 ) ) )
% 5.68/6.03 @ I5 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % norm_prod_diff
% 5.68/6.03 thf(fact_8784_prod_OatMost__shift,axiom,
% 5.68/6.03 ! [G: nat > real,N: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_shift
% 5.68/6.03 thf(fact_8785_prod_OatMost__shift,axiom,
% 5.68/6.03 ! [G: nat > rat,N: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_shift
% 5.68/6.03 thf(fact_8786_prod_OatMost__shift,axiom,
% 5.68/6.03 ! [G: nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_shift
% 5.68/6.03 thf(fact_8787_prod_OatMost__shift,axiom,
% 5.68/6.03 ! [G: nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.68/6.03 @ ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.atMost_shift
% 5.68/6.03 thf(fact_8788_fact__eq__fact__times,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.03 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.68/6.03 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.68/6.03 @ ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [X2: nat] : X2
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % fact_eq_fact_times
% 5.68/6.03 thf(fact_8789_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_real,A2: set_real,F: real > real] :
% 5.68/6.03 ( ( finite_finite_real @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: real] :
% 5.68/6.03 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: real] :
% 5.68/6.03 ( ( member_real @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8790_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_complex,A2: set_complex,F: complex > real] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.03 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: complex] :
% 5.68/6.03 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: complex] :
% 5.68/6.03 ( ( member_complex @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8791_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_nat,A2: set_nat,F: nat > real] :
% 5.68/6.03 ( ( finite_finite_nat @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: nat] :
% 5.68/6.03 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: nat] :
% 5.68/6.03 ( ( member_nat @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8792_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_real,A2: set_real,F: real > rat] :
% 5.68/6.03 ( ( finite_finite_real @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: real] :
% 5.68/6.03 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: real] :
% 5.68/6.03 ( ( member_real @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8793_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_complex,A2: set_complex,F: complex > rat] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.03 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: complex] :
% 5.68/6.03 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: complex] :
% 5.68/6.03 ( ( member_complex @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8794_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_nat,A2: set_nat,F: nat > rat] :
% 5.68/6.03 ( ( finite_finite_nat @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: nat] :
% 5.68/6.03 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: nat] :
% 5.68/6.03 ( ( member_nat @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8795_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_real,A2: set_real,F: real > int] :
% 5.68/6.03 ( ( finite_finite_real @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: real] :
% 5.68/6.03 ( ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: real] :
% 5.68/6.03 ( ( member_real @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8796_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_complex,A2: set_complex,F: complex > int] :
% 5.68/6.03 ( ( finite3207457112153483333omplex @ B4 )
% 5.68/6.03 => ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: complex] :
% 5.68/6.03 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: complex] :
% 5.68/6.03 ( ( member_complex @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8797_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_int,A2: set_int,F: int > real] :
% 5.68/6.03 ( ( finite_finite_int @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: int] :
% 5.68/6.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: int] :
% 5.68/6.03 ( ( member_int @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8798_prod__mono2,axiom,
% 5.68/6.03 ! [B4: set_int,A2: set_int,F: int > rat] :
% 5.68/6.03 ( ( finite_finite_int @ B4 )
% 5.68/6.03 => ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.68/6.03 => ( ! [B2: int] :
% 5.68/6.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) )
% 5.68/6.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 5.68/6.03 => ( ! [A3: int] :
% 5.68/6.03 ( ( member_int @ A3 @ A2 )
% 5.68/6.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 5.68/6.03 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B4 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_mono2
% 5.68/6.03 thf(fact_8799_gbinomial__parallel__sum,axiom,
% 5.68/6.03 ! [A: complex,N: nat] :
% 5.68/6.03 ( ( groups2073611262835488442omplex
% 5.68/6.03 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_parallel_sum
% 5.68/6.03 thf(fact_8800_gbinomial__parallel__sum,axiom,
% 5.68/6.03 ! [A: rat,N: nat] :
% 5.68/6.03 ( ( groups2906978787729119204at_rat
% 5.68/6.03 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_parallel_sum
% 5.68/6.03 thf(fact_8801_gbinomial__parallel__sum,axiom,
% 5.68/6.03 ! [A: real,N: nat] :
% 5.68/6.03 ( ( groups6591440286371151544t_real
% 5.68/6.03 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.03 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_parallel_sum
% 5.68/6.03 thf(fact_8802_sin__minus__converges,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( sums_real
% 5.68/6.03 @ ^ [N2: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N2 ) ) )
% 5.68/6.03 @ ( sin_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_minus_converges
% 5.68/6.03 thf(fact_8803_sin__minus__converges,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( sums_complex
% 5.68/6.03 @ ^ [N2: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N2 ) ) )
% 5.68/6.03 @ ( sin_complex @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_minus_converges
% 5.68/6.03 thf(fact_8804_cos__minus__converges,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( sums_real
% 5.68/6.03 @ ^ [N2: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N2 ) )
% 5.68/6.03 @ ( cos_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_minus_converges
% 5.68/6.03 thf(fact_8805_cos__minus__converges,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( sums_complex
% 5.68/6.03 @ ^ [N2: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N2 ) )
% 5.68/6.03 @ ( cos_complex @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_minus_converges
% 5.68/6.03 thf(fact_8806_gbinomial__factors,axiom,
% 5.68/6.03 ! [A: complex,K: nat] :
% 5.68/6.03 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_factors
% 5.68/6.03 thf(fact_8807_gbinomial__factors,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_factors
% 5.68/6.03 thf(fact_8808_gbinomial__factors,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_factors
% 5.68/6.03 thf(fact_8809_gbinomial__rec,axiom,
% 5.68/6.03 ! [A: complex,K: nat] :
% 5.68/6.03 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_rec
% 5.68/6.03 thf(fact_8810_gbinomial__rec,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_rec
% 5.68/6.03 thf(fact_8811_gbinomial__rec,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.68/6.03 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_rec
% 5.68/6.03 thf(fact_8812_gbinomial__negated__upper,axiom,
% 5.68/6.03 ( gbinomial_complex
% 5.68/6.03 = ( ^ [A4: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A4 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_negated_upper
% 5.68/6.03 thf(fact_8813_gbinomial__negated__upper,axiom,
% 5.68/6.03 ( gbinomial_real
% 5.68/6.03 = ( ^ [A4: 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 ) @ A4 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_negated_upper
% 5.68/6.03 thf(fact_8814_gbinomial__negated__upper,axiom,
% 5.68/6.03 ( gbinomial_rat
% 5.68/6.03 = ( ^ [A4: 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 ) @ A4 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_negated_upper
% 5.68/6.03 thf(fact_8815_gbinomial__index__swap,axiom,
% 5.68/6.03 ! [K: nat,N: nat] :
% 5.68/6.03 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.68/6.03 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_index_swap
% 5.68/6.03 thf(fact_8816_gbinomial__index__swap,axiom,
% 5.68/6.03 ! [K: nat,N: nat] :
% 5.68/6.03 ( ( 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 ) )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_index_swap
% 5.68/6.03 thf(fact_8817_gbinomial__index__swap,axiom,
% 5.68/6.03 ! [K: nat,N: nat] :
% 5.68/6.03 ( ( 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 ) )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_index_swap
% 5.68/6.03 thf(fact_8818_pochhammer__Suc__prod,axiom,
% 5.68/6.03 ! [A: real,N: nat] :
% 5.68/6.03 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod
% 5.68/6.03 thf(fact_8819_pochhammer__Suc__prod,axiom,
% 5.68/6.03 ! [A: rat,N: nat] :
% 5.68/6.03 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod
% 5.68/6.03 thf(fact_8820_pochhammer__Suc__prod,axiom,
% 5.68/6.03 ! [A: nat,N: nat] :
% 5.68/6.03 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod
% 5.68/6.03 thf(fact_8821_pochhammer__Suc__prod,axiom,
% 5.68/6.03 ! [A: int,N: nat] :
% 5.68/6.03 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod
% 5.68/6.03 thf(fact_8822_pochhammer__prod__rev,axiom,
% 5.68/6.03 ( comm_s7457072308508201937r_real
% 5.68/6.03 = ( ^ [A4: real,N2: nat] :
% 5.68/6.03 ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_prod_rev
% 5.68/6.03 thf(fact_8823_pochhammer__prod__rev,axiom,
% 5.68/6.03 ( comm_s4028243227959126397er_rat
% 5.68/6.03 = ( ^ [A4: rat,N2: nat] :
% 5.68/6.03 ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_prod_rev
% 5.68/6.03 thf(fact_8824_pochhammer__prod__rev,axiom,
% 5.68/6.03 ( comm_s4663373288045622133er_nat
% 5.68/6.03 = ( ^ [A4: nat,N2: nat] :
% 5.68/6.03 ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_prod_rev
% 5.68/6.03 thf(fact_8825_pochhammer__prod__rev,axiom,
% 5.68/6.03 ( comm_s4660882817536571857er_int
% 5.68/6.03 = ( ^ [A4: int,N2: nat] :
% 5.68/6.03 ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_prod_rev
% 5.68/6.03 thf(fact_8826_fact__div__fact,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.03 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [X2: nat] : X2
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % fact_div_fact
% 5.68/6.03 thf(fact_8827_gbinomial__minus,axiom,
% 5.68/6.03 ! [A: complex,K: nat] :
% 5.68/6.03 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_minus
% 5.68/6.03 thf(fact_8828_gbinomial__minus,axiom,
% 5.68/6.03 ! [A: real,K: nat] :
% 5.68/6.03 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_minus
% 5.68/6.03 thf(fact_8829_gbinomial__minus,axiom,
% 5.68/6.03 ! [A: rat,K: nat] :
% 5.68/6.03 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_minus
% 5.68/6.03 thf(fact_8830_prod_Oin__pairs,axiom,
% 5.68/6.03 ! [G: nat > real,M: nat,N: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs
% 5.68/6.03 thf(fact_8831_prod_Oin__pairs,axiom,
% 5.68/6.03 ! [G: nat > rat,M: nat,N: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs
% 5.68/6.03 thf(fact_8832_prod_Oin__pairs,axiom,
% 5.68/6.03 ! [G: nat > nat,M: nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs
% 5.68/6.03 thf(fact_8833_prod_Oin__pairs,axiom,
% 5.68/6.03 ! [G: nat > int,M: nat,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs
% 5.68/6.03 thf(fact_8834_prod_Oin__pairs__0,axiom,
% 5.68/6.03 ! [G: nat > real,N: nat] :
% 5.68/6.03 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs_0
% 5.68/6.03 thf(fact_8835_prod_Oin__pairs__0,axiom,
% 5.68/6.03 ! [G: nat > rat,N: nat] :
% 5.68/6.03 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs_0
% 5.68/6.03 thf(fact_8836_prod_Oin__pairs__0,axiom,
% 5.68/6.03 ! [G: nat > nat,N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs_0
% 5.68/6.03 thf(fact_8837_prod_Oin__pairs__0,axiom,
% 5.68/6.03 ! [G: nat > int,N: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.in_pairs_0
% 5.68/6.03 thf(fact_8838_gbinomial__reduce__nat,axiom,
% 5.68/6.03 ! [K: nat,A: complex] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.03 => ( ( gbinomial_complex @ A @ K )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_reduce_nat
% 5.68/6.03 thf(fact_8839_gbinomial__reduce__nat,axiom,
% 5.68/6.03 ! [K: nat,A: real] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.03 => ( ( gbinomial_real @ A @ K )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_reduce_nat
% 5.68/6.03 thf(fact_8840_gbinomial__reduce__nat,axiom,
% 5.68/6.03 ! [K: nat,A: rat] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.03 => ( ( gbinomial_rat @ A @ K )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_reduce_nat
% 5.68/6.03 thf(fact_8841_pochhammer__Suc__prod__rev,axiom,
% 5.68/6.03 ! [A: real,N: nat] :
% 5.68/6.03 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups129246275422532515t_real
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod_rev
% 5.68/6.03 thf(fact_8842_pochhammer__Suc__prod__rev,axiom,
% 5.68/6.03 ! [A: rat,N: nat] :
% 5.68/6.03 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups73079841787564623at_rat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod_rev
% 5.68/6.03 thf(fact_8843_pochhammer__Suc__prod__rev,axiom,
% 5.68/6.03 ! [A: nat,N: nat] :
% 5.68/6.03 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod_rev
% 5.68/6.03 thf(fact_8844_pochhammer__Suc__prod__rev,axiom,
% 5.68/6.03 ! [A: int,N: nat] :
% 5.68/6.03 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 5.68/6.03 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pochhammer_Suc_prod_rev
% 5.68/6.03 thf(fact_8845_gbinomial__pochhammer,axiom,
% 5.68/6.03 ( gbinomial_complex
% 5.68/6.03 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer
% 5.68/6.03 thf(fact_8846_gbinomial__pochhammer,axiom,
% 5.68/6.03 ( gbinomial_rat
% 5.68/6.03 = ( ^ [A4: 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 @ A4 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer
% 5.68/6.03 thf(fact_8847_gbinomial__pochhammer,axiom,
% 5.68/6.03 ( gbinomial_real
% 5.68/6.03 = ( ^ [A4: 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 @ A4 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer
% 5.68/6.03 thf(fact_8848_gbinomial__pochhammer_H,axiom,
% 5.68/6.03 ( gbinomial_complex
% 5.68/6.03 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer'
% 5.68/6.03 thf(fact_8849_gbinomial__pochhammer_H,axiom,
% 5.68/6.03 ( gbinomial_rat
% 5.68/6.03 = ( ^ [A4: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer'
% 5.68/6.03 thf(fact_8850_gbinomial__pochhammer_H,axiom,
% 5.68/6.03 ( gbinomial_real
% 5.68/6.03 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_pochhammer'
% 5.68/6.03 thf(fact_8851_gbinomial__sum__lower__neg,axiom,
% 5.68/6.03 ! [A: complex,M: nat] :
% 5.68/6.03 ( ( groups2073611262835488442omplex
% 5.68/6.03 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.03 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_sum_lower_neg
% 5.68/6.03 thf(fact_8852_gbinomial__sum__lower__neg,axiom,
% 5.68/6.03 ! [A: rat,M: nat] :
% 5.68/6.03 ( ( groups2906978787729119204at_rat
% 5.68/6.03 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.03 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_sum_lower_neg
% 5.68/6.03 thf(fact_8853_gbinomial__sum__lower__neg,axiom,
% 5.68/6.03 ! [A: real,M: nat] :
% 5.68/6.03 ( ( groups6591440286371151544t_real
% 5.68/6.03 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ M ) )
% 5.68/6.03 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % gbinomial_sum_lower_neg
% 5.68/6.03 thf(fact_8854_prod_Ozero__middle,axiom,
% 5.68/6.03 ! [P4: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.03 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.03 => ( ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.03 = ( groups708209901874060359at_nat
% 5.68/6.03 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.zero_middle
% 5.68/6.03 thf(fact_8855_prod_Ozero__middle,axiom,
% 5.68/6.03 ! [P4: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.68/6.03 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.68/6.03 => ( ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ P4 ) )
% 5.68/6.03 = ( groups705719431365010083at_int
% 5.68/6.03 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.68/6.03 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod.zero_middle
% 5.68/6.03 thf(fact_8856_Maclaurin__sin__bound,axiom,
% 5.68/6.03 ! [X: real,N: nat] :
% 5.68/6.03 ( ord_less_eq_real
% 5.68/6.03 @ ( abs_abs_real
% 5.68/6.03 @ ( minus_minus_real @ ( sin_real @ X )
% 5.68/6.03 @ ( groups6591440286371151544t_real
% 5.68/6.03 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.68/6.03 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Maclaurin_sin_bound
% 5.68/6.03 thf(fact_8857_cot__less__zero,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cot_less_zero
% 5.68/6.03 thf(fact_8858_i__even__power,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.03 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % i_even_power
% 5.68/6.03 thf(fact_8859_log__base__10__eq1,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_base_10_eq1
% 5.68/6.03 thf(fact_8860_divide__i,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.68/6.03 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_i
% 5.68/6.03 thf(fact_8861_complex__i__mult__minus,axiom,
% 5.68/6.03 ! [X: complex] :
% 5.68/6.03 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_i_mult_minus
% 5.68/6.03 thf(fact_8862_i__squared,axiom,
% 5.68/6.03 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % i_squared
% 5.68/6.03 thf(fact_8863_divide__numeral__i,axiom,
% 5.68/6.03 ! [Z: complex,N: num] :
% 5.68/6.03 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.68/6.03 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_numeral_i
% 5.68/6.03 thf(fact_8864_log__le__cancel__iff,axiom,
% 5.68/6.03 ! [A: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ A )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 5.68/6.03 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_le_cancel_iff
% 5.68/6.03 thf(fact_8865_log__le__one__cancel__iff,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ A )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.68/6.03 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_le_one_cancel_iff
% 5.68/6.03 thf(fact_8866_one__le__log__cancel__iff,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ A )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.68/6.03 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % one_le_log_cancel_iff
% 5.68/6.03 thf(fact_8867_log__le__zero__cancel__iff,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ A )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.68/6.03 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_le_zero_cancel_iff
% 5.68/6.03 thf(fact_8868_zero__le__log__cancel__iff,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ A )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.68/6.03 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % zero_le_log_cancel_iff
% 5.68/6.03 thf(fact_8869_cot__npi,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.68/6.03 = zero_zero_real ) ).
% 5.68/6.03
% 5.68/6.03 % cot_npi
% 5.68/6.03 thf(fact_8870_log__pow__cancel,axiom,
% 5.68/6.03 ! [A: real,B: nat] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( A != one_one_real )
% 5.68/6.03 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.68/6.03 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_pow_cancel
% 5.68/6.03 thf(fact_8871_cot__periodic,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.68/6.03 = ( cot_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cot_periodic
% 5.68/6.03 thf(fact_8872_power2__i,axiom,
% 5.68/6.03 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % power2_i
% 5.68/6.03 thf(fact_8873_real__sqrt__inverse,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.68/6.03 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_sqrt_inverse
% 5.68/6.03 thf(fact_8874_complex__i__not__numeral,axiom,
% 5.68/6.03 ! [W: num] :
% 5.68/6.03 ( imaginary_unit
% 5.68/6.03 != ( numera6690914467698888265omplex @ W ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_i_not_numeral
% 5.68/6.03 thf(fact_8875_divide__real__def,axiom,
% 5.68/6.03 ( divide_divide_real
% 5.68/6.03 = ( ^ [X2: real,Y: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_real_def
% 5.68/6.03 thf(fact_8876_i__times__eq__iff,axiom,
% 5.68/6.03 ! [W: complex,Z: complex] :
% 5.68/6.03 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.68/6.03 = Z )
% 5.68/6.03 = ( W
% 5.68/6.03 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % i_times_eq_iff
% 5.68/6.03 thf(fact_8877_complex__i__not__neg__numeral,axiom,
% 5.68/6.03 ! [W: num] :
% 5.68/6.03 ( imaginary_unit
% 5.68/6.03 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_i_not_neg_numeral
% 5.68/6.03 thf(fact_8878_Complex__mult__i,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.68/6.03 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.68/6.03
% 5.68/6.03 % Complex_mult_i
% 5.68/6.03 thf(fact_8879_i__mult__Complex,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.68/6.03 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.68/6.03
% 5.68/6.03 % i_mult_Complex
% 5.68/6.03 thf(fact_8880_less__log__of__power,axiom,
% 5.68/6.03 ! [B: real,N: nat,M: real] :
% 5.68/6.03 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_log_of_power
% 5.68/6.03 thf(fact_8881_log__of__power__eq,axiom,
% 5.68/6.03 ! [M: nat,B: real,N: nat] :
% 5.68/6.03 ( ( ( semiri5074537144036343181t_real @ M )
% 5.68/6.03 = ( power_power_real @ B @ N ) )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( semiri5074537144036343181t_real @ N )
% 5.68/6.03 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_of_power_eq
% 5.68/6.03 thf(fact_8882_forall__pos__mono__1,axiom,
% 5.68/6.03 ! [P: real > $o,E: real] :
% 5.68/6.03 ( ! [D3: real,E2: real] :
% 5.68/6.03 ( ( ord_less_real @ D3 @ E2 )
% 5.68/6.03 => ( ( P @ D3 )
% 5.68/6.03 => ( P @ E2 ) ) )
% 5.68/6.03 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.03 => ( P @ E ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % forall_pos_mono_1
% 5.68/6.03 thf(fact_8883_real__arch__inverse,axiom,
% 5.68/6.03 ! [E: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.03 = ( ? [N2: nat] :
% 5.68/6.03 ( ( N2 != zero_zero_nat )
% 5.68/6.03 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.68/6.03 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_arch_inverse
% 5.68/6.03 thf(fact_8884_forall__pos__mono,axiom,
% 5.68/6.03 ! [P: real > $o,E: real] :
% 5.68/6.03 ( ! [D3: real,E2: real] :
% 5.68/6.03 ( ( ord_less_real @ D3 @ E2 )
% 5.68/6.03 => ( ( P @ D3 )
% 5.68/6.03 => ( P @ E2 ) ) )
% 5.68/6.03 => ( ! [N3: nat] :
% 5.68/6.03 ( ( N3 != zero_zero_nat )
% 5.68/6.03 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.68/6.03 => ( P @ E ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % forall_pos_mono
% 5.68/6.03 thf(fact_8885_sqrt__divide__self__eq,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.68/6.03 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sqrt_divide_self_eq
% 5.68/6.03 thf(fact_8886_prod__int__plus__eq,axiom,
% 5.68/6.03 ! [I2: nat,J: nat] :
% 5.68/6.03 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.68/6.03 = ( groups1705073143266064639nt_int
% 5.68/6.03 @ ^ [X2: int] : X2
% 5.68/6.03 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_int_plus_eq
% 5.68/6.03 thf(fact_8887_log__mult,axiom,
% 5.68/6.03 ! [A: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( A != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( log @ A @ ( times_times_real @ X @ Y2 ) )
% 5.68/6.03 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_mult
% 5.68/6.03 thf(fact_8888_le__log__of__power,axiom,
% 5.68/6.03 ! [B: real,N: nat,M: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_log_of_power
% 5.68/6.03 thf(fact_8889_log__base__pow,axiom,
% 5.68/6.03 ! [A: real,N: nat,X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 5.68/6.03 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_base_pow
% 5.68/6.03 thf(fact_8890_log__nat__power,axiom,
% 5.68/6.03 ! [X: real,B: real,N: nat] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 5.68/6.03 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_nat_power
% 5.68/6.03 thf(fact_8891_log2__of__power__eq,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( M
% 5.68/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( semiri5074537144036343181t_real @ N )
% 5.68/6.03 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log2_of_power_eq
% 5.68/6.03 thf(fact_8892_log__of__power__less,axiom,
% 5.68/6.03 ! [M: nat,B: real,N: nat] :
% 5.68/6.03 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.03 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_of_power_less
% 5.68/6.03 thf(fact_8893_log__eq__div__ln__mult__log,axiom,
% 5.68/6.03 ! [A: real,B: real,X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( A != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.03 => ( ( B != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( log @ A @ X )
% 5.68/6.03 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_eq_div_ln_mult_log
% 5.68/6.03 thf(fact_8894_exp__plus__inverse__exp,axiom,
% 5.68/6.03 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % exp_plus_inverse_exp
% 5.68/6.03 thf(fact_8895_log__of__power__le,axiom,
% 5.68/6.03 ! [M: nat,B: real,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.03 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_of_power_le
% 5.68/6.03 thf(fact_8896_plus__inverse__ge__2,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % plus_inverse_ge_2
% 5.68/6.03 thf(fact_8897_real__inv__sqrt__pow2,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( inverse_inverse_real @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_inv_sqrt_pow2
% 5.68/6.03 thf(fact_8898_tan__cot,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.68/6.03 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % tan_cot
% 5.68/6.03 thf(fact_8899_less__log2__of__power,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.68/6.03 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_log2_of_power
% 5.68/6.03 thf(fact_8900_le__log2__of__power,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.68/6.03 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_log2_of_power
% 5.68/6.03 thf(fact_8901_real__le__x__sinh,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( 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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_le_x_sinh
% 5.68/6.03 thf(fact_8902_real__le__abs__sinh,axiom,
% 5.68/6.03 ! [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 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_le_abs_sinh
% 5.68/6.03 thf(fact_8903_log2__of__power__less,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.03 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log2_of_power_less
% 5.68/6.03 thf(fact_8904_cot__gt__zero,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cot_gt_zero
% 5.68/6.03 thf(fact_8905_log2__of__power__le,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.03 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log2_of_power_le
% 5.68/6.03 thf(fact_8906_log__base__10__eq2,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.68/6.03 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_base_10_eq2
% 5.68/6.03 thf(fact_8907_tan__cot_H,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.68/6.03 = ( cot_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % tan_cot'
% 5.68/6.03 thf(fact_8908_Arg__minus__ii,axiom,
% 5.68/6.03 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.68/6.03 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Arg_minus_ii
% 5.68/6.03 thf(fact_8909_ceiling__log__nat__eq__powr__iff,axiom,
% 5.68/6.03 ! [B: nat,K: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.03 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.68/6.03 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.68/6.03 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.68/6.03 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_log_nat_eq_powr_iff
% 5.68/6.03 thf(fact_8910_Arg__ii,axiom,
% 5.68/6.03 ( ( arg @ imaginary_unit )
% 5.68/6.03 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Arg_ii
% 5.68/6.03 thf(fact_8911_ceiling__log__nat__eq__if,axiom,
% 5.68/6.03 ! [B: nat,N: nat,K: nat] :
% 5.68/6.03 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.68/6.03 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.68/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.68/6.03 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.68/6.03 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_log_nat_eq_if
% 5.68/6.03 thf(fact_8912_sinh__real__le__iff,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 5.68/6.03 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % sinh_real_le_iff
% 5.68/6.03 thf(fact_8913_sinh__real__nonneg__iff,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.68/6.03 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sinh_real_nonneg_iff
% 5.68/6.03 thf(fact_8914_sinh__real__nonpos__iff,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.68/6.03 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % sinh_real_nonpos_iff
% 5.68/6.03 thf(fact_8915_ceiling__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [A: num,B: num] :
% 5.68/6.03 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8916_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [A: num,B: num] :
% 5.68/6.03 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_minus_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8917_divide__complex__def,axiom,
% 5.68/6.03 ( divide1717551699836669952omplex
% 5.68/6.03 = ( ^ [X2: complex,Y: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_complex_def
% 5.68/6.03 thf(fact_8918_Arg__bounded,axiom,
% 5.68/6.03 ! [Z: complex] :
% 5.68/6.03 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.68/6.03 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.68/6.03
% 5.68/6.03 % Arg_bounded
% 5.68/6.03 thf(fact_8919_complex__inverse,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_inverse
% 5.68/6.03 thf(fact_8920_sinh__ln__real,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.68/6.03 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sinh_ln_real
% 5.68/6.03 thf(fact_8921_ceiling__log2__div2,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.03 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_log2_div2
% 5.68/6.03 thf(fact_8922_cis__minus__pi__half,axiom,
% 5.68/6.03 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.68/6.03
% 5.68/6.03 % cis_minus_pi_half
% 5.68/6.03 thf(fact_8923_ceiling__log__eq__powr__iff,axiom,
% 5.68/6.03 ! [X: real,B: real,K: nat] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.68/6.03 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.68/6.03 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.68/6.03 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ceiling_log_eq_powr_iff
% 5.68/6.03 thf(fact_8924_floor__log__nat__eq__powr__iff,axiom,
% 5.68/6.03 ! [B: nat,K: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.68/6.03 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.68/6.03 = ( semiri1314217659103216013at_int @ N ) )
% 5.68/6.03 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.68/6.03 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_log_nat_eq_powr_iff
% 5.68/6.03 thf(fact_8925_powr__nonneg__iff,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.68/6.03 = ( A = zero_zero_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_nonneg_iff
% 5.68/6.03 thf(fact_8926_powr__one,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( powr_real @ X @ one_one_real )
% 5.68/6.03 = X ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_one
% 5.68/6.03 thf(fact_8927_powr__one__gt__zero__iff,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ( powr_real @ X @ one_one_real )
% 5.68/6.03 = X )
% 5.68/6.03 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_one_gt_zero_iff
% 5.68/6.03 thf(fact_8928_powr__le__cancel__iff,axiom,
% 5.68/6.03 ! [X: real,A: real,B: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.68/6.03 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_le_cancel_iff
% 5.68/6.03 thf(fact_8929_numeral__powr__numeral__real,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.68/6.03 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % numeral_powr_numeral_real
% 5.68/6.03 thf(fact_8930_floor__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [A: num,B: num] :
% 5.68/6.03 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.68/6.03 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8931_powr__numeral,axiom,
% 5.68/6.03 ! [X: real,N: num] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 5.68/6.03 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_numeral
% 5.68/6.03 thf(fact_8932_cis__pi__half,axiom,
% 5.68/6.03 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 = imaginary_unit ) ).
% 5.68/6.03
% 5.68/6.03 % cis_pi_half
% 5.68/6.03 thf(fact_8933_floor__one__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [B: num] :
% 5.68/6.03 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.68/6.03 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_one_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8934_cis__2pi,axiom,
% 5.68/6.03 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.68/6.03 = one_one_complex ) ).
% 5.68/6.03
% 5.68/6.03 % cis_2pi
% 5.68/6.03 thf(fact_8935_floor__minus__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [A: num,B: num] :
% 5.68/6.03 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.68/6.03 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_minus_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8936_square__powr__half,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 = ( abs_abs_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % square_powr_half
% 5.68/6.03 thf(fact_8937_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.68/6.03 ! [B: num] :
% 5.68/6.03 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.68/6.03 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_minus_one_divide_eq_div_numeral
% 5.68/6.03 thf(fact_8938_sinh__le__cosh__real,axiom,
% 5.68/6.03 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % sinh_le_cosh_real
% 5.68/6.03 thf(fact_8939_powr__powr,axiom,
% 5.68/6.03 ! [X: real,A: real,B: real] :
% 5.68/6.03 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.68/6.03 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_powr
% 5.68/6.03 thf(fact_8940_powr__ge__pzero,axiom,
% 5.68/6.03 ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_ge_pzero
% 5.68/6.03 thf(fact_8941_powr__mono2,axiom,
% 5.68/6.03 ! [A: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mono2
% 5.68/6.03 thf(fact_8942_powr__mono,axiom,
% 5.68/6.03 ! [A: real,B: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.03 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mono
% 5.68/6.03 thf(fact_8943_cosh__real__nonpos__le__iff,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 5.68/6.03 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_nonpos_le_iff
% 5.68/6.03 thf(fact_8944_cosh__real__nonneg__le__iff,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 5.68/6.03 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_nonneg_le_iff
% 5.68/6.03 thf(fact_8945_cosh__real__nonneg,axiom,
% 5.68/6.03 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_nonneg
% 5.68/6.03 thf(fact_8946_cosh__real__ge__1,axiom,
% 5.68/6.03 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_ge_1
% 5.68/6.03 thf(fact_8947_cis__mult,axiom,
% 5.68/6.03 ! [A: real,B: real] :
% 5.68/6.03 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.68/6.03 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cis_mult
% 5.68/6.03 thf(fact_8948_powr__mono2_H,axiom,
% 5.68/6.03 ! [A: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mono2'
% 5.68/6.03 thf(fact_8949_powr__less__mono2,axiom,
% 5.68/6.03 ! [A: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ Y2 )
% 5.68/6.03 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_less_mono2
% 5.68/6.03 thf(fact_8950_powr__le1,axiom,
% 5.68/6.03 ! [A: real,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_le1
% 5.68/6.03 thf(fact_8951_powr__mono__both,axiom,
% 5.68/6.03 ! [A: real,B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ( ord_less_eq_real @ A @ B )
% 5.68/6.03 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mono_both
% 5.68/6.03 thf(fact_8952_ge__one__powr__ge__zero,axiom,
% 5.68/6.03 ! [X: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ge_one_powr_ge_zero
% 5.68/6.03 thf(fact_8953_powr__divide,axiom,
% 5.68/6.03 ! [X: real,Y2: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( powr_real @ ( divide_divide_real @ X @ Y2 ) @ A )
% 5.68/6.03 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_divide
% 5.68/6.03 thf(fact_8954_powr__mult,axiom,
% 5.68/6.03 ! [X: real,Y2: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( powr_real @ ( times_times_real @ X @ Y2 ) @ A )
% 5.68/6.03 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mult
% 5.68/6.03 thf(fact_8955_inverse__powr,axiom,
% 5.68/6.03 ! [Y2: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( powr_real @ ( inverse_inverse_real @ Y2 ) @ A )
% 5.68/6.03 = ( inverse_inverse_real @ ( powr_real @ Y2 @ A ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % inverse_powr
% 5.68/6.03 thf(fact_8956_divide__powr__uminus,axiom,
% 5.68/6.03 ! [A: real,B: real,C: real] :
% 5.68/6.03 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.68/6.03 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_powr_uminus
% 5.68/6.03 thf(fact_8957_ln__powr,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( X != zero_zero_real )
% 5.68/6.03 => ( ( ln_ln_real @ ( powr_real @ X @ Y2 ) )
% 5.68/6.03 = ( times_times_real @ Y2 @ ( ln_ln_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ln_powr
% 5.68/6.03 thf(fact_8958_log__powr,axiom,
% 5.68/6.03 ! [X: real,B: real,Y2: real] :
% 5.68/6.03 ( ( X != zero_zero_real )
% 5.68/6.03 => ( ( log @ B @ ( powr_real @ X @ Y2 ) )
% 5.68/6.03 = ( times_times_real @ Y2 @ ( log @ B @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_powr
% 5.68/6.03 thf(fact_8959_cosh__real__strict__mono,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ Y2 )
% 5.68/6.03 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_strict_mono
% 5.68/6.03 thf(fact_8960_cosh__real__nonneg__less__iff,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.03 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 5.68/6.03 = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_nonneg_less_iff
% 5.68/6.03 thf(fact_8961_cosh__real__nonpos__less__iff,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 5.68/6.03 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 5.68/6.03 = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_real_nonpos_less_iff
% 5.68/6.03 thf(fact_8962_arcosh__cosh__real,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.68/6.03 = X ) ) ).
% 5.68/6.03
% 5.68/6.03 % arcosh_cosh_real
% 5.68/6.03 thf(fact_8963_floor__log__eq__powr__iff,axiom,
% 5.68/6.03 ! [X: real,B: real,K: int] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.68/6.03 = K )
% 5.68/6.03 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.68/6.03 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_log_eq_powr_iff
% 5.68/6.03 thf(fact_8964_powr__realpow,axiom,
% 5.68/6.03 ! [X: real,N: nat] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.68/6.03 = ( power_power_real @ X @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_realpow
% 5.68/6.03 thf(fact_8965_floor__eq,axiom,
% 5.68/6.03 ! [N: int,X: real] :
% 5.68/6.03 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.68/6.03 => ( ( archim6058952711729229775r_real @ X )
% 5.68/6.03 = N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_eq
% 5.68/6.03 thf(fact_8966_real__of__int__floor__add__one__gt,axiom,
% 5.68/6.03 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_of_int_floor_add_one_gt
% 5.68/6.03 thf(fact_8967_real__of__int__floor__add__one__ge,axiom,
% 5.68/6.03 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_of_int_floor_add_one_ge
% 5.68/6.03 thf(fact_8968_real__of__int__floor__gt__diff__one,axiom,
% 5.68/6.03 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_of_int_floor_gt_diff_one
% 5.68/6.03 thf(fact_8969_real__of__int__floor__ge__diff__one,axiom,
% 5.68/6.03 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_of_int_floor_ge_diff_one
% 5.68/6.03 thf(fact_8970_DeMoivre,axiom,
% 5.68/6.03 ! [A: real,N: nat] :
% 5.68/6.03 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.68/6.03 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % DeMoivre
% 5.68/6.03 thf(fact_8971_powr__mult__base,axiom,
% 5.68/6.03 ! [X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( times_times_real @ X @ ( powr_real @ X @ Y2 ) )
% 5.68/6.03 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_mult_base
% 5.68/6.03 thf(fact_8972_le__log__iff,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) )
% 5.68/6.03 = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_log_iff
% 5.68/6.03 thf(fact_8973_log__le__iff,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 )
% 5.68/6.03 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_le_iff
% 5.68/6.03 thf(fact_8974_le__powr__iff,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) )
% 5.68/6.03 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_powr_iff
% 5.68/6.03 thf(fact_8975_powr__le__iff,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ B )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X )
% 5.68/6.03 = ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_le_iff
% 5.68/6.03 thf(fact_8976_floor__eq2,axiom,
% 5.68/6.03 ! [N: int,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.68/6.03 => ( ( archim6058952711729229775r_real @ X )
% 5.68/6.03 = N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_eq2
% 5.68/6.03 thf(fact_8977_floor__divide__real__eq__div,axiom,
% 5.68/6.03 ! [B: int,A: real] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.68/6.03 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.68/6.03 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_divide_real_eq_div
% 5.68/6.03 thf(fact_8978_ln__powr__bound,axiom,
% 5.68/6.03 ! [X: real,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ln_powr_bound
% 5.68/6.03 thf(fact_8979_ln__powr__bound2,axiom,
% 5.68/6.03 ! [X: real,A: real] :
% 5.68/6.03 ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.03 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ln_powr_bound2
% 5.68/6.03 thf(fact_8980_log__add__eq__powr,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.03 => ( ( B != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y2 )
% 5.68/6.03 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_add_eq_powr
% 5.68/6.03 thf(fact_8981_add__log__eq__powr,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.03 => ( ( B != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( plus_plus_real @ Y2 @ ( log @ B @ X ) )
% 5.68/6.03 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % add_log_eq_powr
% 5.68/6.03 thf(fact_8982_log__minus__eq__powr,axiom,
% 5.68/6.03 ! [B: real,X: real,Y2: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.03 => ( ( B != one_one_real )
% 5.68/6.03 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y2 )
% 5.68/6.03 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % log_minus_eq_powr
% 5.68/6.03 thf(fact_8983_powr__half__sqrt,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 = ( sqrt @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_half_sqrt
% 5.68/6.03 thf(fact_8984_powr__neg__numeral,axiom,
% 5.68/6.03 ! [X: real,N: num] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.68/6.03 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_neg_numeral
% 5.68/6.03 thf(fact_8985_cosh__ln__real,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.68/6.03 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cosh_ln_real
% 5.68/6.03 thf(fact_8986_floor__log2__div2,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.03 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_log2_div2
% 5.68/6.03 thf(fact_8987_floor__log__nat__eq__if,axiom,
% 5.68/6.03 ! [B: nat,N: nat,K: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.68/6.03 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.68/6.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.68/6.03 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.68/6.03 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_log_nat_eq_if
% 5.68/6.03 thf(fact_8988_bij__betw__roots__unity,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.03 => ( bij_betw_nat_complex
% 5.68/6.03 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.68/6.03 @ ( set_ord_lessThan_nat @ N )
% 5.68/6.03 @ ( collect_complex
% 5.68/6.03 @ ^ [Z2: complex] :
% 5.68/6.03 ( ( power_power_complex @ Z2 @ N )
% 5.68/6.03 = one_one_complex ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bij_betw_roots_unity
% 5.68/6.03 thf(fact_8989_exp__pi__i,axiom,
% 5.68/6.03 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % exp_pi_i
% 5.68/6.03 thf(fact_8990_exp__pi__i_H,axiom,
% 5.68/6.03 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.68/6.03 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % exp_pi_i'
% 5.68/6.03 thf(fact_8991_exp__two__pi__i,axiom,
% 5.68/6.03 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.68/6.03 = one_one_complex ) ).
% 5.68/6.03
% 5.68/6.03 % exp_two_pi_i
% 5.68/6.03 thf(fact_8992_exp__two__pi__i_H,axiom,
% 5.68/6.03 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.68/6.03 = one_one_complex ) ).
% 5.68/6.03
% 5.68/6.03 % exp_two_pi_i'
% 5.68/6.03 thf(fact_8993_complex__exp__exists,axiom,
% 5.68/6.03 ! [Z: complex] :
% 5.68/6.03 ? [A3: complex,R3: real] :
% 5.68/6.03 ( Z
% 5.68/6.03 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A3 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_exp_exists
% 5.68/6.03 thf(fact_8994_Complex__mult__complex__of__real,axiom,
% 5.68/6.03 ! [X: real,Y2: real,R2: real] :
% 5.68/6.03 ( ( times_times_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.68/6.03 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y2 @ R2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Complex_mult_complex_of_real
% 5.68/6.03 thf(fact_8995_complex__of__real__mult__Complex,axiom,
% 5.68/6.03 ! [R2: real,X: real,Y2: real] :
% 5.68/6.03 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y2 ) )
% 5.68/6.03 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_of_real_mult_Complex
% 5.68/6.03 thf(fact_8996_Complex__add__complex__of__real,axiom,
% 5.68/6.03 ! [X: real,Y2: real,R2: real] :
% 5.68/6.03 ( ( plus_plus_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.68/6.03 = ( complex2 @ ( plus_plus_real @ X @ R2 ) @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % Complex_add_complex_of_real
% 5.68/6.03 thf(fact_8997_complex__of__real__add__Complex,axiom,
% 5.68/6.03 ! [R2: real,X: real,Y2: real] :
% 5.68/6.03 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y2 ) )
% 5.68/6.03 = ( complex2 @ ( plus_plus_real @ R2 @ X ) @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_of_real_add_Complex
% 5.68/6.03 thf(fact_8998_cis__conv__exp,axiom,
% 5.68/6.03 ( cis
% 5.68/6.03 = ( ^ [B3: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cis_conv_exp
% 5.68/6.03 thf(fact_8999_complex__of__real__i,axiom,
% 5.68/6.03 ! [R2: real] :
% 5.68/6.03 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.68/6.03 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_of_real_i
% 5.68/6.03 thf(fact_9000_i__complex__of__real,axiom,
% 5.68/6.03 ! [R2: real] :
% 5.68/6.03 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.68/6.03 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % i_complex_of_real
% 5.68/6.03 thf(fact_9001_Complex__eq,axiom,
% 5.68/6.03 ( complex2
% 5.68/6.03 = ( ^ [A4: real,B3: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Complex_eq
% 5.68/6.03 thf(fact_9002_complex__split__polar,axiom,
% 5.68/6.03 ! [Z: complex] :
% 5.68/6.03 ? [R3: real,A3: real] :
% 5.68/6.03 ( Z
% 5.68/6.03 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % complex_split_polar
% 5.68/6.03 thf(fact_9003_cmod__unit__one,axiom,
% 5.68/6.03 ! [A: real] :
% 5.68/6.03 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.68/6.03 = one_one_real ) ).
% 5.68/6.03
% 5.68/6.03 % cmod_unit_one
% 5.68/6.03 thf(fact_9004_cmod__complex__polar,axiom,
% 5.68/6.03 ! [R2: real,A: real] :
% 5.68/6.03 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.68/6.03 = ( abs_abs_real @ R2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % cmod_complex_polar
% 5.68/6.03 thf(fact_9005_csqrt__ii,axiom,
% 5.68/6.03 ( ( csqrt @ imaginary_unit )
% 5.68/6.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % csqrt_ii
% 5.68/6.03 thf(fact_9006_int__ge__less__than2__def,axiom,
% 5.68/6.03 ( int_ge_less_than2
% 5.68/6.03 = ( ^ [D2: int] :
% 5.68/6.03 ( collec213857154873943460nt_int
% 5.68/6.03 @ ( produc4947309494688390418_int_o
% 5.68/6.03 @ ^ [Z6: int,Z2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ D2 @ Z2 )
% 5.68/6.03 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_ge_less_than2_def
% 5.68/6.03 thf(fact_9007_int__ge__less__than__def,axiom,
% 5.68/6.03 ( int_ge_less_than
% 5.68/6.03 = ( ^ [D2: int] :
% 5.68/6.03 ( collec213857154873943460nt_int
% 5.68/6.03 @ ( produc4947309494688390418_int_o
% 5.68/6.03 @ ^ [Z6: int,Z2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.68/6.03 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_ge_less_than_def
% 5.68/6.03 thf(fact_9008_upto_Opinduct,axiom,
% 5.68/6.03 ! [A0: int,A1: int,P: int > int > $o] :
% 5.68/6.03 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.68/6.03 => ( ! [I4: int,J2: int] :
% 5.68/6.03 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 5.68/6.03 => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 5.68/6.03 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 5.68/6.03 => ( P @ I4 @ J2 ) ) )
% 5.68/6.03 => ( P @ A0 @ A1 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % upto.pinduct
% 5.68/6.03 thf(fact_9009_power2__csqrt,axiom,
% 5.68/6.03 ! [Z: complex] :
% 5.68/6.03 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.03 = Z ) ).
% 5.68/6.03
% 5.68/6.03 % power2_csqrt
% 5.68/6.03 thf(fact_9010_of__real__sqrt,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.68/6.03 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % of_real_sqrt
% 5.68/6.03 thf(fact_9011_arctan__def,axiom,
% 5.68/6.03 ( arctan
% 5.68/6.03 = ( ^ [Y: real] :
% 5.68/6.03 ( the_real
% 5.68/6.03 @ ^ [X2: real] :
% 5.68/6.03 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.68/6.03 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 & ( ( tan_real @ X2 )
% 5.68/6.03 = Y ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % arctan_def
% 5.68/6.03 thf(fact_9012_arcsin__def,axiom,
% 5.68/6.03 ( arcsin
% 5.68/6.03 = ( ^ [Y: real] :
% 5.68/6.03 ( the_real
% 5.68/6.03 @ ^ [X2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.68/6.03 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.03 & ( ( sin_real @ X2 )
% 5.68/6.03 = Y ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % arcsin_def
% 5.68/6.03 thf(fact_9013_even__set__encode__iff,axiom,
% 5.68/6.03 ! [A2: set_nat] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.68/6.03 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_set_encode_iff
% 5.68/6.03 thf(fact_9014_modulo__int__unfold,axiom,
% 5.68/6.03 ! [L2: int,K: int,N: nat,M: nat] :
% 5.68/6.03 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( ( sgn_sgn_int @ K )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( N = zero_zero_nat ) )
% 5.68/6.03 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.68/6.03 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( ( sgn_sgn_int @ K )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( N = zero_zero_nat ) )
% 5.68/6.03 => ( ( ( ( sgn_sgn_int @ K )
% 5.68/6.03 = ( sgn_sgn_int @ L2 ) )
% 5.68/6.03 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.68/6.03 & ( ( ( sgn_sgn_int @ K )
% 5.68/6.03 != ( sgn_sgn_int @ L2 ) )
% 5.68/6.03 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.68/6.03 @ ( minus_minus_int
% 5.68/6.03 @ ( semiri1314217659103216013at_int
% 5.68/6.03 @ ( times_times_nat @ N
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.68/6.03 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % modulo_int_unfold
% 5.68/6.03 thf(fact_9015_dvd__mult__sgn__iff,axiom,
% 5.68/6.03 ! [L2: int,K: int,R2: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.68/6.03 = ( ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 | ( R2 = zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % dvd_mult_sgn_iff
% 5.68/6.03 thf(fact_9016_dvd__sgn__mult__iff,axiom,
% 5.68/6.03 ! [L2: int,R2: int,K: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.68/6.03 = ( ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 | ( R2 = zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % dvd_sgn_mult_iff
% 5.68/6.03 thf(fact_9017_mult__sgn__dvd__iff,axiom,
% 5.68/6.03 ! [L2: int,R2: int,K: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.68/6.03 = ( ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 & ( ( R2 = zero_zero_int )
% 5.68/6.03 => ( K = zero_zero_int ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % mult_sgn_dvd_iff
% 5.68/6.03 thf(fact_9018_sgn__mult__dvd__iff,axiom,
% 5.68/6.03 ! [R2: int,L2: int,K: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 5.68/6.03 = ( ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 & ( ( R2 = zero_zero_int )
% 5.68/6.03 => ( K = zero_zero_int ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sgn_mult_dvd_iff
% 5.68/6.03 thf(fact_9019_int__sgnE,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ~ ! [N3: nat,L4: int] :
% 5.68/6.03 ( K
% 5.68/6.03 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_sgnE
% 5.68/6.03 thf(fact_9020_sgn__mod,axiom,
% 5.68/6.03 ! [L2: int,K: int] :
% 5.68/6.03 ( ( L2 != zero_zero_int )
% 5.68/6.03 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.68/6.03 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sgn_mod
% 5.68/6.03 thf(fact_9021_ln__neg__is__const,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ( ln_ln_real @ X )
% 5.68/6.03 = ( the_real
% 5.68/6.03 @ ^ [X2: real] : $false ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ln_neg_is_const
% 5.68/6.03 thf(fact_9022_div__sgn__abs__cancel,axiom,
% 5.68/6.03 ! [V: int,K: int,L2: int] :
% 5.68/6.03 ( ( V != zero_zero_int )
% 5.68/6.03 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 5.68/6.03 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % div_sgn_abs_cancel
% 5.68/6.03 thf(fact_9023_div__dvd__sgn__abs,axiom,
% 5.68/6.03 ! [L2: int,K: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ L2 @ K )
% 5.68/6.03 => ( ( divide_divide_int @ K @ L2 )
% 5.68/6.03 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % div_dvd_sgn_abs
% 5.68/6.03 thf(fact_9024_arccos__def,axiom,
% 5.68/6.03 ( arccos
% 5.68/6.03 = ( ^ [Y: real] :
% 5.68/6.03 ( the_real
% 5.68/6.03 @ ^ [X2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.68/6.03 & ( ord_less_eq_real @ X2 @ pi )
% 5.68/6.03 & ( ( cos_real @ X2 )
% 5.68/6.03 = Y ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % arccos_def
% 5.68/6.03 thf(fact_9025_eucl__rel__int__remainderI,axiom,
% 5.68/6.03 ! [R2: int,L2: int,K: int,Q2: int] :
% 5.68/6.03 ( ( ( sgn_sgn_int @ R2 )
% 5.68/6.03 = ( sgn_sgn_int @ L2 ) )
% 5.68/6.03 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 5.68/6.03 => ( ( K
% 5.68/6.03 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 5.68/6.03 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % eucl_rel_int_remainderI
% 5.68/6.03 thf(fact_9026_eucl__rel__int_Ocases,axiom,
% 5.68/6.03 ! [A1: int,A22: int,A32: product_prod_int_int] :
% 5.68/6.03 ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 5.68/6.03 => ( ( ( A22 = zero_zero_int )
% 5.68/6.03 => ( A32
% 5.68/6.03 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.68/6.03 => ( ! [Q3: int] :
% 5.68/6.03 ( ( A32
% 5.68/6.03 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.68/6.03 => ( ( A22 != zero_zero_int )
% 5.68/6.03 => ( A1
% 5.68/6.03 != ( times_times_int @ Q3 @ A22 ) ) ) )
% 5.68/6.03 => ~ ! [R3: int,Q3: int] :
% 5.68/6.03 ( ( A32
% 5.68/6.03 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.68/6.03 => ( ( ( sgn_sgn_int @ R3 )
% 5.68/6.03 = ( sgn_sgn_int @ A22 ) )
% 5.68/6.03 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.68/6.03 => ( A1
% 5.68/6.03 != ( plus_plus_int @ ( times_times_int @ Q3 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % eucl_rel_int.cases
% 5.68/6.03 thf(fact_9027_eucl__rel__int_Osimps,axiom,
% 5.68/6.03 ( eucl_rel_int
% 5.68/6.03 = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 5.68/6.03 ( ? [K3: int] :
% 5.68/6.03 ( ( A12 = K3 )
% 5.68/6.03 & ( A23 = zero_zero_int )
% 5.68/6.03 & ( A33
% 5.68/6.03 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.68/6.03 | ? [L: int,K3: int,Q4: int] :
% 5.68/6.03 ( ( A12 = K3 )
% 5.68/6.03 & ( A23 = L )
% 5.68/6.03 & ( A33
% 5.68/6.03 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.68/6.03 & ( L != zero_zero_int )
% 5.68/6.03 & ( K3
% 5.68/6.03 = ( times_times_int @ Q4 @ L ) ) )
% 5.68/6.03 | ? [R5: int,L: int,K3: int,Q4: int] :
% 5.68/6.03 ( ( A12 = K3 )
% 5.68/6.03 & ( A23 = L )
% 5.68/6.03 & ( A33
% 5.68/6.03 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.68/6.03 & ( ( sgn_sgn_int @ R5 )
% 5.68/6.03 = ( sgn_sgn_int @ L ) )
% 5.68/6.03 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.68/6.03 & ( K3
% 5.68/6.03 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % eucl_rel_int.simps
% 5.68/6.03 thf(fact_9028_set__encode__def,axiom,
% 5.68/6.03 ( nat_set_encode
% 5.68/6.03 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_encode_def
% 5.68/6.03 thf(fact_9029_pi__half,axiom,
% 5.68/6.03 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( the_real
% 5.68/6.03 @ ^ [X2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.68/6.03 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.03 & ( ( cos_real @ X2 )
% 5.68/6.03 = zero_zero_real ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pi_half
% 5.68/6.03 thf(fact_9030_pi__def,axiom,
% 5.68/6.03 ( pi
% 5.68/6.03 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.68/6.03 @ ( the_real
% 5.68/6.03 @ ^ [X2: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.68/6.03 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.68/6.03 & ( ( cos_real @ X2 )
% 5.68/6.03 = zero_zero_real ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % pi_def
% 5.68/6.03 thf(fact_9031_divide__int__unfold,axiom,
% 5.68/6.03 ! [L2: int,K: int,N: nat,M: nat] :
% 5.68/6.03 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( ( sgn_sgn_int @ K )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( N = zero_zero_nat ) )
% 5.68/6.03 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = zero_zero_int ) )
% 5.68/6.03 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( ( sgn_sgn_int @ K )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 | ( N = zero_zero_nat ) )
% 5.68/6.03 => ( ( ( ( sgn_sgn_int @ K )
% 5.68/6.03 = ( sgn_sgn_int @ L2 ) )
% 5.68/6.03 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.68/6.03 & ( ( ( sgn_sgn_int @ K )
% 5.68/6.03 != ( sgn_sgn_int @ L2 ) )
% 5.68/6.03 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.68/6.03 = ( uminus_uminus_int
% 5.68/6.03 @ ( semiri1314217659103216013at_int
% 5.68/6.03 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_int_unfold
% 5.68/6.03 thf(fact_9032_modulo__int__def,axiom,
% 5.68/6.03 ( modulo_modulo_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.68/6.03 @ ( if_int
% 5.68/6.03 @ ( ( sgn_sgn_int @ K3 )
% 5.68/6.03 = ( sgn_sgn_int @ L ) )
% 5.68/6.03 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.68/6.03 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.68/6.03 @ ( minus_minus_int
% 5.68/6.03 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.68/6.03 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % modulo_int_def
% 5.68/6.03 thf(fact_9033_divide__int__def,axiom,
% 5.68/6.03 ( divide_divide_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.68/6.03 @ ( if_int
% 5.68/6.03 @ ( ( sgn_sgn_int @ K3 )
% 5.68/6.03 = ( sgn_sgn_int @ L ) )
% 5.68/6.03 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.68/6.03 @ ( uminus_uminus_int
% 5.68/6.03 @ ( semiri1314217659103216013at_int
% 5.68/6.03 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divide_int_def
% 5.68/6.03 thf(fact_9034_num_Osize__gen_I3_J,axiom,
% 5.68/6.03 ! [X32: num] :
% 5.68/6.03 ( ( size_num @ ( bit1 @ X32 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % num.size_gen(3)
% 5.68/6.03 thf(fact_9035_mask__nat__positive__iff,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.68/6.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_nat_positive_iff
% 5.68/6.03 thf(fact_9036_sgn__le__0__iff,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.68/6.03 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % sgn_le_0_iff
% 5.68/6.03 thf(fact_9037_zero__le__sgn__iff,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.68/6.03 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % zero_le_sgn_iff
% 5.68/6.03 thf(fact_9038_nat__numeral,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.68/6.03 = ( numeral_numeral_nat @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_numeral
% 5.68/6.03 thf(fact_9039_nat__1,axiom,
% 5.68/6.03 ( ( nat2 @ one_one_int )
% 5.68/6.03 = ( suc @ zero_zero_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_1
% 5.68/6.03 thf(fact_9040_nat__le__0,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.68/6.03 => ( ( nat2 @ Z )
% 5.68/6.03 = zero_zero_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_le_0
% 5.68/6.03 thf(fact_9041_nat__0__iff,axiom,
% 5.68/6.03 ! [I2: int] :
% 5.68/6.03 ( ( ( nat2 @ I2 )
% 5.68/6.03 = zero_zero_nat )
% 5.68/6.03 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_0_iff
% 5.68/6.03 thf(fact_9042_zless__nat__conj,axiom,
% 5.68/6.03 ! [W: int,Z: int] :
% 5.68/6.03 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/6.03 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % zless_nat_conj
% 5.68/6.03 thf(fact_9043_nat__neg__numeral,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.03 = zero_zero_nat ) ).
% 5.68/6.03
% 5.68/6.03 % nat_neg_numeral
% 5.68/6.03 thf(fact_9044_int__nat__eq,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.68/6.03 = Z ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.68/6.03 = zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_nat_eq
% 5.68/6.03 thf(fact_9045_zero__less__nat__eq,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.68/6.03
% 5.68/6.03 % zero_less_nat_eq
% 5.68/6.03 thf(fact_9046_diff__nat__numeral,axiom,
% 5.68/6.03 ! [V: num,V3: num] :
% 5.68/6.03 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.68/6.03 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % diff_nat_numeral
% 5.68/6.03 thf(fact_9047_nat__eq__numeral__power__cancel__iff,axiom,
% 5.68/6.03 ! [Y2: int,X: num,N: nat] :
% 5.68/6.03 ( ( ( nat2 @ Y2 )
% 5.68/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.68/6.03 = ( Y2
% 5.68/6.03 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_eq_numeral_power_cancel_iff
% 5.68/6.03 thf(fact_9048_numeral__power__eq__nat__cancel__iff,axiom,
% 5.68/6.03 ! [X: num,N: nat,Y2: int] :
% 5.68/6.03 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.68/6.03 = ( nat2 @ Y2 ) )
% 5.68/6.03 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.68/6.03 = Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % numeral_power_eq_nat_cancel_iff
% 5.68/6.03 thf(fact_9049_nat__ceiling__le__eq,axiom,
% 5.68/6.03 ! [X: real,A: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.68/6.03 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_ceiling_le_eq
% 5.68/6.03 thf(fact_9050_one__less__nat__eq,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.68/6.03
% 5.68/6.03 % one_less_nat_eq
% 5.68/6.03 thf(fact_9051_nat__numeral__diff__1,axiom,
% 5.68/6.03 ! [V: num] :
% 5.68/6.03 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.68/6.03 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_numeral_diff_1
% 5.68/6.03 thf(fact_9052_nat__less__numeral__power__cancel__iff,axiom,
% 5.68/6.03 ! [A: int,X: num,N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.68/6.03 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_less_numeral_power_cancel_iff
% 5.68/6.03 thf(fact_9053_numeral__power__less__nat__cancel__iff,axiom,
% 5.68/6.03 ! [X: num,N: nat,A: int] :
% 5.68/6.03 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.68/6.03 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.03
% 5.68/6.03 % numeral_power_less_nat_cancel_iff
% 5.68/6.03 thf(fact_9054_nat__le__numeral__power__cancel__iff,axiom,
% 5.68/6.03 ! [A: int,X: num,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.68/6.03 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_le_numeral_power_cancel_iff
% 5.68/6.03 thf(fact_9055_numeral__power__le__nat__cancel__iff,axiom,
% 5.68/6.03 ! [X: num,N: nat,A: int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.68/6.03 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.68/6.03
% 5.68/6.03 % numeral_power_le_nat_cancel_iff
% 5.68/6.03 thf(fact_9056_less__eq__mask,axiom,
% 5.68/6.03 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_eq_mask
% 5.68/6.03 thf(fact_9057_nat__mask__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.68/6.03 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mask_eq
% 5.68/6.03 thf(fact_9058_nat__numeral__as__int,axiom,
% 5.68/6.03 ( numeral_numeral_nat
% 5.68/6.03 = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_numeral_as_int
% 5.68/6.03 thf(fact_9059_nat__mono,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ X @ Y2 )
% 5.68/6.03 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mono
% 5.68/6.03 thf(fact_9060_ex__nat,axiom,
% 5.68/6.03 ( ( ^ [P2: nat > $o] :
% 5.68/6.03 ? [X4: nat] : ( P2 @ X4 ) )
% 5.68/6.03 = ( ^ [P3: nat > $o] :
% 5.68/6.03 ? [X2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.68/6.03 & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ex_nat
% 5.68/6.03 thf(fact_9061_all__nat,axiom,
% 5.68/6.03 ( ( ^ [P2: nat > $o] :
% 5.68/6.03 ! [X4: nat] : ( P2 @ X4 ) )
% 5.68/6.03 = ( ^ [P3: nat > $o] :
% 5.68/6.03 ! [X2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.68/6.03 => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % all_nat
% 5.68/6.03 thf(fact_9062_eq__nat__nat__iff,axiom,
% 5.68/6.03 ! [Z: int,Z7: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.68/6.03 => ( ( ( nat2 @ Z )
% 5.68/6.03 = ( nat2 @ Z7 ) )
% 5.68/6.03 = ( Z = Z7 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % eq_nat_nat_iff
% 5.68/6.03 thf(fact_9063_unset__bit__nat__def,axiom,
% 5.68/6.03 ( bit_se4205575877204974255it_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % unset_bit_nat_def
% 5.68/6.03 thf(fact_9064_mask__nonnegative__int,axiom,
% 5.68/6.03 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_nonnegative_int
% 5.68/6.03 thf(fact_9065_not__mask__negative__int,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % not_mask_negative_int
% 5.68/6.03 thf(fact_9066_nat__mono__iff,axiom,
% 5.68/6.03 ! [Z: int,W: int] :
% 5.68/6.03 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mono_iff
% 5.68/6.03 thf(fact_9067_zless__nat__eq__int__zless,axiom,
% 5.68/6.03 ! [M: nat,Z: int] :
% 5.68/6.03 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.68/6.03
% 5.68/6.03 % zless_nat_eq_int_zless
% 5.68/6.03 thf(fact_9068_nat__le__iff,axiom,
% 5.68/6.03 ! [X: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.68/6.03 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_le_iff
% 5.68/6.03 thf(fact_9069_nat__0__le,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.68/6.03 = Z ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_0_le
% 5.68/6.03 thf(fact_9070_int__eq__iff,axiom,
% 5.68/6.03 ! [M: nat,Z: int] :
% 5.68/6.03 ( ( ( semiri1314217659103216013at_int @ M )
% 5.68/6.03 = Z )
% 5.68/6.03 = ( ( M
% 5.68/6.03 = ( nat2 @ Z ) )
% 5.68/6.03 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_eq_iff
% 5.68/6.03 thf(fact_9071_nat__int__add,axiom,
% 5.68/6.03 ! [A: nat,B: nat] :
% 5.68/6.03 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.68/6.03 = ( plus_plus_nat @ A @ B ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_int_add
% 5.68/6.03 thf(fact_9072_nat__abs__mult__distrib,axiom,
% 5.68/6.03 ! [W: int,Z: int] :
% 5.68/6.03 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.68/6.03 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_abs_mult_distrib
% 5.68/6.03 thf(fact_9073_nat__plus__as__int,axiom,
% 5.68/6.03 ( plus_plus_nat
% 5.68/6.03 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_plus_as_int
% 5.68/6.03 thf(fact_9074_nat__times__as__int,axiom,
% 5.68/6.03 ( times_times_nat
% 5.68/6.03 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_times_as_int
% 5.68/6.03 thf(fact_9075_real__nat__ceiling__ge,axiom,
% 5.68/6.03 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % real_nat_ceiling_ge
% 5.68/6.03 thf(fact_9076_less__mask,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_mask
% 5.68/6.03 thf(fact_9077_nat__div__as__int,axiom,
% 5.68/6.03 ( divide_divide_nat
% 5.68/6.03 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_div_as_int
% 5.68/6.03 thf(fact_9078_sgn__real__def,axiom,
% 5.68/6.03 ( sgn_sgn_real
% 5.68/6.03 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sgn_real_def
% 5.68/6.03 thf(fact_9079_nat__less__eq__zless,axiom,
% 5.68/6.03 ! [W: int,Z: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_less_eq_zless
% 5.68/6.03 thf(fact_9080_nat__le__eq__zle,axiom,
% 5.68/6.03 ! [W: int,Z: int] :
% 5.68/6.03 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.68/6.03 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.68/6.03 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.68/6.03 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_le_eq_zle
% 5.68/6.03 thf(fact_9081_nat__eq__iff,axiom,
% 5.68/6.03 ! [W: int,M: nat] :
% 5.68/6.03 ( ( ( nat2 @ W )
% 5.68/6.03 = M )
% 5.68/6.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( W
% 5.68/6.03 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( M = zero_zero_nat ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_eq_iff
% 5.68/6.03 thf(fact_9082_nat__eq__iff2,axiom,
% 5.68/6.03 ! [M: nat,W: int] :
% 5.68/6.03 ( ( M
% 5.68/6.03 = ( nat2 @ W ) )
% 5.68/6.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( W
% 5.68/6.03 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( M = zero_zero_nat ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_eq_iff2
% 5.68/6.03 thf(fact_9083_le__nat__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.68/6.03 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_nat_iff
% 5.68/6.03 thf(fact_9084_nat__add__distrib,axiom,
% 5.68/6.03 ! [Z: int,Z7: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.68/6.03 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_add_distrib
% 5.68/6.03 thf(fact_9085_nat__mult__distrib,axiom,
% 5.68/6.03 ! [Z: int,Z7: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.68/6.03 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mult_distrib
% 5.68/6.03 thf(fact_9086_Suc__as__int,axiom,
% 5.68/6.03 ( suc
% 5.68/6.03 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_as_int
% 5.68/6.03 thf(fact_9087_nat__diff__distrib_H,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( nat2 @ ( minus_minus_int @ X @ Y2 ) )
% 5.68/6.03 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_diff_distrib'
% 5.68/6.03 thf(fact_9088_nat__diff__distrib,axiom,
% 5.68/6.03 ! [Z7: int,Z: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.68/6.03 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.68/6.03 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.68/6.03 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_diff_distrib
% 5.68/6.03 thf(fact_9089_nat__abs__triangle__ineq,axiom,
% 5.68/6.03 ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_abs_triangle_ineq
% 5.68/6.03 thf(fact_9090_nat__div__distrib_H,axiom,
% 5.68/6.03 ! [Y2: int,X: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 5.68/6.03 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_div_distrib'
% 5.68/6.03 thf(fact_9091_nat__div__distrib,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 5.68/6.03 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_div_distrib
% 5.68/6.03 thf(fact_9092_nat__power__eq,axiom,
% 5.68/6.03 ! [Z: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.68/6.03 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_power_eq
% 5.68/6.03 thf(fact_9093_nat__floor__neg,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.68/6.03 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.68/6.03 = zero_zero_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_floor_neg
% 5.68/6.03 thf(fact_9094_nat__mod__distrib,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y2 ) )
% 5.68/6.03 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mod_distrib
% 5.68/6.03 thf(fact_9095_div__abs__eq__div__nat,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.68/6.03 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % div_abs_eq_div_nat
% 5.68/6.03 thf(fact_9096_floor__eq3,axiom,
% 5.68/6.03 ! [N: nat,X: real] :
% 5.68/6.03 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.68/6.03 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.68/6.03 = N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_eq3
% 5.68/6.03 thf(fact_9097_le__nat__floor,axiom,
% 5.68/6.03 ! [X: nat,A: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.68/6.03 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % le_nat_floor
% 5.68/6.03 thf(fact_9098_nat__2,axiom,
% 5.68/6.03 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_2
% 5.68/6.03 thf(fact_9099_sgn__power__injE,axiom,
% 5.68/6.03 ! [A: real,N: nat,X: real,B: real] :
% 5.68/6.03 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.68/6.03 = X )
% 5.68/6.03 => ( ( X
% 5.68/6.03 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.03 => ( A = B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % sgn_power_injE
% 5.68/6.03 thf(fact_9100_Suc__nat__eq__nat__zadd1,axiom,
% 5.68/6.03 ! [Z: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( ( suc @ ( nat2 @ Z ) )
% 5.68/6.03 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_nat_eq_nat_zadd1
% 5.68/6.03 thf(fact_9101_nat__less__iff,axiom,
% 5.68/6.03 ! [W: int,M: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.68/6.03 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.68/6.03 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_less_iff
% 5.68/6.03 thf(fact_9102_nat__mult__distrib__neg,axiom,
% 5.68/6.03 ! [Z: int,Z7: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.68/6.03 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.68/6.03 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_mult_distrib_neg
% 5.68/6.03 thf(fact_9103_nat__abs__int__diff,axiom,
% 5.68/6.03 ! [A: nat,B: nat] :
% 5.68/6.03 ( ( ( ord_less_eq_nat @ A @ B )
% 5.68/6.03 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.68/6.03 = ( minus_minus_nat @ B @ A ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.68/6.03 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.68/6.03 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_abs_int_diff
% 5.68/6.03 thf(fact_9104_floor__eq4,axiom,
% 5.68/6.03 ! [N: nat,X: real] :
% 5.68/6.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.68/6.03 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.68/6.03 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.68/6.03 = N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % floor_eq4
% 5.68/6.03 thf(fact_9105_num_Osize__gen_I1_J,axiom,
% 5.68/6.03 ( ( size_num @ one )
% 5.68/6.03 = zero_zero_nat ) ).
% 5.68/6.03
% 5.68/6.03 % num.size_gen(1)
% 5.68/6.03 thf(fact_9106_Suc__mask__eq__exp,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.68/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_mask_eq_exp
% 5.68/6.03 thf(fact_9107_mask__nat__less__exp,axiom,
% 5.68/6.03 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_nat_less_exp
% 5.68/6.03 thf(fact_9108_nat__dvd__iff,axiom,
% 5.68/6.03 ! [Z: int,M: nat] :
% 5.68/6.03 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.68/6.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.68/6.03 => ( M = zero_zero_nat ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_dvd_iff
% 5.68/6.03 thf(fact_9109_cis__Arg__unique,axiom,
% 5.68/6.03 ! [Z: complex,X: real] :
% 5.68/6.03 ( ( ( sgn_sgn_complex @ Z )
% 5.68/6.03 = ( cis @ X ) )
% 5.68/6.03 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.68/6.03 => ( ( ord_less_eq_real @ X @ pi )
% 5.68/6.03 => ( ( arg @ Z )
% 5.68/6.03 = X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % cis_Arg_unique
% 5.68/6.03 thf(fact_9110_mask__nat__def,axiom,
% 5.68/6.03 ( bit_se2002935070580805687sk_nat
% 5.68/6.03 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_nat_def
% 5.68/6.03 thf(fact_9111_mask__half__int,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_half_int
% 5.68/6.03 thf(fact_9112_mask__int__def,axiom,
% 5.68/6.03 ( bit_se2000444600071755411sk_int
% 5.68/6.03 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % mask_int_def
% 5.68/6.03 thf(fact_9113_Arg__correct,axiom,
% 5.68/6.03 ! [Z: complex] :
% 5.68/6.03 ( ( Z != zero_zero_complex )
% 5.68/6.03 => ( ( ( sgn_sgn_complex @ Z )
% 5.68/6.03 = ( cis @ ( arg @ Z ) ) )
% 5.68/6.03 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.68/6.03 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Arg_correct
% 5.68/6.03 thf(fact_9114_even__nat__iff,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.68/6.03 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_nat_iff
% 5.68/6.03 thf(fact_9115_powr__real__of__int,axiom,
% 5.68/6.03 ! [X: real,N: int] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.68/6.03 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.68/6.03 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.68/6.03 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.68/6.03 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_real_of_int
% 5.68/6.03 thf(fact_9116_arctan__inverse,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( X != zero_zero_real )
% 5.68/6.03 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.68/6.03 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % arctan_inverse
% 5.68/6.03 thf(fact_9117_num_Osize__gen_I2_J,axiom,
% 5.68/6.03 ! [X22: num] :
% 5.68/6.03 ( ( size_num @ ( bit0 @ X22 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % num.size_gen(2)
% 5.68/6.03 thf(fact_9118_powr__int,axiom,
% 5.68/6.03 ! [X: real,I2: int] :
% 5.68/6.03 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.03 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.68/6.03 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.68/6.03 = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.68/6.03 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.68/6.03 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % powr_int
% 5.68/6.03 thf(fact_9119_and__int__unfold,axiom,
% 5.68/6.03 ( bit_se725231765392027082nd_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int
% 5.68/6.03 @ ( ( K3 = zero_zero_int )
% 5.68/6.03 | ( L = zero_zero_int ) )
% 5.68/6.03 @ zero_zero_int
% 5.68/6.03 @ ( if_int
% 5.68/6.03 @ ( K3
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 @ L
% 5.68/6.03 @ ( if_int
% 5.68/6.03 @ ( L
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 @ K3
% 5.68/6.03 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( 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 @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int_unfold
% 5.68/6.03 thf(fact_9120_concat__bit__of__zero__2,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.68/6.03 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_of_zero_2
% 5.68/6.03 thf(fact_9121_and__nonnegative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.68/6.03 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_nonnegative_int_iff
% 5.68/6.03 thf(fact_9122_and__negative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.68/6.03 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.68/6.03 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_negative_int_iff
% 5.68/6.03 thf(fact_9123_take__bit__of__Suc__0,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_of_Suc_0
% 5.68/6.03 thf(fact_9124_and__minus__numerals_I2_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = one_one_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_minus_numerals(2)
% 5.68/6.03 thf(fact_9125_and__minus__numerals_I6_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.68/6.03 = one_one_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_minus_numerals(6)
% 5.68/6.03 thf(fact_9126_and__minus__numerals_I5_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.68/6.03 = zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_minus_numerals(5)
% 5.68/6.03 thf(fact_9127_and__minus__numerals_I1_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_minus_numerals(1)
% 5.68/6.03 thf(fact_9128_take__bit__nat__eq,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.68/6.03 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_eq
% 5.68/6.03 thf(fact_9129_nat__take__bit__eq,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.68/6.03 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % nat_take_bit_eq
% 5.68/6.03 thf(fact_9130_take__bit__diff,axiom,
% 5.68/6.03 ! [N: nat,K: int,L2: int] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.68/6.03 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_diff
% 5.68/6.03 thf(fact_9131_take__bit__nat__less__eq__self,axiom,
% 5.68/6.03 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_less_eq_self
% 5.68/6.03 thf(fact_9132_take__bit__tightened__less__eq__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat,Q2: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_tightened_less_eq_nat
% 5.68/6.03 thf(fact_9133_take__bit__mult,axiom,
% 5.68/6.03 ! [N: nat,K: int,L2: int] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.68/6.03 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_mult
% 5.68/6.03 thf(fact_9134_take__bit__minus,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.68/6.03 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_minus
% 5.68/6.03 thf(fact_9135_concat__bit__take__bit__eq,axiom,
% 5.68/6.03 ! [N: nat,B: int] :
% 5.68/6.03 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.68/6.03 = ( bit_concat_bit @ N @ B ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_take_bit_eq
% 5.68/6.03 thf(fact_9136_concat__bit__eq__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int,L2: int,R2: int,S2: int] :
% 5.68/6.03 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 5.68/6.03 = ( bit_concat_bit @ N @ R2 @ S2 ) )
% 5.68/6.03 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 5.68/6.03 & ( L2 = S2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_eq_iff
% 5.68/6.03 thf(fact_9137_take__bit__tightened__less__eq__int,axiom,
% 5.68/6.03 ! [M: nat,N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_tightened_less_eq_int
% 5.68/6.03 thf(fact_9138_AND__upper2_H,axiom,
% 5.68/6.03 ! [Y2: int,Z: int,X: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper2'
% 5.68/6.03 thf(fact_9139_AND__upper1_H,axiom,
% 5.68/6.03 ! [Y2: int,Z: int,Ya: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( ord_less_eq_int @ Y2 @ Z )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper1'
% 5.68/6.03 thf(fact_9140_AND__upper2,axiom,
% 5.68/6.03 ! [Y2: int,X: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper2
% 5.68/6.03 thf(fact_9141_AND__upper1,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper1
% 5.68/6.03 thf(fact_9142_AND__lower,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_lower
% 5.68/6.03 thf(fact_9143_take__bit__int__less__eq__self__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.68/6.03 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_less_eq_self_iff
% 5.68/6.03 thf(fact_9144_take__bit__nonnegative,axiom,
% 5.68/6.03 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nonnegative
% 5.68/6.03 thf(fact_9145_take__bit__int__greater__self__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.68/6.03 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_greater_self_iff
% 5.68/6.03 thf(fact_9146_not__take__bit__negative,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % not_take_bit_negative
% 5.68/6.03 thf(fact_9147_pow_Osimps_I1_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( pow @ X @ one )
% 5.68/6.03 = X ) ).
% 5.68/6.03
% 5.68/6.03 % pow.simps(1)
% 5.68/6.03 thf(fact_9148_and__less__eq,axiom,
% 5.68/6.03 ! [L2: int,K: int] :
% 5.68/6.03 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_less_eq
% 5.68/6.03 thf(fact_9149_AND__upper1_H_H,axiom,
% 5.68/6.03 ! [Y2: int,Z: int,Ya: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( ord_less_int @ Y2 @ Z )
% 5.68/6.03 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper1''
% 5.68/6.03 thf(fact_9150_AND__upper2_H_H,axiom,
% 5.68/6.03 ! [Y2: int,Z: int,X: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ( ord_less_int @ Y2 @ Z )
% 5.68/6.03 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % AND_upper2''
% 5.68/6.03 thf(fact_9151_take__bit__eq__mask__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.68/6.03 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.68/6.03 = zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_eq_mask_iff
% 5.68/6.03 thf(fact_9152_take__bit__decr__eq,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 != zero_zero_int )
% 5.68/6.03 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.68/6.03 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_decr_eq
% 5.68/6.03 thf(fact_9153_even__and__iff__int,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.68/6.03 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.68/6.03 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_and_iff_int
% 5.68/6.03 thf(fact_9154_take__bit__nat__eq__self,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.68/6.03 = M ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_eq_self
% 5.68/6.03 thf(fact_9155_take__bit__nat__less__exp,axiom,
% 5.68/6.03 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_less_exp
% 5.68/6.03 thf(fact_9156_take__bit__nat__eq__self__iff,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.68/6.03 = M )
% 5.68/6.03 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_eq_self_iff
% 5.68/6.03 thf(fact_9157_take__bit__nat__def,axiom,
% 5.68/6.03 ( bit_se2925701944663578781it_nat
% 5.68/6.03 = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_def
% 5.68/6.03 thf(fact_9158_take__bit__int__less__exp,axiom,
% 5.68/6.03 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_less_exp
% 5.68/6.03 thf(fact_9159_take__bit__int__def,axiom,
% 5.68/6.03 ( bit_se2923211474154528505it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_def
% 5.68/6.03 thf(fact_9160_take__bit__nat__less__self__iff,axiom,
% 5.68/6.03 ! [N: nat,M: nat] :
% 5.68/6.03 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.68/6.03 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_nat_less_self_iff
% 5.68/6.03 thf(fact_9161_take__bit__Suc__minus__bit0,axiom,
% 5.68/6.03 ! [N: nat,K: num] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_Suc_minus_bit0
% 5.68/6.03 thf(fact_9162_take__bit__int__greater__eq__self__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.68/6.03 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_greater_eq_self_iff
% 5.68/6.03 thf(fact_9163_take__bit__int__less__self__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.68/6.03 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_less_self_iff
% 5.68/6.03 thf(fact_9164_take__bit__int__eq__self,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 = K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_eq_self
% 5.68/6.03 thf(fact_9165_take__bit__int__eq__self__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 = K )
% 5.68/6.03 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_eq_self_iff
% 5.68/6.03 thf(fact_9166_take__bit__numeral__minus__bit0,axiom,
% 5.68/6.03 ! [L2: num,K: num] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_numeral_minus_bit0
% 5.68/6.03 thf(fact_9167_take__bit__incr__eq,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.68/6.03 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.68/6.03 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_incr_eq
% 5.68/6.03 thf(fact_9168_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.68/6.03 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.68/6.03 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_eq_mask_iff_exp_dvd
% 5.68/6.03 thf(fact_9169_take__bit__int__less__eq,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.68/6.03 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.03 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_less_eq
% 5.68/6.03 thf(fact_9170_take__bit__int__greater__eq,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_int @ K @ zero_zero_int )
% 5.68/6.03 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_int_greater_eq
% 5.68/6.03 thf(fact_9171_signed__take__bit__eq__take__bit__shift,axiom,
% 5.68/6.03 ( bit_ri631733984087533419it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % signed_take_bit_eq_take_bit_shift
% 5.68/6.03 thf(fact_9172_and__int__rec,axiom,
% 5.68/6.03 ( bit_se725231765392027082nd_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int_rec
% 5.68/6.03 thf(fact_9173_take__bit__minus__small__eq,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( ord_less_int @ zero_zero_int @ K )
% 5.68/6.03 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.68/6.03 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_minus_small_eq
% 5.68/6.03 thf(fact_9174_take__bit__numeral__minus__bit1,axiom,
% 5.68/6.03 ! [L2: num,K: num] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/6.03 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_numeral_minus_bit1
% 5.68/6.03 thf(fact_9175_and__int_Osimps,axiom,
% 5.68/6.03 ( bit_se725231765392027082nd_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int
% 5.68/6.03 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 @ ( uminus_uminus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.68/6.03 @ ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int.simps
% 5.68/6.03 thf(fact_9176_and__int_Oelims,axiom,
% 5.68/6.03 ! [X: int,Xa2: int,Y2: int] :
% 5.68/6.03 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.68/6.03 = Y2 )
% 5.68/6.03 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 = ( uminus_uminus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.68/6.03 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 = ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int.elims
% 5.68/6.03 thf(fact_9177_take__bit__Suc__minus__bit1,axiom,
% 5.68/6.03 ! [N: nat,K: num] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/6.03 = ( 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 ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_Suc_minus_bit1
% 5.68/6.03 thf(fact_9178_pred__numeral__inc,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( pred_numeral @ ( inc @ K ) )
% 5.68/6.03 = ( numeral_numeral_nat @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % pred_numeral_inc
% 5.68/6.03 thf(fact_9179_and__nat__numerals_I1_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.68/6.03 = zero_zero_nat ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_numerals(1)
% 5.68/6.03 thf(fact_9180_and__nat__numerals_I3_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = zero_zero_nat ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_numerals(3)
% 5.68/6.03 thf(fact_9181_and__nat__numerals_I2_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.68/6.03 = one_one_nat ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_numerals(2)
% 5.68/6.03 thf(fact_9182_and__nat__numerals_I4_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = one_one_nat ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_numerals(4)
% 5.68/6.03 thf(fact_9183_and__Suc__0__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_Suc_0_eq
% 5.68/6.03 thf(fact_9184_Suc__0__and__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_0_and_eq
% 5.68/6.03 thf(fact_9185_num__induct,axiom,
% 5.68/6.03 ! [P: num > $o,X: num] :
% 5.68/6.03 ( ( P @ one )
% 5.68/6.03 => ( ! [X3: num] :
% 5.68/6.03 ( ( P @ X3 )
% 5.68/6.03 => ( P @ ( inc @ X3 ) ) )
% 5.68/6.03 => ( P @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % num_induct
% 5.68/6.03 thf(fact_9186_add__inc,axiom,
% 5.68/6.03 ! [X: num,Y2: num] :
% 5.68/6.03 ( ( plus_plus_num @ X @ ( inc @ Y2 ) )
% 5.68/6.03 = ( inc @ ( plus_plus_num @ X @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % add_inc
% 5.68/6.03 thf(fact_9187_inc_Osimps_I1_J,axiom,
% 5.68/6.03 ( ( inc @ one )
% 5.68/6.03 = ( bit0 @ one ) ) ).
% 5.68/6.03
% 5.68/6.03 % inc.simps(1)
% 5.68/6.03 thf(fact_9188_inc_Osimps_I2_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( inc @ ( bit0 @ X ) )
% 5.68/6.03 = ( bit1 @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % inc.simps(2)
% 5.68/6.03 thf(fact_9189_inc_Osimps_I3_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( inc @ ( bit1 @ X ) )
% 5.68/6.03 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % inc.simps(3)
% 5.68/6.03 thf(fact_9190_add__One,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( plus_plus_num @ X @ one )
% 5.68/6.03 = ( inc @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % add_One
% 5.68/6.03 thf(fact_9191_inc__BitM__eq,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( inc @ ( bitM @ N ) )
% 5.68/6.03 = ( bit0 @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % inc_BitM_eq
% 5.68/6.03 thf(fact_9192_BitM__inc__eq,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bitM @ ( inc @ N ) )
% 5.68/6.03 = ( bit1 @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % BitM_inc_eq
% 5.68/6.03 thf(fact_9193_and__nat__def,axiom,
% 5.68/6.03 ( bit_se727722235901077358nd_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_def
% 5.68/6.03 thf(fact_9194_mult__inc,axiom,
% 5.68/6.03 ! [X: num,Y2: num] :
% 5.68/6.03 ( ( times_times_num @ X @ ( inc @ Y2 ) )
% 5.68/6.03 = ( plus_plus_num @ ( times_times_num @ X @ Y2 ) @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % mult_inc
% 5.68/6.03 thf(fact_9195_atLeastAtMostPlus1__int__conv,axiom,
% 5.68/6.03 ! [M: int,N: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.68/6.03 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.68/6.03 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastAtMostPlus1_int_conv
% 5.68/6.03 thf(fact_9196_simp__from__to,axiom,
% 5.68/6.03 ( set_or1266510415728281911st_int
% 5.68/6.03 = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % simp_from_to
% 5.68/6.03 thf(fact_9197_and__nat__unfold,axiom,
% 5.68/6.03 ( bit_se727722235901077358nd_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.03 ( if_nat
% 5.68/6.03 @ ( ( M6 = zero_zero_nat )
% 5.68/6.03 | ( N2 = zero_zero_nat ) )
% 5.68/6.03 @ zero_zero_nat
% 5.68/6.03 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_unfold
% 5.68/6.03 thf(fact_9198_and__nat__rec,axiom,
% 5.68/6.03 ( bit_se727722235901077358nd_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.03 ( plus_plus_nat
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.68/6.03 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.03 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_nat_rec
% 5.68/6.03 thf(fact_9199_and__int_Opelims,axiom,
% 5.68/6.03 ! [X: int,Xa2: int,Y2: int] :
% 5.68/6.03 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.68/6.03 = Y2 )
% 5.68/6.03 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.68/6.03 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 = ( uminus_uminus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.68/6.03 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 = ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.68/6.03 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int.pelims
% 5.68/6.03 thf(fact_9200_and__int_Opsimps,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.68/6.03 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.68/6.03 = ( uminus_uminus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.68/6.03 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.68/6.03 = ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.68/6.03 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int.psimps
% 5.68/6.03 thf(fact_9201_and__int_Opinduct,axiom,
% 5.68/6.03 ! [A0: int,A1: int,P: int > int > $o] :
% 5.68/6.03 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.68/6.03 => ( ! [K2: int,L4: int] :
% 5.68/6.03 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.68/6.03 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.68/6.03 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.68/6.03 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.03 => ( P @ K2 @ L4 ) ) )
% 5.68/6.03 => ( P @ A0 @ A1 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_int.pinduct
% 5.68/6.03 thf(fact_9202_Arg__def,axiom,
% 5.68/6.03 ( arg
% 5.68/6.03 = ( ^ [Z2: complex] :
% 5.68/6.03 ( if_real @ ( Z2 = zero_zero_complex ) @ zero_zero_real
% 5.68/6.03 @ ( fChoice_real
% 5.68/6.03 @ ^ [A4: real] :
% 5.68/6.03 ( ( ( sgn_sgn_complex @ Z2 )
% 5.68/6.03 = ( cis @ A4 ) )
% 5.68/6.03 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.68/6.03 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Arg_def
% 5.68/6.03 thf(fact_9203_set__encode__insert,axiom,
% 5.68/6.03 ! [A2: set_nat,N: nat] :
% 5.68/6.03 ( ( finite_finite_nat @ A2 )
% 5.68/6.03 => ( ~ ( member_nat @ N @ A2 )
% 5.68/6.03 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_encode_insert
% 5.68/6.03 thf(fact_9204_lessThan__Suc,axiom,
% 5.68/6.03 ! [K: nat] :
% 5.68/6.03 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.68/6.03 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % lessThan_Suc
% 5.68/6.03 thf(fact_9205_atMost__Suc,axiom,
% 5.68/6.03 ! [K: nat] :
% 5.68/6.03 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.68/6.03 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atMost_Suc
% 5.68/6.03 thf(fact_9206_atLeast0__atMost__Suc,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.68/6.03 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeast0_atMost_Suc
% 5.68/6.03 thf(fact_9207_atLeastAtMost__insertL,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.68/6.03 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastAtMost_insertL
% 5.68/6.03 thf(fact_9208_atLeastAtMostSuc__conv,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.68/6.03 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.68/6.03 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastAtMostSuc_conv
% 5.68/6.03 thf(fact_9209_Icc__eq__insert__lb__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.68/6.03 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Icc_eq_insert_lb_nat
% 5.68/6.03 thf(fact_9210_lessThan__nat__numeral,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.68/6.03 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % lessThan_nat_numeral
% 5.68/6.03 thf(fact_9211_atMost__nat__numeral,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.68/6.03 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atMost_nat_numeral
% 5.68/6.03 thf(fact_9212_atLeast1__atMost__eq__remove0,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeast1_atMost_eq_remove0
% 5.68/6.03 thf(fact_9213_set__decode__plus__power__2,axiom,
% 5.68/6.03 ! [N: nat,Z: nat] :
% 5.68/6.03 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.68/6.03 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.68/6.03 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_decode_plus_power_2
% 5.68/6.03 thf(fact_9214_signed__take__bit__eq__take__bit__minus,axiom,
% 5.68/6.03 ( bit_ri631733984087533419it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % signed_take_bit_eq_take_bit_minus
% 5.68/6.03 thf(fact_9215_or__int__unfold,axiom,
% 5.68/6.03 ( bit_se1409905431419307370or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int
% 5.68/6.03 @ ( ( K3
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 | ( L
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.68/6.03 @ ( uminus_uminus_int @ one_one_int )
% 5.68/6.03 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( 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 @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_int_unfold
% 5.68/6.03 thf(fact_9216_cis__multiple__2pi,axiom,
% 5.68/6.03 ! [N: real] :
% 5.68/6.03 ( ( member_real @ N @ ring_1_Ints_real )
% 5.68/6.03 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.68/6.03 = one_one_complex ) ) ).
% 5.68/6.03
% 5.68/6.03 % cis_multiple_2pi
% 5.68/6.03 thf(fact_9217_take__bit__Suc__from__most,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.68/6.03 = ( 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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % take_bit_Suc_from_most
% 5.68/6.03 thf(fact_9218_or__nonnegative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.68/6.03 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nonnegative_int_iff
% 5.68/6.03 thf(fact_9219_or__negative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.68/6.03 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.68/6.03 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_negative_int_iff
% 5.68/6.03 thf(fact_9220_signed__take__bit__nonnegative__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % signed_take_bit_nonnegative_iff
% 5.68/6.03 thf(fact_9221_signed__take__bit__negative__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.68/6.03 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % signed_take_bit_negative_iff
% 5.68/6.03 thf(fact_9222_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.68/6.03 ! [W: num,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.68/6.03 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_minus_numeral_Bit0_Suc_iff
% 5.68/6.03 thf(fact_9223_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.68/6.03 ! [W: num,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_minus_numeral_Bit1_Suc_iff
% 5.68/6.03 thf(fact_9224_or__minus__numerals_I6_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(6)
% 5.68/6.03 thf(fact_9225_or__minus__numerals_I2_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(2)
% 5.68/6.03 thf(fact_9226_bit__minus__numeral__int_I1_J,axiom,
% 5.68/6.03 ! [W: num,N: num] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.03 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_minus_numeral_int(1)
% 5.68/6.03 thf(fact_9227_bit__minus__numeral__int_I2_J,axiom,
% 5.68/6.03 ! [W: num,N: num] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_minus_numeral_int(2)
% 5.68/6.03 thf(fact_9228_bit__or__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 5.68/6.03 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.68/6.03 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_or_int_iff
% 5.68/6.03 thf(fact_9229_bit__and__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 5.68/6.03 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.68/6.03 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_and_int_iff
% 5.68/6.03 thf(fact_9230_OR__lower,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % OR_lower
% 5.68/6.03 thf(fact_9231_or__greater__eq,axiom,
% 5.68/6.03 ! [L2: int,K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.68/6.03 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_greater_eq
% 5.68/6.03 thf(fact_9232_plus__and__or,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Y2 ) )
% 5.68/6.03 = ( plus_plus_int @ X @ Y2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % plus_and_or
% 5.68/6.03 thf(fact_9233_bit__not__int__iff_H,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_not_int_iff'
% 5.68/6.03 thf(fact_9234_bit__imp__take__bit__positive,axiom,
% 5.68/6.03 ! [N: nat,M: nat,K: int] :
% 5.68/6.03 ( ( ord_less_nat @ N @ M )
% 5.68/6.03 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.68/6.03 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_imp_take_bit_positive
% 5.68/6.03 thf(fact_9235_bit__concat__bit__iff,axiom,
% 5.68/6.03 ! [M: nat,K: int,L2: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.68/6.03 = ( ( ( ord_less_nat @ N @ M )
% 5.68/6.03 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.68/6.03 | ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_concat_bit_iff
% 5.68/6.03 thf(fact_9236_sin__times__pi__eq__0,axiom,
% 5.68/6.03 ! [X: real] :
% 5.68/6.03 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.68/6.03 = zero_zero_real )
% 5.68/6.03 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_times_pi_eq_0
% 5.68/6.03 thf(fact_9237_signed__take__bit__eq__concat__bit,axiom,
% 5.68/6.03 ( bit_ri631733984087533419it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % signed_take_bit_eq_concat_bit
% 5.68/6.03 thf(fact_9238_int__bit__bound,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ~ ! [N3: nat] :
% 5.68/6.03 ( ! [M2: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.68/6.03 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.68/6.03 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.68/6.03 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.68/6.03 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_bit_bound
% 5.68/6.03 thf(fact_9239_bit__int__def,axiom,
% 5.68/6.03 ( bit_se1146084159140164899it_int
% 5.68/6.03 = ( ^ [K3: int,N2: nat] :
% 5.68/6.03 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_int_def
% 5.68/6.03 thf(fact_9240_OR__upper,axiom,
% 5.68/6.03 ! [X: int,N: nat,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % OR_upper
% 5.68/6.03 thf(fact_9241_sin__integer__2pi,axiom,
% 5.68/6.03 ! [N: real] :
% 5.68/6.03 ( ( member_real @ N @ ring_1_Ints_real )
% 5.68/6.03 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.68/6.03 = zero_zero_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % sin_integer_2pi
% 5.68/6.03 thf(fact_9242_cos__integer__2pi,axiom,
% 5.68/6.03 ! [N: real] :
% 5.68/6.03 ( ( member_real @ N @ ring_1_Ints_real )
% 5.68/6.03 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.68/6.03 = one_one_real ) ) ).
% 5.68/6.03
% 5.68/6.03 % cos_integer_2pi
% 5.68/6.03 thf(fact_9243_or__int__rec,axiom,
% 5.68/6.03 ( bit_se1409905431419307370or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.68/6.03 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_int_rec
% 5.68/6.03 thf(fact_9244_set__bit__eq,axiom,
% 5.68/6.03 ( bit_se7879613467334960850it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] :
% 5.68/6.03 ( plus_plus_int @ K3
% 5.68/6.03 @ ( times_times_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 5.68/6.03 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_bit_eq
% 5.68/6.03 thf(fact_9245_unset__bit__eq,axiom,
% 5.68/6.03 ( bit_se4203085406695923979it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % unset_bit_eq
% 5.68/6.03 thf(fact_9246_or__minus__numerals_I1_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(1)
% 5.68/6.03 thf(fact_9247_or__minus__numerals_I5_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(5)
% 5.68/6.03 thf(fact_9248_xor__Suc__0__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_Suc_0_eq
% 5.68/6.03 thf(fact_9249_Suc__0__xor__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_0_xor_eq
% 5.68/6.03 thf(fact_9250_or__nat__numerals_I2_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_numerals(2)
% 5.68/6.03 thf(fact_9251_or__nat__numerals_I4_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_numerals(4)
% 5.68/6.03 thf(fact_9252_or__nat__numerals_I1_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_numerals(1)
% 5.68/6.03 thf(fact_9253_or__nat__numerals_I3_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_numerals(3)
% 5.68/6.03 thf(fact_9254_xor__nat__numerals_I1_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_numerals(1)
% 5.68/6.03 thf(fact_9255_xor__nat__numerals_I2_J,axiom,
% 5.68/6.03 ! [Y2: num] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_numerals(2)
% 5.68/6.03 thf(fact_9256_xor__nat__numerals_I3_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_numerals(3)
% 5.68/6.03 thf(fact_9257_xor__nat__numerals_I4_J,axiom,
% 5.68/6.03 ! [X: num] :
% 5.68/6.03 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_numerals(4)
% 5.68/6.03 thf(fact_9258_or__minus__numerals_I4_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(4)
% 5.68/6.03 thf(fact_9259_or__minus__numerals_I8_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(8)
% 5.68/6.03 thf(fact_9260_or__minus__numerals_I3_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(3)
% 5.68/6.03 thf(fact_9261_or__minus__numerals_I7_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_numerals(7)
% 5.68/6.03 thf(fact_9262_or__not__num__neg_Osimps_I1_J,axiom,
% 5.68/6.03 ( ( bit_or_not_num_neg @ one @ one )
% 5.68/6.03 = one ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(1)
% 5.68/6.03 thf(fact_9263_bit__Suc__0__iff,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( N = zero_zero_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_Suc_0_iff
% 5.68/6.03 thf(fact_9264_not__bit__Suc__0__Suc,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_bit_Suc_0_Suc
% 5.68/6.03 thf(fact_9265_or__not__num__neg_Osimps_I4_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.68/6.03 = ( bit0 @ one ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(4)
% 5.68/6.03 thf(fact_9266_or__not__num__neg_Osimps_I6_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.68/6.03 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(6)
% 5.68/6.03 thf(fact_9267_or__not__num__neg_Osimps_I7_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.68/6.03 = one ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(7)
% 5.68/6.03 thf(fact_9268_or__not__num__neg_Osimps_I3_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.68/6.03 = ( bit1 @ M ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(3)
% 5.68/6.03 thf(fact_9269_or__not__num__neg_Osimps_I5_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(5)
% 5.68/6.03 thf(fact_9270_not__bit__Suc__0__numeral,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_bit_Suc_0_numeral
% 5.68/6.03 thf(fact_9271_or__not__num__neg_Osimps_I9_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(9)
% 5.68/6.03 thf(fact_9272_or__nat__def,axiom,
% 5.68/6.03 ( bit_se1412395901928357646or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_def
% 5.68/6.03 thf(fact_9273_or__not__num__neg_Osimps_I2_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.68/6.03 = ( bit1 @ M ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(2)
% 5.68/6.03 thf(fact_9274_or__not__num__neg_Osimps_I8_J,axiom,
% 5.68/6.03 ! [N: num,M: num] :
% 5.68/6.03 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.simps(8)
% 5.68/6.03 thf(fact_9275_bit__nat__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.68/6.03 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_nat_iff
% 5.68/6.03 thf(fact_9276_or__not__num__neg_Oelims,axiom,
% 5.68/6.03 ! [X: num,Xa2: num,Y2: num] :
% 5.68/6.03 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.68/6.03 = Y2 )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( Y2 != one ) ) )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bit1 @ M5 ) ) ) )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bit1 @ M5 ) ) ) )
% 5.68/6.03 => ( ( ? [N3: num] :
% 5.68/6.03 ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bit0 @ one ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.68/6.03 => ( ( ? [N3: num] :
% 5.68/6.03 ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( Y2 != one ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.68/6.03 => ~ ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( Y2
% 5.68/6.03 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.elims
% 5.68/6.03 thf(fact_9277_bit__nat__def,axiom,
% 5.68/6.03 ( bit_se1148574629649215175it_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.03 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_nat_def
% 5.68/6.03 thf(fact_9278_Suc__0__or__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Suc_0_or_eq
% 5.68/6.03 thf(fact_9279_or__Suc__0__eq,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_Suc_0_eq
% 5.68/6.03 thf(fact_9280_or__nat__rec,axiom,
% 5.68/6.03 ( bit_se1412395901928357646or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.03 ( plus_plus_nat
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.68/6.03 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.03 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_rec
% 5.68/6.03 thf(fact_9281_xor__nat__unfold,axiom,
% 5.68/6.03 ( bit_se6528837805403552850or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_unfold
% 5.68/6.03 thf(fact_9282_xor__nat__rec,axiom,
% 5.68/6.03 ( bit_se6528837805403552850or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.03 ( plus_plus_nat
% 5.68/6.03 @ ( zero_n2687167440665602831ol_nat
% 5.68/6.03 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.68/6.03 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.68/6.03 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_rec
% 5.68/6.03 thf(fact_9283_or__nat__unfold,axiom,
% 5.68/6.03 ( bit_se1412395901928357646or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_nat_unfold
% 5.68/6.03 thf(fact_9284_or__not__num__neg_Opelims,axiom,
% 5.68/6.03 ! [X: num,Xa2: num,Y2: num] :
% 5.68/6.03 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.68/6.03 = Y2 )
% 5.68/6.03 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( ( Y2 = one )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 5.68/6.03 => ( ( ( X = one )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bit0 @ one ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit0 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ( ( Xa2 = one )
% 5.68/6.03 => ( ( Y2 = one )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.68/6.03 => ( ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit0 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.68/6.03 => ~ ! [N3: num] :
% 5.68/6.03 ( ( X
% 5.68/6.03 = ( bit1 @ N3 ) )
% 5.68/6.03 => ! [M5: num] :
% 5.68/6.03 ( ( Xa2
% 5.68/6.03 = ( bit1 @ M5 ) )
% 5.68/6.03 => ( ( Y2
% 5.68/6.03 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.68/6.03 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_num_neg.pelims
% 5.68/6.03 thf(fact_9285_horner__sum__of__bool__2__less,axiom,
% 5.68/6.03 ! [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 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % horner_sum_of_bool_2_less
% 5.68/6.03 thf(fact_9286_push__bit__nonnegative__int__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.68/6.03 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_nonnegative_int_iff
% 5.68/6.03 thf(fact_9287_push__bit__negative__int__iff,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.68/6.03 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_negative_int_iff
% 5.68/6.03 thf(fact_9288_concat__bit__of__zero__1,axiom,
% 5.68/6.03 ! [N: nat,L2: int] :
% 5.68/6.03 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 5.68/6.03 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_of_zero_1
% 5.68/6.03 thf(fact_9289_xor__nonnegative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.68/6.03 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.68/6.03 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nonnegative_int_iff
% 5.68/6.03 thf(fact_9290_xor__negative__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.68/6.03 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.68/6.03 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_negative_int_iff
% 5.68/6.03 thf(fact_9291_push__bit__of__Suc__0,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_of_Suc_0
% 5.68/6.03 thf(fact_9292_bit__xor__int__iff,axiom,
% 5.68/6.03 ! [K: int,L2: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 5.68/6.03 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.68/6.03 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_xor_int_iff
% 5.68/6.03 thf(fact_9293_flip__bit__int__def,axiom,
% 5.68/6.03 ( bit_se2159334234014336723it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % flip_bit_int_def
% 5.68/6.03 thf(fact_9294_push__bit__nat__eq,axiom,
% 5.68/6.03 ! [N: nat,K: int] :
% 5.68/6.03 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.68/6.03 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_nat_eq
% 5.68/6.03 thf(fact_9295_XOR__lower,axiom,
% 5.68/6.03 ! [X: int,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.03 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % XOR_lower
% 5.68/6.03 thf(fact_9296_flip__bit__nat__def,axiom,
% 5.68/6.03 ( bit_se2161824704523386999it_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % flip_bit_nat_def
% 5.68/6.03 thf(fact_9297_set__bit__nat__def,axiom,
% 5.68/6.03 ( bit_se7882103937844011126it_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_bit_nat_def
% 5.68/6.03 thf(fact_9298_bit__push__bit__iff__int,axiom,
% 5.68/6.03 ! [M: nat,K: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.68/6.03 = ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_push_bit_iff_int
% 5.68/6.03 thf(fact_9299_xor__nat__def,axiom,
% 5.68/6.03 ( bit_se6528837805403552850or_nat
% 5.68/6.03 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_nat_def
% 5.68/6.03 thf(fact_9300_bit__push__bit__iff__nat,axiom,
% 5.68/6.03 ! [M: nat,Q2: nat,N: nat] :
% 5.68/6.03 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.68/6.03 = ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_push_bit_iff_nat
% 5.68/6.03 thf(fact_9301_concat__bit__eq,axiom,
% 5.68/6.03 ( bit_concat_bit
% 5.68/6.03 = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_eq
% 5.68/6.03 thf(fact_9302_concat__bit__def,axiom,
% 5.68/6.03 ( bit_concat_bit
% 5.68/6.03 = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % concat_bit_def
% 5.68/6.03 thf(fact_9303_set__bit__int__def,axiom,
% 5.68/6.03 ( bit_se7879613467334960850it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % set_bit_int_def
% 5.68/6.03 thf(fact_9304_push__bit__int__def,axiom,
% 5.68/6.03 ( bit_se545348938243370406it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_int_def
% 5.68/6.03 thf(fact_9305_push__bit__nat__def,axiom,
% 5.68/6.03 ( bit_se547839408752420682it_nat
% 5.68/6.03 = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_nat_def
% 5.68/6.03 thf(fact_9306_push__bit__minus__one,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % push_bit_minus_one
% 5.68/6.03 thf(fact_9307_XOR__upper,axiom,
% 5.68/6.03 ! [X: int,N: nat,Y2: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.03 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.68/6.03 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % XOR_upper
% 5.68/6.03 thf(fact_9308_xor__int__rec,axiom,
% 5.68/6.03 ( bit_se6526347334894502574or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( plus_plus_int
% 5.68/6.03 @ ( zero_n2684676970156552555ol_int
% 5.68/6.03 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.68/6.03 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.68/6.03 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_int_rec
% 5.68/6.03 thf(fact_9309_xor__int__unfold,axiom,
% 5.68/6.03 ( bit_se6526347334894502574or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] :
% 5.68/6.03 ( if_int
% 5.68/6.03 @ ( K3
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.68/6.03 @ ( if_int
% 5.68/6.03 @ ( L
% 5.68/6.03 = ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.03 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.68/6.03 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = 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 @ L @ ( 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 @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_int_unfold
% 5.68/6.03 thf(fact_9310_Sum__Ico__nat,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( groups3542108847815614940at_nat
% 5.68/6.03 @ ^ [X2: nat] : X2
% 5.68/6.03 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Sum_Ico_nat
% 5.68/6.03 thf(fact_9311_VEBT_Osize_I3_J,axiom,
% 5.68/6.03 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.68/6.03 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % VEBT.size(3)
% 5.68/6.03 thf(fact_9312_not__negative__int__iff,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.68/6.03 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_negative_int_iff
% 5.68/6.03 thf(fact_9313_not__nonnegative__int__iff,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.68/6.03 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_nonnegative_int_iff
% 5.68/6.03 thf(fact_9314_atLeastLessThan__singleton,axiom,
% 5.68/6.03 ! [M: nat] :
% 5.68/6.03 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.68/6.03 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastLessThan_singleton
% 5.68/6.03 thf(fact_9315_and__minus__minus__numerals,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_minus_minus_numerals
% 5.68/6.03 thf(fact_9316_or__minus__minus__numerals,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_minus_minus_numerals
% 5.68/6.03 thf(fact_9317_bit__not__int__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.68/6.03 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_not_int_iff
% 5.68/6.03 thf(fact_9318_ex__nat__less__eq,axiom,
% 5.68/6.03 ! [N: nat,P: nat > $o] :
% 5.68/6.03 ( ( ? [M6: nat] :
% 5.68/6.03 ( ( ord_less_nat @ M6 @ N )
% 5.68/6.03 & ( P @ M6 ) ) )
% 5.68/6.03 = ( ? [X2: nat] :
% 5.68/6.03 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.68/6.03 & ( P @ X2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % ex_nat_less_eq
% 5.68/6.03 thf(fact_9319_all__nat__less__eq,axiom,
% 5.68/6.03 ! [N: nat,P: nat > $o] :
% 5.68/6.03 ( ( ! [M6: nat] :
% 5.68/6.03 ( ( ord_less_nat @ M6 @ N )
% 5.68/6.03 => ( P @ M6 ) ) )
% 5.68/6.03 = ( ! [X2: nat] :
% 5.68/6.03 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.68/6.03 => ( P @ X2 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % all_nat_less_eq
% 5.68/6.03 thf(fact_9320_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.68/6.03 ! [L2: nat,U: nat] :
% 5.68/6.03 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.68/6.03 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastLessThanSuc_atLeastAtMost
% 5.68/6.03 thf(fact_9321_or__int__def,axiom,
% 5.68/6.03 ( bit_se1409905431419307370or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_int_def
% 5.68/6.03 thf(fact_9322_not__int__def,axiom,
% 5.68/6.03 ( bit_ri7919022796975470100ot_int
% 5.68/6.03 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_int_def
% 5.68/6.03 thf(fact_9323_and__not__numerals_I1_J,axiom,
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(1)
% 5.68/6.03 thf(fact_9324_or__not__numerals_I1_J,axiom,
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(1)
% 5.68/6.03 thf(fact_9325_atLeast0__lessThan__Suc,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.68/6.03 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeast0_lessThan_Suc
% 5.68/6.03 thf(fact_9326_unset__bit__int__def,axiom,
% 5.68/6.03 ( bit_se4203085406695923979it_int
% 5.68/6.03 = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % unset_bit_int_def
% 5.68/6.03 thf(fact_9327_xor__int__def,axiom,
% 5.68/6.03 ( bit_se6526347334894502574or_int
% 5.68/6.03 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % xor_int_def
% 5.68/6.03 thf(fact_9328_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.68/6.03 ! [N5: set_nat,N: nat] :
% 5.68/6.03 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.68/6.03 => ( finite_finite_nat @ N5 ) ) ).
% 5.68/6.03
% 5.68/6.03 % subset_eq_atLeast0_lessThan_finite
% 5.68/6.03 thf(fact_9329_not__int__div__2,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_int_div_2
% 5.68/6.03 thf(fact_9330_even__not__iff__int,axiom,
% 5.68/6.03 ! [K: int] :
% 5.68/6.03 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.68/6.03 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % even_not_iff_int
% 5.68/6.03 thf(fact_9331_and__not__numerals_I2_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = one_one_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(2)
% 5.68/6.03 thf(fact_9332_and__not__numerals_I4_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(4)
% 5.68/6.03 thf(fact_9333_or__not__numerals_I2_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(2)
% 5.68/6.03 thf(fact_9334_or__not__numerals_I4_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(4)
% 5.68/6.03 thf(fact_9335_bit__minus__int__iff,axiom,
% 5.68/6.03 ! [K: int,N: nat] :
% 5.68/6.03 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.68/6.03 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % bit_minus_int_iff
% 5.68/6.03 thf(fact_9336_numeral__or__not__num__eq,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % numeral_or_not_num_eq
% 5.68/6.03 thf(fact_9337_int__numeral__not__or__num__neg,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_numeral_not_or_num_neg
% 5.68/6.03 thf(fact_9338_int__numeral__or__not__num__neg,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.03 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_numeral_or_not_num_neg
% 5.68/6.03 thf(fact_9339_atLeastLessThanSuc,axiom,
% 5.68/6.03 ! [M: nat,N: nat] :
% 5.68/6.03 ( ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.68/6.03 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.68/6.03 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.68/6.03 = bot_bot_set_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastLessThanSuc
% 5.68/6.03 thf(fact_9340_prod__Suc__Suc__fact,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.68/6.03 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_Suc_Suc_fact
% 5.68/6.03 thf(fact_9341_prod__Suc__fact,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.68/6.03 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.68/6.03
% 5.68/6.03 % prod_Suc_fact
% 5.68/6.03 thf(fact_9342_and__not__numerals_I5_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(5)
% 5.68/6.03 thf(fact_9343_and__not__numerals_I7_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(7)
% 5.68/6.03 thf(fact_9344_or__not__numerals_I3_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(3)
% 5.68/6.03 thf(fact_9345_and__not__numerals_I3_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = zero_zero_int ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(3)
% 5.68/6.03 thf(fact_9346_or__not__numerals_I7_J,axiom,
% 5.68/6.03 ! [M: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.68/6.03 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(7)
% 5.68/6.03 thf(fact_9347_atLeastLessThan__nat__numeral,axiom,
% 5.68/6.03 ! [M: nat,K: num] :
% 5.68/6.03 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.68/6.03 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.68/6.03 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.68/6.03 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.68/6.03 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.68/6.03 = bot_bot_set_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastLessThan_nat_numeral
% 5.68/6.03 thf(fact_9348_and__not__numerals_I9_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(9)
% 5.68/6.03 thf(fact_9349_and__not__numerals_I6_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(6)
% 5.68/6.03 thf(fact_9350_or__not__numerals_I6_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(6)
% 5.68/6.03 thf(fact_9351_or__not__numerals_I5_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(5)
% 5.68/6.03 thf(fact_9352_atLeast1__lessThan__eq__remove0,axiom,
% 5.68/6.03 ! [N: nat] :
% 5.68/6.03 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.68/6.03 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeast1_lessThan_eq_remove0
% 5.68/6.03 thf(fact_9353_and__not__numerals_I8_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % and_not_numerals(8)
% 5.68/6.03 thf(fact_9354_or__not__numerals_I8_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(8)
% 5.68/6.03 thf(fact_9355_or__not__numerals_I9_J,axiom,
% 5.68/6.03 ! [M: num,N: num] :
% 5.68/6.03 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.03 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % or_not_numerals(9)
% 5.68/6.03 thf(fact_9356_not__int__rec,axiom,
% 5.68/6.03 ( bit_ri7919022796975470100ot_int
% 5.68/6.03 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % not_int_rec
% 5.68/6.03 thf(fact_9357_sum__power2,axiom,
% 5.68/6.03 ! [K: nat] :
% 5.68/6.03 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.68/6.03 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.68/6.03
% 5.68/6.03 % sum_power2
% 5.68/6.03 thf(fact_9358_Chebyshev__sum__upper__nat,axiom,
% 5.68/6.03 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.68/6.03 ( ! [I4: nat,J2: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.68/6.03 => ( ( ord_less_nat @ J2 @ N )
% 5.68/6.03 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 5.68/6.03 => ( ! [I4: nat,J2: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.68/6.03 => ( ( ord_less_nat @ J2 @ N )
% 5.68/6.03 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 5.68/6.03 => ( ord_less_eq_nat
% 5.68/6.03 @ ( times_times_nat @ N
% 5.68/6.03 @ ( groups3542108847815614940at_nat
% 5.68/6.03 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 5.68/6.03 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.68/6.03 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Chebyshev_sum_upper_nat
% 5.68/6.03 thf(fact_9359_VEBT_Osize__gen_I1_J,axiom,
% 5.68/6.03 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.68/6.03 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.68/6.03 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % VEBT.size_gen(1)
% 5.68/6.03 thf(fact_9360_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.68/6.03 ! [L2: int,U: int] :
% 5.68/6.03 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 5.68/6.03 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.68/6.03
% 5.68/6.03 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.68/6.03 thf(fact_9361_Cauchy__iff2,axiom,
% 5.68/6.03 ( topolo4055970368930404560y_real
% 5.68/6.03 = ( ^ [X6: nat > real] :
% 5.68/6.03 ! [J3: nat] :
% 5.68/6.03 ? [M9: nat] :
% 5.68/6.03 ! [M6: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M9 @ M6 )
% 5.68/6.03 => ! [N2: nat] :
% 5.68/6.03 ( ( ord_less_eq_nat @ M9 @ N2 )
% 5.68/6.03 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % Cauchy_iff2
% 5.68/6.03 thf(fact_9362_valid__eq,axiom,
% 5.68/6.03 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.68/6.03
% 5.68/6.03 % valid_eq
% 5.68/6.03 thf(fact_9363_valid__eq2,axiom,
% 5.68/6.03 ! [T: vEBT_VEBT,D: nat] :
% 5.68/6.03 ( ( vEBT_VEBT_valid @ T @ D )
% 5.68/6.03 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.68/6.03
% 5.68/6.03 % valid_eq2
% 5.68/6.03 thf(fact_9364_valid__eq1,axiom,
% 5.68/6.03 ! [T: vEBT_VEBT,D: nat] :
% 5.68/6.03 ( ( vEBT_invar_vebt @ T @ D )
% 5.68/6.03 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.68/6.03
% 5.68/6.03 % valid_eq1
% 5.68/6.03 thf(fact_9365_Code__Target__Int_Opositive__def,axiom,
% 5.68/6.03 code_Target_positive = numeral_numeral_int ).
% 5.68/6.03
% 5.68/6.03 % Code_Target_Int.positive_def
% 5.68/6.03 thf(fact_9366_divmod__step__integer__def,axiom,
% 5.68/6.03 ( unique4921790084139445826nteger
% 5.68/6.03 = ( ^ [L: num] :
% 5.68/6.03 ( produc6916734918728496179nteger
% 5.68/6.03 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divmod_step_integer_def
% 5.68/6.03 thf(fact_9367_divmod__integer_H__def,axiom,
% 5.68/6.03 ( unique3479559517661332726nteger
% 5.68/6.03 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % divmod_integer'_def
% 5.68/6.03 thf(fact_9368_times__integer__code_I2_J,axiom,
% 5.68/6.03 ! [L2: code_integer] :
% 5.68/6.03 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.68/6.03 = zero_z3403309356797280102nteger ) ).
% 5.68/6.03
% 5.68/6.03 % times_integer_code(2)
% 5.68/6.03 thf(fact_9369_times__integer__code_I1_J,axiom,
% 5.68/6.03 ! [K: code_integer] :
% 5.68/6.03 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.68/6.03 = zero_z3403309356797280102nteger ) ).
% 5.68/6.03
% 5.68/6.03 % times_integer_code(1)
% 5.68/6.03 thf(fact_9370_plus__integer__code_I1_J,axiom,
% 5.68/6.03 ! [K: code_integer] :
% 5.68/6.03 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.68/6.03 = K ) ).
% 5.68/6.03
% 5.68/6.03 % plus_integer_code(1)
% 5.68/6.03 thf(fact_9371_plus__integer__code_I2_J,axiom,
% 5.68/6.03 ! [L2: code_integer] :
% 5.68/6.03 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.68/6.03 = L2 ) ).
% 5.68/6.03
% 5.68/6.03 % plus_integer_code(2)
% 5.68/6.03 thf(fact_9372_less__eq__integer__code_I1_J,axiom,
% 5.68/6.03 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.68/6.03
% 5.68/6.03 % less_eq_integer_code(1)
% 5.68/6.03 thf(fact_9373_exhaustive__integer_H_Ocases,axiom,
% 5.68/6.03 ! [X: produc8763457246119570046nteger] :
% 5.68/6.03 ~ ! [F2: code_integer > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 5.68/6.03 ( X
% 5.68/6.03 != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % exhaustive_integer'.cases
% 5.68/6.03 thf(fact_9374_full__exhaustive__integer_H_Ocases,axiom,
% 5.68/6.03 ! [X: produc1908205239877642774nteger] :
% 5.68/6.03 ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 5.68/6.03 ( X
% 5.68/6.03 != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % full_exhaustive_integer'.cases
% 5.68/6.03 thf(fact_9375_integer__of__int__code,axiom,
% 5.68/6.03 ( code_integer_of_int
% 5.68/6.03 = ( ^ [K3: int] :
% 5.68/6.03 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.68/6.03 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.68/6.03 @ ( if_Code_integer
% 5.68/6.03 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.68/6.03 = zero_zero_int )
% 5.68/6.03 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.68/6.03 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % integer_of_int_code
% 5.68/6.03 thf(fact_9376_Code__Numeral_Opositive__def,axiom,
% 5.68/6.03 code_positive = numera6620942414471956472nteger ).
% 5.68/6.03
% 5.68/6.03 % Code_Numeral.positive_def
% 5.68/6.03 thf(fact_9377_plus__integer_Oabs__eq,axiom,
% 5.68/6.03 ! [Xa2: int,X: int] :
% 5.68/6.03 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.68/6.03 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % plus_integer.abs_eq
% 5.68/6.03 thf(fact_9378_times__integer_Oabs__eq,axiom,
% 5.68/6.03 ! [Xa2: int,X: int] :
% 5.68/6.03 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.68/6.03 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % times_integer.abs_eq
% 5.68/6.03 thf(fact_9379_less__eq__integer_Oabs__eq,axiom,
% 5.68/6.03 ! [Xa2: int,X: int] :
% 5.68/6.03 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.68/6.03 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_eq_integer.abs_eq
% 5.68/6.03 thf(fact_9380_integer__of__num_I3_J,axiom,
% 5.68/6.03 ! [N: num] :
% 5.68/6.03 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.68/6.03 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.68/6.03
% 5.68/6.03 % integer_of_num(3)
% 5.68/6.03 thf(fact_9381_int__of__integer__code,axiom,
% 5.68/6.03 ( code_int_of_integer
% 5.68/6.03 = ( ^ [K3: code_integer] :
% 5.68/6.03 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.68/6.03 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.68/6.03 @ ( produc1553301316500091796er_int
% 5.68/6.03 @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 5.68/6.03 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_of_integer_code
% 5.68/6.03 thf(fact_9382_int__of__integer__numeral,axiom,
% 5.68/6.03 ! [K: num] :
% 5.68/6.03 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.68/6.03 = ( numeral_numeral_int @ K ) ) ).
% 5.68/6.03
% 5.68/6.03 % int_of_integer_numeral
% 5.68/6.03 thf(fact_9383_plus__integer_Orep__eq,axiom,
% 5.68/6.03 ! [X: code_integer,Xa2: code_integer] :
% 5.68/6.03 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 5.68/6.03 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % plus_integer.rep_eq
% 5.68/6.03 thf(fact_9384_times__integer_Orep__eq,axiom,
% 5.68/6.03 ! [X: code_integer,Xa2: code_integer] :
% 5.68/6.03 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.68/6.03 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % times_integer.rep_eq
% 5.68/6.03 thf(fact_9385_less__eq__integer_Orep__eq,axiom,
% 5.68/6.03 ( ord_le3102999989581377725nteger
% 5.68/6.03 = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % less_eq_integer.rep_eq
% 5.68/6.03 thf(fact_9386_integer__less__eq__iff,axiom,
% 5.68/6.03 ( ord_le3102999989581377725nteger
% 5.68/6.03 = ( ^ [K3: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.68/6.03
% 5.68/6.03 % integer_less_eq_iff
% 5.68/6.03 thf(fact_9387_integer__of__num__def,axiom,
% 5.68/6.03 code_integer_of_num = numera6620942414471956472nteger ).
% 5.68/6.04
% 5.68/6.04 % integer_of_num_def
% 5.68/6.04 thf(fact_9388_integer__of__num__triv_I1_J,axiom,
% 5.68/6.04 ( ( code_integer_of_num @ one )
% 5.68/6.04 = one_one_Code_integer ) ).
% 5.68/6.04
% 5.68/6.04 % integer_of_num_triv(1)
% 5.68/6.04 thf(fact_9389_integer__of__num_I2_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.68/6.04 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % integer_of_num(2)
% 5.68/6.04 thf(fact_9390_integer__of__num__triv_I2_J,axiom,
% 5.68/6.04 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.68/6.04 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % integer_of_num_triv(2)
% 5.68/6.04 thf(fact_9391_divmod__integer__def,axiom,
% 5.68/6.04 ( code_divmod_integer
% 5.68/6.04 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L ) @ ( modulo364778990260209775nteger @ K3 @ L ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_integer_def
% 5.68/6.04 thf(fact_9392_num__of__integer__code,axiom,
% 5.68/6.04 ( code_num_of_integer
% 5.68/6.04 = ( ^ [K3: code_integer] :
% 5.68/6.04 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.68/6.04 @ ( produc7336495610019696514er_num
% 5.68/6.04 @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 5.68/6.04 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_integer_code
% 5.68/6.04 thf(fact_9393_nat__of__integer__code,axiom,
% 5.68/6.04 ( code_nat_of_integer
% 5.68/6.04 = ( ^ [K3: code_integer] :
% 5.68/6.04 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.68/6.04 @ ( produc1555791787009142072er_nat
% 5.68/6.04 @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 5.68/6.04 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat_of_integer_code
% 5.68/6.04 thf(fact_9394_bit__cut__integer__def,axiom,
% 5.68/6.04 ( code_bit_cut_integer
% 5.68/6.04 = ( ^ [K3: code_integer] :
% 5.68/6.04 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.68/6.04 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bit_cut_integer_def
% 5.68/6.04 thf(fact_9395_nat__of__integer__non__positive,axiom,
% 5.68/6.04 ! [K: code_integer] :
% 5.68/6.04 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.68/6.04 => ( ( code_nat_of_integer @ K )
% 5.68/6.04 = zero_zero_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat_of_integer_non_positive
% 5.68/6.04 thf(fact_9396_nat__of__integer__code__post_I3_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.68/6.04 = ( numeral_numeral_nat @ K ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat_of_integer_code_post(3)
% 5.68/6.04 thf(fact_9397_bit__cut__integer__code,axiom,
% 5.68/6.04 ( code_bit_cut_integer
% 5.68/6.04 = ( ^ [K3: code_integer] :
% 5.68/6.04 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.68/6.04 @ ( produc9125791028180074456eger_o
% 5.68/6.04 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.68/6.04 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bit_cut_integer_code
% 5.68/6.04 thf(fact_9398_csqrt_Osimps_I1_J,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( re @ ( csqrt @ Z ) )
% 5.68/6.04 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt.simps(1)
% 5.68/6.04 thf(fact_9399_card__Collect__less__nat,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 5.68/6.04 = N ) ).
% 5.68/6.04
% 5.68/6.04 % card_Collect_less_nat
% 5.68/6.04 thf(fact_9400_card__atMost,axiom,
% 5.68/6.04 ! [U: nat] :
% 5.68/6.04 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.68/6.04 = ( suc @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_atMost
% 5.68/6.04 thf(fact_9401_card__Collect__le__nat,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 5.68/6.04 = ( suc @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_Collect_le_nat
% 5.68/6.04 thf(fact_9402_card__atLeastAtMost,axiom,
% 5.68/6.04 ! [L2: nat,U: nat] :
% 5.68/6.04 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.68/6.04 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_atLeastAtMost
% 5.68/6.04 thf(fact_9403_complex__Re__numeral,axiom,
% 5.68/6.04 ! [V: num] :
% 5.68/6.04 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.68/6.04 = ( numeral_numeral_real @ V ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_Re_numeral
% 5.68/6.04 thf(fact_9404_card__atLeastAtMost__int,axiom,
% 5.68/6.04 ! [L2: int,U: int] :
% 5.68/6.04 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.68/6.04 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_atLeastAtMost_int
% 5.68/6.04 thf(fact_9405_Re__divide__numeral,axiom,
% 5.68/6.04 ! [Z: complex,W: num] :
% 5.68/6.04 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.04 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_divide_numeral
% 5.68/6.04 thf(fact_9406_complex__Re__le__cmod,axiom,
% 5.68/6.04 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_Re_le_cmod
% 5.68/6.04 thf(fact_9407_plus__complex_Osimps_I1_J,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( re @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.04 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % plus_complex.simps(1)
% 5.68/6.04 thf(fact_9408_scaleR__complex_Osimps_I1_J,axiom,
% 5.68/6.04 ! [R2: real,X: complex] :
% 5.68/6.04 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.68/6.04 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % scaleR_complex.simps(1)
% 5.68/6.04 thf(fact_9409_abs__Re__le__cmod,axiom,
% 5.68/6.04 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % abs_Re_le_cmod
% 5.68/6.04 thf(fact_9410_Re__csqrt,axiom,
% 5.68/6.04 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_csqrt
% 5.68/6.04 thf(fact_9411_card__less,axiom,
% 5.68/6.04 ! [M7: set_nat,I2: nat] :
% 5.68/6.04 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.68/6.04 => ( ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [K3: nat] :
% 5.68/6.04 ( ( member_nat @ K3 @ M7 )
% 5.68/6.04 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.68/6.04 != zero_zero_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_less
% 5.68/6.04 thf(fact_9412_card__less__Suc,axiom,
% 5.68/6.04 ! [M7: set_nat,I2: nat] :
% 5.68/6.04 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.68/6.04 => ( ( suc
% 5.68/6.04 @ ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [K3: nat] :
% 5.68/6.04 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.68/6.04 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.68/6.04 = ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [K3: nat] :
% 5.68/6.04 ( ( member_nat @ K3 @ M7 )
% 5.68/6.04 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_less_Suc
% 5.68/6.04 thf(fact_9413_card__less__Suc2,axiom,
% 5.68/6.04 ! [M7: set_nat,I2: nat] :
% 5.68/6.04 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.68/6.04 => ( ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [K3: nat] :
% 5.68/6.04 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.68/6.04 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.68/6.04 = ( finite_card_nat
% 5.68/6.04 @ ( collect_nat
% 5.68/6.04 @ ^ [K3: nat] :
% 5.68/6.04 ( ( member_nat @ K3 @ M7 )
% 5.68/6.04 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_less_Suc2
% 5.68/6.04 thf(fact_9414_subset__card__intvl__is__intvl,axiom,
% 5.68/6.04 ! [A2: set_nat,K: nat] :
% 5.68/6.04 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.68/6.04 => ( A2
% 5.68/6.04 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % subset_card_intvl_is_intvl
% 5.68/6.04 thf(fact_9415_divmod__abs__code_I5_J,axiom,
% 5.68/6.04 ! [J: code_integer] :
% 5.68/6.04 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.68/6.04 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_abs_code(5)
% 5.68/6.04 thf(fact_9416_divmod__abs__code_I6_J,axiom,
% 5.68/6.04 ! [J: code_integer] :
% 5.68/6.04 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.68/6.04 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_abs_code(6)
% 5.68/6.04 thf(fact_9417_subset__eq__atLeast0__lessThan__card,axiom,
% 5.68/6.04 ! [N5: set_nat,N: nat] :
% 5.68/6.04 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.68/6.04 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % subset_eq_atLeast0_lessThan_card
% 5.68/6.04 thf(fact_9418_card__sum__le__nat__sum,axiom,
% 5.68/6.04 ! [S3: set_nat] :
% 5.68/6.04 ( ord_less_eq_nat
% 5.68/6.04 @ ( groups3542108847815614940at_nat
% 5.68/6.04 @ ^ [X2: nat] : X2
% 5.68/6.04 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.68/6.04 @ ( groups3542108847815614940at_nat
% 5.68/6.04 @ ^ [X2: nat] : X2
% 5.68/6.04 @ S3 ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_sum_le_nat_sum
% 5.68/6.04 thf(fact_9419_card__nth__roots,axiom,
% 5.68/6.04 ! [C: complex,N: nat] :
% 5.68/6.04 ( ( C != zero_zero_complex )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( finite_card_complex
% 5.68/6.04 @ ( collect_complex
% 5.68/6.04 @ ^ [Z2: complex] :
% 5.68/6.04 ( ( power_power_complex @ Z2 @ N )
% 5.68/6.04 = C ) ) )
% 5.68/6.04 = N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_nth_roots
% 5.68/6.04 thf(fact_9420_card__roots__unity__eq,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( finite_card_complex
% 5.68/6.04 @ ( collect_complex
% 5.68/6.04 @ ^ [Z2: complex] :
% 5.68/6.04 ( ( power_power_complex @ Z2 @ N )
% 5.68/6.04 = one_one_complex ) ) )
% 5.68/6.04 = N ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_roots_unity_eq
% 5.68/6.04 thf(fact_9421_cmod__plus__Re__le__0__iff,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.68/6.04 = ( ( re @ Z )
% 5.68/6.04 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cmod_plus_Re_le_0_iff
% 5.68/6.04 thf(fact_9422_cos__n__Re__cis__pow__n,axiom,
% 5.68/6.04 ! [N: nat,A: real] :
% 5.68/6.04 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.68/6.04 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cos_n_Re_cis_pow_n
% 5.68/6.04 thf(fact_9423_divmod__abs__def,axiom,
% 5.68/6.04 ( code_divmod_abs
% 5.68/6.04 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_abs_def
% 5.68/6.04 thf(fact_9424_divmod__integer__code,axiom,
% 5.68/6.04 ( code_divmod_integer
% 5.68/6.04 = ( ^ [K3: code_integer,L: code_integer] :
% 5.68/6.04 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 5.68/6.04 @ ( produc6916734918728496179nteger
% 5.68/6.04 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S6 ) ) )
% 5.68/6.04 @ ( code_divmod_abs @ K3 @ L ) ) )
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.68/6.04 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 5.68/6.04 @ ( produc6916734918728496179nteger
% 5.68/6.04 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S6 ) ) )
% 5.68/6.04 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_integer_code
% 5.68/6.04 thf(fact_9425_csqrt_Ocode,axiom,
% 5.68/6.04 ( csqrt
% 5.68/6.04 = ( ^ [Z2: complex] :
% 5.68/6.04 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.04 @ ( times_times_real
% 5.68/6.04 @ ( if_real
% 5.68/6.04 @ ( ( im @ Z2 )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 @ one_one_real
% 5.68/6.04 @ ( sgn_sgn_real @ ( im @ Z2 ) ) )
% 5.68/6.04 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt.code
% 5.68/6.04 thf(fact_9426_csqrt_Osimps_I2_J,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( im @ ( csqrt @ Z ) )
% 5.68/6.04 = ( times_times_real
% 5.68/6.04 @ ( if_real
% 5.68/6.04 @ ( ( im @ Z )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 @ one_one_real
% 5.68/6.04 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.68/6.04 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt.simps(2)
% 5.68/6.04 thf(fact_9427_Im__power__real,axiom,
% 5.68/6.04 ! [X: complex,N: nat] :
% 5.68/6.04 ( ( ( im @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 => ( ( im @ ( power_power_complex @ X @ N ) )
% 5.68/6.04 = zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_power_real
% 5.68/6.04 thf(fact_9428_complex__Im__numeral,axiom,
% 5.68/6.04 ! [V: num] :
% 5.68/6.04 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.68/6.04 = zero_zero_real ) ).
% 5.68/6.04
% 5.68/6.04 % complex_Im_numeral
% 5.68/6.04 thf(fact_9429_Im__i__times,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.68/6.04 = ( re @ Z ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_i_times
% 5.68/6.04 thf(fact_9430_Re__power__real,axiom,
% 5.68/6.04 ! [X: complex,N: nat] :
% 5.68/6.04 ( ( ( im @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 => ( ( re @ ( power_power_complex @ X @ N ) )
% 5.68/6.04 = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_power_real
% 5.68/6.04 thf(fact_9431_Re__i__times,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.68/6.04 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_i_times
% 5.68/6.04 thf(fact_9432_Im__divide__numeral,axiom,
% 5.68/6.04 ! [Z: complex,W: num] :
% 5.68/6.04 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.04 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_divide_numeral
% 5.68/6.04 thf(fact_9433_csqrt__of__real__nonneg,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( ( im @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.68/6.04 => ( ( csqrt @ X )
% 5.68/6.04 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_of_real_nonneg
% 5.68/6.04 thf(fact_9434_csqrt__minus,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.68/6.04 | ( ( ( im @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.68/6.04 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.68/6.04 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_minus
% 5.68/6.04 thf(fact_9435_csqrt__of__real__nonpos,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( ( im @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.68/6.04 => ( ( csqrt @ X )
% 5.68/6.04 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_of_real_nonpos
% 5.68/6.04 thf(fact_9436_plus__complex_Osimps_I2_J,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( im @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.04 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % plus_complex.simps(2)
% 5.68/6.04 thf(fact_9437_scaleR__complex_Osimps_I2_J,axiom,
% 5.68/6.04 ! [R2: real,X: complex] :
% 5.68/6.04 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.68/6.04 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % scaleR_complex.simps(2)
% 5.68/6.04 thf(fact_9438_abs__Im__le__cmod,axiom,
% 5.68/6.04 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % abs_Im_le_cmod
% 5.68/6.04 thf(fact_9439_times__complex_Osimps_I2_J,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( im @ ( times_times_complex @ X @ Y2 ) )
% 5.68/6.04 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % times_complex.simps(2)
% 5.68/6.04 thf(fact_9440_cmod__Re__le__iff,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( ( im @ X )
% 5.68/6.04 = ( im @ Y2 ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 5.68/6.04 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cmod_Re_le_iff
% 5.68/6.04 thf(fact_9441_cmod__Im__le__iff,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( ( re @ X )
% 5.68/6.04 = ( re @ Y2 ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 5.68/6.04 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cmod_Im_le_iff
% 5.68/6.04 thf(fact_9442_times__complex_Osimps_I1_J,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( re @ ( times_times_complex @ X @ Y2 ) )
% 5.68/6.04 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % times_complex.simps(1)
% 5.68/6.04 thf(fact_9443_plus__complex_Ocode,axiom,
% 5.68/6.04 ( plus_plus_complex
% 5.68/6.04 = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % plus_complex.code
% 5.68/6.04 thf(fact_9444_scaleR__complex_Ocode,axiom,
% 5.68/6.04 ( real_V2046097035970521341omplex
% 5.68/6.04 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % scaleR_complex.code
% 5.68/6.04 thf(fact_9445_csqrt__principal,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.68/6.04 | ( ( ( re @ ( csqrt @ Z ) )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_principal
% 5.68/6.04 thf(fact_9446_cmod__le,axiom,
% 5.68/6.04 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cmod_le
% 5.68/6.04 thf(fact_9447_sin__n__Im__cis__pow__n,axiom,
% 5.68/6.04 ! [N: nat,A: real] :
% 5.68/6.04 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.68/6.04 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sin_n_Im_cis_pow_n
% 5.68/6.04 thf(fact_9448_Re__exp,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( re @ ( exp_complex @ Z ) )
% 5.68/6.04 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_exp
% 5.68/6.04 thf(fact_9449_Im__exp,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( im @ ( exp_complex @ Z ) )
% 5.68/6.04 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_exp
% 5.68/6.04 thf(fact_9450_complex__eq,axiom,
% 5.68/6.04 ! [A: complex] :
% 5.68/6.04 ( A
% 5.68/6.04 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_eq
% 5.68/6.04 thf(fact_9451_times__complex_Ocode,axiom,
% 5.68/6.04 ( times_times_complex
% 5.68/6.04 = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % times_complex.code
% 5.68/6.04 thf(fact_9452_exp__eq__polar,axiom,
% 5.68/6.04 ( exp_complex
% 5.68/6.04 = ( ^ [Z2: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z2 ) ) ) @ ( cis @ ( im @ Z2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % exp_eq_polar
% 5.68/6.04 thf(fact_9453_cmod__power2,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.04 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cmod_power2
% 5.68/6.04 thf(fact_9454_Im__power2,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_power2
% 5.68/6.04 thf(fact_9455_Re__power2,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_power2
% 5.68/6.04 thf(fact_9456_complex__eq__0,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( Z = zero_zero_complex )
% 5.68/6.04 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_eq_0
% 5.68/6.04 thf(fact_9457_norm__complex__def,axiom,
% 5.68/6.04 ( real_V1022390504157884413omplex
% 5.68/6.04 = ( ^ [Z2: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % norm_complex_def
% 5.68/6.04 thf(fact_9458_inverse__complex_Osimps_I1_J,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % inverse_complex.simps(1)
% 5.68/6.04 thf(fact_9459_complex__neq__0,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( Z != zero_zero_complex )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_neq_0
% 5.68/6.04 thf(fact_9460_Re__divide,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( re @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 5.68/6.04 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_divide
% 5.68/6.04 thf(fact_9461_csqrt__unique,axiom,
% 5.68/6.04 ! [W: complex,Z: complex] :
% 5.68/6.04 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.68/6.04 = Z )
% 5.68/6.04 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.68/6.04 | ( ( ( re @ W )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.68/6.04 => ( ( csqrt @ Z )
% 5.68/6.04 = W ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_unique
% 5.68/6.04 thf(fact_9462_csqrt__square,axiom,
% 5.68/6.04 ! [B: complex] :
% 5.68/6.04 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.68/6.04 | ( ( ( re @ B )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.68/6.04 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = B ) ) ).
% 5.68/6.04
% 5.68/6.04 % csqrt_square
% 5.68/6.04 thf(fact_9463_inverse__complex_Osimps_I2_J,axiom,
% 5.68/6.04 ! [X: complex] :
% 5.68/6.04 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % inverse_complex.simps(2)
% 5.68/6.04 thf(fact_9464_Im__divide,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( im @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 5.68/6.04 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_divide
% 5.68/6.04 thf(fact_9465_complex__abs__le__norm,axiom,
% 5.68/6.04 ! [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 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_abs_le_norm
% 5.68/6.04 thf(fact_9466_complex__unit__circle,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( Z != zero_zero_complex )
% 5.68/6.04 => ( ( 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 ) ) ) )
% 5.68/6.04 = one_one_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_unit_circle
% 5.68/6.04 thf(fact_9467_inverse__complex_Ocode,axiom,
% 5.68/6.04 ( invers8013647133539491842omplex
% 5.68/6.04 = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % inverse_complex.code
% 5.68/6.04 thf(fact_9468_Complex__divide,axiom,
% 5.68/6.04 ( divide1717551699836669952omplex
% 5.68/6.04 = ( ^ [X2: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Complex_divide
% 5.68/6.04 thf(fact_9469_Im__Reals__divide,axiom,
% 5.68/6.04 ! [R2: complex,Z: complex] :
% 5.68/6.04 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.68/6.04 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_Reals_divide
% 5.68/6.04 thf(fact_9470_imaginary__eq__real__iff,axiom,
% 5.68/6.04 ! [Y2: complex,X: complex] :
% 5.68/6.04 ( ( member_complex @ Y2 @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( ( times_times_complex @ imaginary_unit @ Y2 )
% 5.68/6.04 = X )
% 5.68/6.04 = ( ( X = zero_zero_complex )
% 5.68/6.04 & ( Y2 = zero_zero_complex ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % imaginary_eq_real_iff
% 5.68/6.04 thf(fact_9471_real__eq__imaginary__iff,axiom,
% 5.68/6.04 ! [Y2: complex,X: complex] :
% 5.68/6.04 ( ( member_complex @ Y2 @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( X
% 5.68/6.04 = ( times_times_complex @ imaginary_unit @ Y2 ) )
% 5.68/6.04 = ( ( X = zero_zero_complex )
% 5.68/6.04 & ( Y2 = zero_zero_complex ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_eq_imaginary_iff
% 5.68/6.04 thf(fact_9472_Re__Reals__divide,axiom,
% 5.68/6.04 ! [R2: complex,Z: complex] :
% 5.68/6.04 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.68/6.04 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.68/6.04 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_Reals_divide
% 5.68/6.04 thf(fact_9473_complex__mult__cnj,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_mult_cnj
% 5.68/6.04 thf(fact_9474_cnj__add__mult__eq__Re,axiom,
% 5.68/6.04 ! [Z: complex,W: complex] :
% 5.68/6.04 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.68/6.04 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % cnj_add_mult_eq_Re
% 5.68/6.04 thf(fact_9475_complex__div__cnj,axiom,
% 5.68/6.04 ( divide1717551699836669952omplex
% 5.68/6.04 = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_div_cnj
% 5.68/6.04 thf(fact_9476_complex__cnj__mult,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( cnj @ ( times_times_complex @ X @ Y2 ) )
% 5.68/6.04 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_cnj_mult
% 5.68/6.04 thf(fact_9477_complex__cnj__power,axiom,
% 5.68/6.04 ! [X: complex,N: nat] :
% 5.68/6.04 ( ( cnj @ ( power_power_complex @ X @ N ) )
% 5.68/6.04 = ( power_power_complex @ ( cnj @ X ) @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_cnj_power
% 5.68/6.04 thf(fact_9478_complex__cnj__add,axiom,
% 5.68/6.04 ! [X: complex,Y2: complex] :
% 5.68/6.04 ( ( cnj @ ( plus_plus_complex @ X @ Y2 ) )
% 5.68/6.04 = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_cnj_add
% 5.68/6.04 thf(fact_9479_complex__cnj__numeral,axiom,
% 5.68/6.04 ! [W: num] :
% 5.68/6.04 ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 5.68/6.04 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_cnj_numeral
% 5.68/6.04 thf(fact_9480_complex__cnj__neg__numeral,axiom,
% 5.68/6.04 ! [W: num] :
% 5.68/6.04 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.68/6.04 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_cnj_neg_numeral
% 5.68/6.04 thf(fact_9481_complex__In__mult__cnj__zero,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.68/6.04 = zero_zero_real ) ).
% 5.68/6.04
% 5.68/6.04 % complex_In_mult_cnj_zero
% 5.68/6.04 thf(fact_9482_Re__complex__div__eq__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.68/6.04 = zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_complex_div_eq_0
% 5.68/6.04 thf(fact_9483_Im__complex__div__eq__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.68/6.04 = zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_complex_div_eq_0
% 5.68/6.04 thf(fact_9484_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.68/6.04 ( real_V1022390504157884413omplex
% 5.68/6.04 = ( ^ [Z2: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z2 @ ( cnj @ Z2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_mod_sqrt_Re_mult_cnj
% 5.68/6.04 thf(fact_9485_Re__complex__div__gt__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_complex_div_gt_0
% 5.68/6.04 thf(fact_9486_Re__complex__div__lt__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_complex_div_lt_0
% 5.68/6.04 thf(fact_9487_Re__complex__div__le__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_complex_div_le_0
% 5.68/6.04 thf(fact_9488_Re__complex__div__ge__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Re_complex_div_ge_0
% 5.68/6.04 thf(fact_9489_Im__complex__div__gt__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_complex_div_gt_0
% 5.68/6.04 thf(fact_9490_Im__complex__div__lt__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_complex_div_lt_0
% 5.68/6.04 thf(fact_9491_Im__complex__div__le__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_complex_div_le_0
% 5.68/6.04 thf(fact_9492_Im__complex__div__ge__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Im_complex_div_ge_0
% 5.68/6.04 thf(fact_9493_complex__mod__mult__cnj,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.68/6.04 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_mod_mult_cnj
% 5.68/6.04 thf(fact_9494_complex__div__gt__0,axiom,
% 5.68/6.04 ! [A: complex,B: complex] :
% 5.68/6.04 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.68/6.04 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.68/6.04 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_div_gt_0
% 5.68/6.04 thf(fact_9495_complex__norm__square,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_norm_square
% 5.68/6.04 thf(fact_9496_complex__add__cnj,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.68/6.04 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_add_cnj
% 5.68/6.04 thf(fact_9497_complex__diff__cnj,axiom,
% 5.68/6.04 ! [Z: complex] :
% 5.68/6.04 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.68/6.04 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.68/6.04
% 5.68/6.04 % complex_diff_cnj
% 5.68/6.04 thf(fact_9498_nat_Odisc__eq__case_I2_J,axiom,
% 5.68/6.04 ! [Nat: nat] :
% 5.68/6.04 ( ( Nat != zero_zero_nat )
% 5.68/6.04 = ( case_nat_o @ $false
% 5.68/6.04 @ ^ [Uu2: nat] : $true
% 5.68/6.04 @ Nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat.disc_eq_case(2)
% 5.68/6.04 thf(fact_9499_nat_Odisc__eq__case_I1_J,axiom,
% 5.68/6.04 ! [Nat: nat] :
% 5.68/6.04 ( ( Nat = zero_zero_nat )
% 5.68/6.04 = ( case_nat_o @ $true
% 5.68/6.04 @ ^ [Uu2: nat] : $false
% 5.68/6.04 @ Nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat.disc_eq_case(1)
% 5.68/6.04 thf(fact_9500_less__eq__nat_Osimps_I2_J,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.68/6.04 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_eq_nat.simps(2)
% 5.68/6.04 thf(fact_9501_max__Suc1,axiom,
% 5.68/6.04 ! [N: nat,M: nat] :
% 5.68/6.04 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.68/6.04 = ( case_nat_nat @ ( suc @ N )
% 5.68/6.04 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N @ M3 ) )
% 5.68/6.04 @ M ) ) ).
% 5.68/6.04
% 5.68/6.04 % max_Suc1
% 5.68/6.04 thf(fact_9502_max__Suc2,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.68/6.04 = ( case_nat_nat @ ( suc @ N )
% 5.68/6.04 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N ) )
% 5.68/6.04 @ M ) ) ).
% 5.68/6.04
% 5.68/6.04 % max_Suc2
% 5.68/6.04 thf(fact_9503_diff__Suc,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.68/6.04 = ( case_nat_nat @ zero_zero_nat
% 5.68/6.04 @ ^ [K3: nat] : K3
% 5.68/6.04 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % diff_Suc
% 5.68/6.04 thf(fact_9504_pred__def,axiom,
% 5.68/6.04 ( pred
% 5.68/6.04 = ( case_nat_nat @ zero_zero_nat
% 5.68/6.04 @ ^ [X24: nat] : X24 ) ) ).
% 5.68/6.04
% 5.68/6.04 % pred_def
% 5.68/6.04 thf(fact_9505_floor__real__def,axiom,
% 5.68/6.04 ( archim6058952711729229775r_real
% 5.68/6.04 = ( ^ [X2: real] :
% 5.68/6.04 ( the_int
% 5.68/6.04 @ ^ [Z2: int] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X2 )
% 5.68/6.04 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % floor_real_def
% 5.68/6.04 thf(fact_9506_floor__rat__def,axiom,
% 5.68/6.04 ( archim3151403230148437115or_rat
% 5.68/6.04 = ( ^ [X2: rat] :
% 5.68/6.04 ( the_int
% 5.68/6.04 @ ^ [Z2: int] :
% 5.68/6.04 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 5.68/6.04 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % floor_rat_def
% 5.68/6.04 thf(fact_9507_bezw__0,axiom,
% 5.68/6.04 ! [X: nat] :
% 5.68/6.04 ( ( bezw @ X @ zero_zero_nat )
% 5.68/6.04 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw_0
% 5.68/6.04 thf(fact_9508_prod__decode__aux_Osimps,axiom,
% 5.68/6.04 ( nat_prod_decode_aux
% 5.68/6.04 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % prod_decode_aux.simps
% 5.68/6.04 thf(fact_9509_less__eq__rat__def,axiom,
% 5.68/6.04 ( ord_less_eq_rat
% 5.68/6.04 = ( ^ [X2: rat,Y: rat] :
% 5.68/6.04 ( ( ord_less_rat @ X2 @ Y )
% 5.68/6.04 | ( X2 = Y ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_eq_rat_def
% 5.68/6.04 thf(fact_9510_obtain__pos__sum,axiom,
% 5.68/6.04 ! [R2: rat] :
% 5.68/6.04 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.68/6.04 => ~ ! [S: rat] :
% 5.68/6.04 ( ( ord_less_rat @ zero_zero_rat @ S )
% 5.68/6.04 => ! [T4: rat] :
% 5.68/6.04 ( ( ord_less_rat @ zero_zero_rat @ T4 )
% 5.68/6.04 => ( R2
% 5.68/6.04 != ( plus_plus_rat @ S @ T4 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % obtain_pos_sum
% 5.68/6.04 thf(fact_9511_prod__decode__aux_Oelims,axiom,
% 5.68/6.04 ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.68/6.04 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % prod_decode_aux.elims
% 5.68/6.04 thf(fact_9512_prod__decode__aux_Opelims,axiom,
% 5.68/6.04 ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 5.68/6.04 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.68/6.04 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.68/6.04 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % prod_decode_aux.pelims
% 5.68/6.04 thf(fact_9513_rat__inverse__code,axiom,
% 5.68/6.04 ! [P4: rat] :
% 5.68/6.04 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A4 ) @ B3 ) @ ( abs_abs_int @ A4 ) ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_inverse_code
% 5.68/6.04 thf(fact_9514_normalize__negative,axiom,
% 5.68/6.04 ! [Q2: int,P4: int] :
% 5.68/6.04 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.68/6.04 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_negative
% 5.68/6.04 thf(fact_9515_rat__one__code,axiom,
% 5.68/6.04 ( ( quotient_of @ one_one_rat )
% 5.68/6.04 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_one_code
% 5.68/6.04 thf(fact_9516_quotient__of__number_I3_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.68/6.04 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_number(3)
% 5.68/6.04 thf(fact_9517_quotient__of__number_I4_J,axiom,
% 5.68/6.04 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.68/6.04 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_number(4)
% 5.68/6.04 thf(fact_9518_normalize__denom__zero,axiom,
% 5.68/6.04 ! [P4: int] :
% 5.68/6.04 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 5.68/6.04 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_denom_zero
% 5.68/6.04 thf(fact_9519_quotient__of__number_I5_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.68/6.04 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_number(5)
% 5.68/6.04 thf(fact_9520_rat__zero__code,axiom,
% 5.68/6.04 ( ( quotient_of @ zero_zero_rat )
% 5.68/6.04 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_zero_code
% 5.68/6.04 thf(fact_9521_divide__rat__def,axiom,
% 5.68/6.04 ( divide_divide_rat
% 5.68/6.04 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divide_rat_def
% 5.68/6.04 thf(fact_9522_diff__rat__def,axiom,
% 5.68/6.04 ( minus_minus_rat
% 5.68/6.04 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % diff_rat_def
% 5.68/6.04 thf(fact_9523_rat__divide__code,axiom,
% 5.68/6.04 ! [P4: rat,Q2: rat] :
% 5.68/6.04 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q2 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B3 ) ) )
% 5.68/6.04 @ ( quotient_of @ Q2 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_divide_code
% 5.68/6.04 thf(fact_9524_rat__times__code,axiom,
% 5.68/6.04 ! [P4: rat,Q2: rat] :
% 5.68/6.04 ( ( quotient_of @ ( times_times_rat @ P4 @ Q2 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B3 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.68/6.04 @ ( quotient_of @ Q2 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_times_code
% 5.68/6.04 thf(fact_9525_quotient__of__div,axiom,
% 5.68/6.04 ! [R2: rat,N: int,D: int] :
% 5.68/6.04 ( ( ( quotient_of @ R2 )
% 5.68/6.04 = ( product_Pair_int_int @ N @ D ) )
% 5.68/6.04 => ( R2
% 5.68/6.04 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_div
% 5.68/6.04 thf(fact_9526_rat__plus__code,axiom,
% 5.68/6.04 ! [P4: rat,Q2: rat] :
% 5.68/6.04 ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q2 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B3 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.68/6.04 @ ( quotient_of @ Q2 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_plus_code
% 5.68/6.04 thf(fact_9527_rat__minus__code,axiom,
% 5.68/6.04 ! [P4: rat,Q2: rat] :
% 5.68/6.04 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q2 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B3 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.68/6.04 @ ( quotient_of @ Q2 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_minus_code
% 5.68/6.04 thf(fact_9528_quotient__of__denom__pos,axiom,
% 5.68/6.04 ! [R2: rat,P4: int,Q2: int] :
% 5.68/6.04 ( ( ( quotient_of @ R2 )
% 5.68/6.04 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_denom_pos
% 5.68/6.04 thf(fact_9529_rat__uminus__code,axiom,
% 5.68/6.04 ! [P4: rat] :
% 5.68/6.04 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A4 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_uminus_code
% 5.68/6.04 thf(fact_9530_rat__abs__code,axiom,
% 5.68/6.04 ! [P4: rat] :
% 5.68/6.04 ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 5.68/6.04 = ( produc4245557441103728435nt_int
% 5.68/6.04 @ ^ [A4: int] : ( product_Pair_int_int @ ( abs_abs_int @ A4 ) )
% 5.68/6.04 @ ( quotient_of @ P4 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_abs_code
% 5.68/6.04 thf(fact_9531_normalize__denom__pos,axiom,
% 5.68/6.04 ! [R2: product_prod_int_int,P4: int,Q2: int] :
% 5.68/6.04 ( ( ( normalize @ R2 )
% 5.68/6.04 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_denom_pos
% 5.68/6.04 thf(fact_9532_normalize__crossproduct,axiom,
% 5.68/6.04 ! [Q2: int,S2: int,P4: int,R2: int] :
% 5.68/6.04 ( ( Q2 != zero_zero_int )
% 5.68/6.04 => ( ( S2 != zero_zero_int )
% 5.68/6.04 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.68/6.04 => ( ( times_times_int @ P4 @ S2 )
% 5.68/6.04 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_crossproduct
% 5.68/6.04 thf(fact_9533_rat__less__code,axiom,
% 5.68/6.04 ( ord_less_rat
% 5.68/6.04 = ( ^ [P5: rat,Q4: rat] :
% 5.68/6.04 ( produc4947309494688390418_int_o
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4947309494688390418_int_o
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( ord_less_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B3 ) )
% 5.68/6.04 @ ( quotient_of @ Q4 ) )
% 5.68/6.04 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_less_code
% 5.68/6.04 thf(fact_9534_rat__less__eq__code,axiom,
% 5.68/6.04 ( ord_less_eq_rat
% 5.68/6.04 = ( ^ [P5: rat,Q4: rat] :
% 5.68/6.04 ( produc4947309494688390418_int_o
% 5.68/6.04 @ ^ [A4: int,C3: int] :
% 5.68/6.04 ( produc4947309494688390418_int_o
% 5.68/6.04 @ ^ [B3: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B3 ) )
% 5.68/6.04 @ ( quotient_of @ Q4 ) )
% 5.68/6.04 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_less_eq_code
% 5.68/6.04 thf(fact_9535_quotient__of__int,axiom,
% 5.68/6.04 ! [A: int] :
% 5.68/6.04 ( ( quotient_of @ ( of_int @ A ) )
% 5.68/6.04 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_int
% 5.68/6.04 thf(fact_9536_drop__bit__numeral__minus__bit1,axiom,
% 5.68/6.04 ! [L2: num,K: num] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/6.04 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_numeral_minus_bit1
% 5.68/6.04 thf(fact_9537_Suc__0__div__numeral,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.68/6.04 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Suc_0_div_numeral
% 5.68/6.04 thf(fact_9538_drop__bit__nonnegative__int__iff,axiom,
% 5.68/6.04 ! [N: nat,K: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.68/6.04 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_nonnegative_int_iff
% 5.68/6.04 thf(fact_9539_drop__bit__negative__int__iff,axiom,
% 5.68/6.04 ! [N: nat,K: int] :
% 5.68/6.04 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.68/6.04 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_negative_int_iff
% 5.68/6.04 thf(fact_9540_drop__bit__minus__one,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.68/6.04 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_minus_one
% 5.68/6.04 thf(fact_9541_fst__divmod__nat,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.68/6.04 = ( divide_divide_nat @ M @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % fst_divmod_nat
% 5.68/6.04 thf(fact_9542_drop__bit__Suc__minus__bit0,axiom,
% 5.68/6.04 ! [N: nat,K: num] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/6.04 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_Suc_minus_bit0
% 5.68/6.04 thf(fact_9543_drop__bit__numeral__minus__bit0,axiom,
% 5.68/6.04 ! [L2: num,K: num] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.68/6.04 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_numeral_minus_bit0
% 5.68/6.04 thf(fact_9544_drop__bit__Suc__minus__bit1,axiom,
% 5.68/6.04 ! [N: nat,K: num] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.68/6.04 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_Suc_minus_bit1
% 5.68/6.04 thf(fact_9545_drop__bit__push__bit__int,axiom,
% 5.68/6.04 ! [M: nat,N: nat,K: int] :
% 5.68/6.04 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.68/6.04 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_push_bit_int
% 5.68/6.04 thf(fact_9546_drop__bit__int__def,axiom,
% 5.68/6.04 ( bit_se8568078237143864401it_int
% 5.68/6.04 = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_int_def
% 5.68/6.04 thf(fact_9547_Frct__code__post_I5_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.68/6.04 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(5)
% 5.68/6.04 thf(fact_9548_Frct__code__post_I6_J,axiom,
% 5.68/6.04 ! [K: num,L2: num] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.68/6.04 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(6)
% 5.68/6.04 thf(fact_9549_Suc__0__mod__numeral,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.68/6.04 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Suc_0_mod_numeral
% 5.68/6.04 thf(fact_9550_drop__bit__of__Suc__0,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.68/6.04 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_of_Suc_0
% 5.68/6.04 thf(fact_9551_drop__bit__nat__eq,axiom,
% 5.68/6.04 ! [N: nat,K: int] :
% 5.68/6.04 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.68/6.04 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_nat_eq
% 5.68/6.04 thf(fact_9552_rat__sgn__code,axiom,
% 5.68/6.04 ! [P4: rat] :
% 5.68/6.04 ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 5.68/6.04 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_sgn_code
% 5.68/6.04 thf(fact_9553_drop__bit__nat__def,axiom,
% 5.68/6.04 ( bit_se8570568707652914677it_nat
% 5.68/6.04 = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % drop_bit_nat_def
% 5.68/6.04 thf(fact_9554_Frct__code__post_I1_J,axiom,
% 5.68/6.04 ! [A: int] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.68/6.04 = zero_zero_rat ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(1)
% 5.68/6.04 thf(fact_9555_Frct__code__post_I2_J,axiom,
% 5.68/6.04 ! [A: int] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.68/6.04 = zero_zero_rat ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(2)
% 5.68/6.04 thf(fact_9556_Frct__code__post_I8_J,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.68/6.04 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(8)
% 5.68/6.04 thf(fact_9557_Frct__code__post_I7_J,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.68/6.04 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(7)
% 5.68/6.04 thf(fact_9558_Frct__code__post_I3_J,axiom,
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.68/6.04 = one_one_rat ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(3)
% 5.68/6.04 thf(fact_9559_Frct__code__post_I4_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.68/6.04 = ( numeral_numeral_rat @ K ) ) ).
% 5.68/6.04
% 5.68/6.04 % Frct_code_post(4)
% 5.68/6.04 thf(fact_9560_bezw__non__0,axiom,
% 5.68/6.04 ! [Y2: nat,X: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 5.68/6.04 => ( ( bezw @ X @ Y2 )
% 5.68/6.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y2 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw_non_0
% 5.68/6.04 thf(fact_9561_bezw_Osimps,axiom,
% 5.68/6.04 ( bezw
% 5.68/6.04 = ( ^ [X2: nat,Y: nat] : ( if_Pro3027730157355071871nt_int @ ( Y = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw.simps
% 5.68/6.04 thf(fact_9562_bezw_Oelims,axiom,
% 5.68/6.04 ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.68/6.04 ( ( ( bezw @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( Xa2 = zero_zero_nat )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.68/6.04 & ( ( Xa2 != zero_zero_nat )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw.elims
% 5.68/6.04 thf(fact_9563_bezw_Opelims,axiom,
% 5.68/6.04 ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 5.68/6.04 ( ( ( bezw @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.68/6.04 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.68/6.04 & ( ( Xa2 != zero_zero_nat )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 5.68/6.04 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw.pelims
% 5.68/6.04 thf(fact_9564_minus__one__mod__numeral,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % minus_one_mod_numeral
% 5.68/6.04 thf(fact_9565_one__mod__minus__numeral,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % one_mod_minus_numeral
% 5.68/6.04 thf(fact_9566_minus__numeral__mod__numeral,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % minus_numeral_mod_numeral
% 5.68/6.04 thf(fact_9567_numeral__mod__minus__numeral,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % numeral_mod_minus_numeral
% 5.68/6.04 thf(fact_9568_normalize__def,axiom,
% 5.68/6.04 ( normalize
% 5.68/6.04 = ( ^ [P5: product_prod_int_int] :
% 5.68/6.04 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.68/6.04 @ ( if_Pro3027730157355071871nt_int
% 5.68/6.04 @ ( ( product_snd_int_int @ P5 )
% 5.68/6.04 = zero_zero_int )
% 5.68/6.04 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.04 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_def
% 5.68/6.04 thf(fact_9569_finite__enumerate,axiom,
% 5.68/6.04 ! [S3: set_nat] :
% 5.68/6.04 ( ( finite_finite_nat @ S3 )
% 5.68/6.04 => ? [R3: nat > nat] :
% 5.68/6.04 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.68/6.04 & ! [N7: nat] :
% 5.68/6.04 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S3 ) )
% 5.68/6.04 => ( member_nat @ ( R3 @ N7 ) @ S3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % finite_enumerate
% 5.68/6.04 thf(fact_9570_gcd__neg__numeral__2__int,axiom,
% 5.68/6.04 ! [X: int,N: num] :
% 5.68/6.04 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_neg_numeral_2_int
% 5.68/6.04 thf(fact_9571_gcd__neg__numeral__1__int,axiom,
% 5.68/6.04 ! [N: num,X: int] :
% 5.68/6.04 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 5.68/6.04 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_neg_numeral_1_int
% 5.68/6.04 thf(fact_9572_gcd__ge__0__int,axiom,
% 5.68/6.04 ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_ge_0_int
% 5.68/6.04 thf(fact_9573_bezout__int,axiom,
% 5.68/6.04 ! [X: int,Y2: int] :
% 5.68/6.04 ? [U3: int,V2: int] :
% 5.68/6.04 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y2 ) )
% 5.68/6.04 = ( gcd_gcd_int @ X @ Y2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezout_int
% 5.68/6.04 thf(fact_9574_gcd__mult__distrib__int,axiom,
% 5.68/6.04 ! [K: int,M: int,N: int] :
% 5.68/6.04 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.68/6.04 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_mult_distrib_int
% 5.68/6.04 thf(fact_9575_gcd__le2__int,axiom,
% 5.68/6.04 ! [B: int,A: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ B )
% 5.68/6.04 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_le2_int
% 5.68/6.04 thf(fact_9576_gcd__le1__int,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ A )
% 5.68/6.04 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_le1_int
% 5.68/6.04 thf(fact_9577_gcd__cases__int,axiom,
% 5.68/6.04 ! [X: int,Y2: int,P: int > $o] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.04 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.04 => ( P @ ( gcd_gcd_int @ X @ Y2 ) ) ) )
% 5.68/6.04 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.68/6.04 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 5.68/6.04 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y2 ) ) ) ) )
% 5.68/6.04 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.68/6.04 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 5.68/6.04 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y2 ) ) ) )
% 5.68/6.04 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.68/6.04 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 5.68/6.04 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y2 ) ) ) ) )
% 5.68/6.04 => ( P @ ( gcd_gcd_int @ X @ Y2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_cases_int
% 5.68/6.04 thf(fact_9578_gcd__unique__int,axiom,
% 5.68/6.04 ! [D: int,A: int,B: int] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.68/6.04 & ( dvd_dvd_int @ D @ A )
% 5.68/6.04 & ( dvd_dvd_int @ D @ B )
% 5.68/6.04 & ! [E3: int] :
% 5.68/6.04 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.68/6.04 & ( dvd_dvd_int @ E3 @ B ) )
% 5.68/6.04 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.68/6.04 = ( D
% 5.68/6.04 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_unique_int
% 5.68/6.04 thf(fact_9579_nat__descend__induct,axiom,
% 5.68/6.04 ! [N: nat,P: nat > $o,M: nat] :
% 5.68/6.04 ( ! [K2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ N @ K2 )
% 5.68/6.04 => ( P @ K2 ) )
% 5.68/6.04 => ( ! [K2: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ K2 @ N )
% 5.68/6.04 => ( ! [I: nat] :
% 5.68/6.04 ( ( ord_less_nat @ K2 @ I )
% 5.68/6.04 => ( P @ I ) )
% 5.68/6.04 => ( P @ K2 ) ) )
% 5.68/6.04 => ( P @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat_descend_induct
% 5.68/6.04 thf(fact_9580_gcd__Suc__0,axiom,
% 5.68/6.04 ! [M: nat] :
% 5.68/6.04 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.68/6.04 = ( suc @ zero_zero_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_Suc_0
% 5.68/6.04 thf(fact_9581_gcd__pos__nat,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.68/6.04 = ( ( M != zero_zero_nat )
% 5.68/6.04 | ( N != zero_zero_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_pos_nat
% 5.68/6.04 thf(fact_9582_gcd__mult__distrib__nat,axiom,
% 5.68/6.04 ! [K: nat,M: nat,N: nat] :
% 5.68/6.04 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.68/6.04 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_mult_distrib_nat
% 5.68/6.04 thf(fact_9583_gcd__le2__nat,axiom,
% 5.68/6.04 ! [B: nat,A: nat] :
% 5.68/6.04 ( ( B != zero_zero_nat )
% 5.68/6.04 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_le2_nat
% 5.68/6.04 thf(fact_9584_gcd__le1__nat,axiom,
% 5.68/6.04 ! [A: nat,B: nat] :
% 5.68/6.04 ( ( A != zero_zero_nat )
% 5.68/6.04 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_le1_nat
% 5.68/6.04 thf(fact_9585_gcd__diff2__nat,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.04 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.68/6.04 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_diff2_nat
% 5.68/6.04 thf(fact_9586_gcd__diff1__nat,axiom,
% 5.68/6.04 ! [N: nat,M: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ N @ M )
% 5.68/6.04 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.68/6.04 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_diff1_nat
% 5.68/6.04 thf(fact_9587_bezout__nat,axiom,
% 5.68/6.04 ! [A: nat,B: nat] :
% 5.68/6.04 ( ( A != zero_zero_nat )
% 5.68/6.04 => ? [X3: nat,Y3: nat] :
% 5.68/6.04 ( ( times_times_nat @ A @ X3 )
% 5.68/6.04 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezout_nat
% 5.68/6.04 thf(fact_9588_bezout__gcd__nat_H,axiom,
% 5.68/6.04 ! [B: nat,A: nat] :
% 5.68/6.04 ? [X3: nat,Y3: nat] :
% 5.68/6.04 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.68/6.04 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.68/6.04 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.68/6.04 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.68/6.04 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.68/6.04 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezout_gcd_nat'
% 5.68/6.04 thf(fact_9589_bezw__aux,axiom,
% 5.68/6.04 ! [X: nat,Y2: nat] :
% 5.68/6.04 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y2 ) )
% 5.68/6.04 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y2 ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y2 ) ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bezw_aux
% 5.68/6.04 thf(fact_9590_gcd__nat_Opelims,axiom,
% 5.68/6.04 ! [X: nat,Xa2: nat,Y2: nat] :
% 5.68/6.04 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.68/6.04 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.68/6.04 => ( Y2 = X ) )
% 5.68/6.04 & ( ( Xa2 != zero_zero_nat )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.68/6.04 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % gcd_nat.pelims
% 5.68/6.04 thf(fact_9591_root__powr__inverse,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( root @ N @ X )
% 5.68/6.04 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % root_powr_inverse
% 5.68/6.04 thf(fact_9592_card__greaterThanLessThan__int,axiom,
% 5.68/6.04 ! [L2: int,U: int] :
% 5.68/6.04 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.68/6.04 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_greaterThanLessThan_int
% 5.68/6.04 thf(fact_9593_real__root__zero,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( root @ N @ zero_zero_real )
% 5.68/6.04 = zero_zero_real ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_zero
% 5.68/6.04 thf(fact_9594_real__root__Suc__0,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.68/6.04 = X ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_Suc_0
% 5.68/6.04 thf(fact_9595_root__0,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( root @ zero_zero_nat @ X )
% 5.68/6.04 = zero_zero_real ) ).
% 5.68/6.04
% 5.68/6.04 % root_0
% 5.68/6.04 thf(fact_9596_real__root__eq__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( root @ N @ X )
% 5.68/6.04 = ( root @ N @ Y2 ) )
% 5.68/6.04 = ( X = Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_eq_iff
% 5.68/6.04 thf(fact_9597_real__root__eq__0__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( root @ N @ X )
% 5.68/6.04 = zero_zero_real )
% 5.68/6.04 = ( X = zero_zero_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_eq_0_iff
% 5.68/6.04 thf(fact_9598_real__root__less__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_real @ X @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_less_iff
% 5.68/6.04 thf(fact_9599_real__root__le__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_le_iff
% 5.68/6.04 thf(fact_9600_real__root__eq__1__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( root @ N @ X )
% 5.68/6.04 = one_one_real )
% 5.68/6.04 = ( X = one_one_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_eq_1_iff
% 5.68/6.04 thf(fact_9601_real__root__one,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( root @ N @ one_one_real )
% 5.68/6.04 = one_one_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_one
% 5.68/6.04 thf(fact_9602_real__root__gt__0__iff,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_gt_0_iff
% 5.68/6.04 thf(fact_9603_real__root__lt__0__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_lt_0_iff
% 5.68/6.04 thf(fact_9604_real__root__le__0__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.68/6.04 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_le_0_iff
% 5.68/6.04 thf(fact_9605_real__root__ge__0__iff,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_ge_0_iff
% 5.68/6.04 thf(fact_9606_real__root__gt__1__iff,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_gt_1_iff
% 5.68/6.04 thf(fact_9607_real__root__lt__1__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.68/6.04 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_lt_1_iff
% 5.68/6.04 thf(fact_9608_real__root__le__1__iff,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.68/6.04 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_le_1_iff
% 5.68/6.04 thf(fact_9609_real__root__ge__1__iff,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 5.68/6.04 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_ge_1_iff
% 5.68/6.04 thf(fact_9610_real__root__pow__pos2,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.68/6.04 = X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_pow_pos2
% 5.68/6.04 thf(fact_9611_real__root__minus,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 5.68/6.04 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_minus
% 5.68/6.04 thf(fact_9612_real__root__divide,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( root @ N @ ( divide_divide_real @ X @ Y2 ) )
% 5.68/6.04 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_divide
% 5.68/6.04 thf(fact_9613_real__root__mult__exp,axiom,
% 5.68/6.04 ! [M: nat,N: nat,X: real] :
% 5.68/6.04 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 5.68/6.04 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_mult_exp
% 5.68/6.04 thf(fact_9614_real__root__mult,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( root @ N @ ( times_times_real @ X @ Y2 ) )
% 5.68/6.04 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_mult
% 5.68/6.04 thf(fact_9615_real__root__commute,axiom,
% 5.68/6.04 ! [M: nat,N: nat,X: real] :
% 5.68/6.04 ( ( root @ M @ ( root @ N @ X ) )
% 5.68/6.04 = ( root @ N @ ( root @ M @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_commute
% 5.68/6.04 thf(fact_9616_real__root__inverse,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 5.68/6.04 = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_inverse
% 5.68/6.04 thf(fact_9617_real__root__pos__pos__le,axiom,
% 5.68/6.04 ! [X: real,N: nat] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_pos_pos_le
% 5.68/6.04 thf(fact_9618_real__root__less__mono,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ X @ Y2 )
% 5.68/6.04 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_less_mono
% 5.68/6.04 thf(fact_9619_real__root__le__mono,axiom,
% 5.68/6.04 ! [N: nat,X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ X @ Y2 )
% 5.68/6.04 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_le_mono
% 5.68/6.04 thf(fact_9620_real__root__power,axiom,
% 5.68/6.04 ! [N: nat,X: real,K: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 5.68/6.04 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_power
% 5.68/6.04 thf(fact_9621_real__root__abs,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.68/6.04 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_abs
% 5.68/6.04 thf(fact_9622_sgn__root,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.68/6.04 = ( sgn_sgn_real @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sgn_root
% 5.68/6.04 thf(fact_9623_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.68/6.04 ! [L2: int,U: int] :
% 5.68/6.04 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.68/6.04 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.68/6.04 thf(fact_9624_real__root__gt__zero,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_gt_zero
% 5.68/6.04 thf(fact_9625_real__root__strict__decreasing,axiom,
% 5.68/6.04 ! [N: nat,N5: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_nat @ N @ N5 )
% 5.68/6.04 => ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.04 => ( ord_less_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_strict_decreasing
% 5.68/6.04 thf(fact_9626_sqrt__def,axiom,
% 5.68/6.04 ( sqrt
% 5.68/6.04 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sqrt_def
% 5.68/6.04 thf(fact_9627_root__abs__power,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 5.68/6.04 = ( abs_abs_real @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % root_abs_power
% 5.68/6.04 thf(fact_9628_real__root__pos__pos,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_pos_pos
% 5.68/6.04 thf(fact_9629_real__root__strict__increasing,axiom,
% 5.68/6.04 ! [N: nat,N5: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_nat @ N @ N5 )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( ord_less_real @ X @ one_one_real )
% 5.68/6.04 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_strict_increasing
% 5.68/6.04 thf(fact_9630_real__root__decreasing,axiom,
% 5.68/6.04 ! [N: nat,N5: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.68/6.04 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.68/6.04 => ( ord_less_eq_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_decreasing
% 5.68/6.04 thf(fact_9631_real__root__pow__pos,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.68/6.04 = X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_pow_pos
% 5.68/6.04 thf(fact_9632_real__root__power__cancel,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.68/6.04 = X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_power_cancel
% 5.68/6.04 thf(fact_9633_real__root__pos__unique,axiom,
% 5.68/6.04 ! [N: nat,Y2: real,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.68/6.04 => ( ( ( power_power_real @ Y2 @ N )
% 5.68/6.04 = X )
% 5.68/6.04 => ( ( root @ N @ X )
% 5.68/6.04 = Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_pos_unique
% 5.68/6.04 thf(fact_9634_odd__real__root__pow,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.68/6.04 = X ) ) ).
% 5.68/6.04
% 5.68/6.04 % odd_real_root_pow
% 5.68/6.04 thf(fact_9635_odd__real__root__unique,axiom,
% 5.68/6.04 ! [N: nat,Y2: real,X: real] :
% 5.68/6.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( ( power_power_real @ Y2 @ N )
% 5.68/6.04 = X )
% 5.68/6.04 => ( ( root @ N @ X )
% 5.68/6.04 = Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % odd_real_root_unique
% 5.68/6.04 thf(fact_9636_odd__real__root__power__cancel,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.68/6.04 = X ) ) ).
% 5.68/6.04
% 5.68/6.04 % odd_real_root_power_cancel
% 5.68/6.04 thf(fact_9637_real__root__increasing,axiom,
% 5.68/6.04 ! [N: nat,N5: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.68/6.04 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.04 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_root_increasing
% 5.68/6.04 thf(fact_9638_sgn__power__root,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.68/6.04 = X ) ) ).
% 5.68/6.04
% 5.68/6.04 % sgn_power_root
% 5.68/6.04 thf(fact_9639_root__sgn__power,axiom,
% 5.68/6.04 ! [N: nat,Y2: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 5.68/6.04 = Y2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % root_sgn_power
% 5.68/6.04 thf(fact_9640_ln__root,axiom,
% 5.68/6.04 ! [N: nat,B: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.04 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.68/6.04 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % ln_root
% 5.68/6.04 thf(fact_9641_log__root,axiom,
% 5.68/6.04 ! [N: nat,A: real,B: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.68/6.04 => ( ( log @ B @ ( root @ N @ A ) )
% 5.68/6.04 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % log_root
% 5.68/6.04 thf(fact_9642_log__base__root,axiom,
% 5.68/6.04 ! [N: nat,B: real,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.68/6.04 => ( ( log @ ( root @ N @ B ) @ X )
% 5.68/6.04 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % log_base_root
% 5.68/6.04 thf(fact_9643_split__root,axiom,
% 5.68/6.04 ! [P: real > $o,N: nat,X: real] :
% 5.68/6.04 ( ( P @ ( root @ N @ X ) )
% 5.68/6.04 = ( ( ( N = zero_zero_nat )
% 5.68/6.04 => ( P @ zero_zero_real ) )
% 5.68/6.04 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ! [Y: real] :
% 5.68/6.04 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.68/6.04 = X )
% 5.68/6.04 => ( P @ Y ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % split_root
% 5.68/6.04 thf(fact_9644_bij__betw__nth__root__unity,axiom,
% 5.68/6.04 ! [C: complex,N: nat] :
% 5.68/6.04 ( ( C != zero_zero_complex )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.68/6.04 @ ( collect_complex
% 5.68/6.04 @ ^ [Z2: complex] :
% 5.68/6.04 ( ( power_power_complex @ Z2 @ N )
% 5.68/6.04 = one_one_complex ) )
% 5.68/6.04 @ ( collect_complex
% 5.68/6.04 @ ^ [Z2: complex] :
% 5.68/6.04 ( ( power_power_complex @ Z2 @ N )
% 5.68/6.04 = C ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % bij_betw_nth_root_unity
% 5.68/6.04 thf(fact_9645_xor__minus__numerals_I1_J,axiom,
% 5.68/6.04 ! [N: num,K: int] :
% 5.68/6.04 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.68/6.04 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_minus_numerals(1)
% 5.68/6.04 thf(fact_9646_xor__minus__numerals_I2_J,axiom,
% 5.68/6.04 ! [K: int,N: num] :
% 5.68/6.04 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_minus_numerals(2)
% 5.68/6.04 thf(fact_9647_card__greaterThanLessThan,axiom,
% 5.68/6.04 ! [L2: nat,U: nat] :
% 5.68/6.04 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.68/6.04 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_greaterThanLessThan
% 5.68/6.04 thf(fact_9648_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.68/6.04 ! [L2: nat,U: nat] :
% 5.68/6.04 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.68/6.04 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastSucLessThan_greaterThanLessThan
% 5.68/6.04 thf(fact_9649_sub__BitM__One__eq,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.68/6.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sub_BitM_One_eq
% 5.68/6.04 thf(fact_9650_Suc__funpow,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( compow_nat_nat @ N @ suc )
% 5.68/6.04 = ( plus_plus_nat @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % Suc_funpow
% 5.68/6.04 thf(fact_9651_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.68/6.04 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X2 )
% 5.68/6.04 @ ^ [X2: nat,Y: nat] : ( ord_less_nat @ Y @ X2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % max_nat.semilattice_neutr_order_axioms
% 5.68/6.04 thf(fact_9652_divmod__integer__eq__cases,axiom,
% 5.68/6.04 ( code_divmod_integer
% 5.68/6.04 = ( ^ [K3: code_integer,L: code_integer] :
% 5.68/6.04 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.68/6.04 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.68/6.04 @ ( if_Pro6119634080678213985nteger
% 5.68/6.04 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.68/6.04 = ( sgn_sgn_Code_integer @ L ) )
% 5.68/6.04 @ ( code_divmod_abs @ K3 @ L )
% 5.68/6.04 @ ( produc6916734918728496179nteger
% 5.68/6.04 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S6 ) ) )
% 5.68/6.04 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divmod_integer_eq_cases
% 5.68/6.04 thf(fact_9653_times__int_Oabs__eq,axiom,
% 5.68/6.04 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.68/6.04 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( abs_Integ
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 5.68/6.04 @ Xa2
% 5.68/6.04 @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % times_int.abs_eq
% 5.68/6.04 thf(fact_9654_eq__Abs__Integ,axiom,
% 5.68/6.04 ! [Z: int] :
% 5.68/6.04 ~ ! [X3: nat,Y3: nat] :
% 5.68/6.04 ( Z
% 5.68/6.04 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % eq_Abs_Integ
% 5.68/6.04 thf(fact_9655_zero__int__def,axiom,
% 5.68/6.04 ( zero_zero_int
% 5.68/6.04 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % zero_int_def
% 5.68/6.04 thf(fact_9656_int__def,axiom,
% 5.68/6.04 ( semiri1314217659103216013at_int
% 5.68/6.04 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % int_def
% 5.68/6.04 thf(fact_9657_uminus__int_Oabs__eq,axiom,
% 5.68/6.04 ! [X: product_prod_nat_nat] :
% 5.68/6.04 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( abs_Integ
% 5.68/6.04 @ ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 )
% 5.68/6.04 @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % uminus_int.abs_eq
% 5.68/6.04 thf(fact_9658_one__int__def,axiom,
% 5.68/6.04 ( one_one_int
% 5.68/6.04 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % one_int_def
% 5.68/6.04 thf(fact_9659_less__int_Oabs__eq,axiom,
% 5.68/6.04 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.68/6.04 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( produc8739625826339149834_nat_o
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.68/6.04 @ Xa2
% 5.68/6.04 @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_int.abs_eq
% 5.68/6.04 thf(fact_9660_less__eq__int_Oabs__eq,axiom,
% 5.68/6.04 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.68/6.04 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( produc8739625826339149834_nat_o
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.68/6.04 @ Xa2
% 5.68/6.04 @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_eq_int.abs_eq
% 5.68/6.04 thf(fact_9661_plus__int_Oabs__eq,axiom,
% 5.68/6.04 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.68/6.04 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( abs_Integ
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.68/6.04 @ Xa2
% 5.68/6.04 @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % plus_int.abs_eq
% 5.68/6.04 thf(fact_9662_minus__int_Oabs__eq,axiom,
% 5.68/6.04 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.68/6.04 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.68/6.04 = ( abs_Integ
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 5.68/6.04 @ Xa2
% 5.68/6.04 @ X ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % minus_int.abs_eq
% 5.68/6.04 thf(fact_9663_card_Ocomp__fun__commute__on,axiom,
% 5.68/6.04 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.68/6.04 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.68/6.04
% 5.68/6.04 % card.comp_fun_commute_on
% 5.68/6.04 thf(fact_9664_Code__Numeral_Onegative__def,axiom,
% 5.68/6.04 ( code_negative
% 5.68/6.04 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 5.68/6.04
% 5.68/6.04 % Code_Numeral.negative_def
% 5.68/6.04 thf(fact_9665_Code__Target__Int_Onegative__def,axiom,
% 5.68/6.04 ( code_Target_negative
% 5.68/6.04 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % Code_Target_Int.negative_def
% 5.68/6.04 thf(fact_9666_less__eq__int_Orep__eq,axiom,
% 5.68/6.04 ( ord_less_eq_int
% 5.68/6.04 = ( ^ [X2: int,Xa4: int] :
% 5.68/6.04 ( produc8739625826339149834_nat_o
% 5.68/6.04 @ ^ [Y: nat,Z2: nat] :
% 5.68/6.04 ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.68/6.04 @ ( rep_Integ @ X2 )
% 5.68/6.04 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_eq_int.rep_eq
% 5.68/6.04 thf(fact_9667_less__int_Orep__eq,axiom,
% 5.68/6.04 ( ord_less_int
% 5.68/6.04 = ( ^ [X2: int,Xa4: int] :
% 5.68/6.04 ( produc8739625826339149834_nat_o
% 5.68/6.04 @ ^ [Y: nat,Z2: nat] :
% 5.68/6.04 ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.68/6.04 @ ( rep_Integ @ X2 )
% 5.68/6.04 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_int.rep_eq
% 5.68/6.04 thf(fact_9668_uminus__int__def,axiom,
% 5.68/6.04 ( uminus_uminus_int
% 5.68/6.04 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.68/6.04 @ ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % uminus_int_def
% 5.68/6.04 thf(fact_9669_times__int__def,axiom,
% 5.68/6.04 ( times_times_int
% 5.68/6.04 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % times_int_def
% 5.68/6.04 thf(fact_9670_minus__int__def,axiom,
% 5.68/6.04 ( minus_minus_int
% 5.68/6.04 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % minus_int_def
% 5.68/6.04 thf(fact_9671_plus__int__def,axiom,
% 5.68/6.04 ( plus_plus_int
% 5.68/6.04 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.68/6.04 @ ( produc27273713700761075at_nat
% 5.68/6.04 @ ^ [X2: nat,Y: nat] :
% 5.68/6.04 ( produc2626176000494625587at_nat
% 5.68/6.04 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % plus_int_def
% 5.68/6.04 thf(fact_9672_num__of__nat_Osimps_I2_J,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( num_of_nat @ ( suc @ N ) )
% 5.68/6.04 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( num_of_nat @ ( suc @ N ) )
% 5.68/6.04 = one ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat.simps(2)
% 5.68/6.04 thf(fact_9673_pred__nat__def,axiom,
% 5.68/6.04 ( pred_nat
% 5.68/6.04 = ( collec3392354462482085612at_nat
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [M6: nat,N2: nat] :
% 5.68/6.04 ( N2
% 5.68/6.04 = ( suc @ M6 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % pred_nat_def
% 5.68/6.04 thf(fact_9674_num__of__nat__numeral__eq,axiom,
% 5.68/6.04 ! [Q2: num] :
% 5.68/6.04 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.68/6.04 = Q2 ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat_numeral_eq
% 5.68/6.04 thf(fact_9675_num__of__nat_Osimps_I1_J,axiom,
% 5.68/6.04 ( ( num_of_nat @ zero_zero_nat )
% 5.68/6.04 = one ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat.simps(1)
% 5.68/6.04 thf(fact_9676_numeral__num__of__nat,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.68/6.04 = N ) ) ).
% 5.68/6.04
% 5.68/6.04 % numeral_num_of_nat
% 5.68/6.04 thf(fact_9677_num__of__nat__One,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.68/6.04 => ( ( num_of_nat @ N )
% 5.68/6.04 = one ) ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat_One
% 5.68/6.04 thf(fact_9678_num__of__nat__double,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.68/6.04 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat_double
% 5.68/6.04 thf(fact_9679_num__of__nat__plus__distrib,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.68/6.04 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % num_of_nat_plus_distrib
% 5.68/6.04 thf(fact_9680_pow_Osimps_I3_J,axiom,
% 5.68/6.04 ! [X: num,Y2: num] :
% 5.68/6.04 ( ( pow @ X @ ( bit1 @ Y2 ) )
% 5.68/6.04 = ( times_times_num @ ( sqr @ ( pow @ X @ Y2 ) ) @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % pow.simps(3)
% 5.68/6.04 thf(fact_9681_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.68/6.04 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( Xa2 = one_one_nat ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X3: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.elims(3)
% 5.68/6.04 thf(fact_9682_sqr_Osimps_I2_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( sqr @ ( bit0 @ N ) )
% 5.68/6.04 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sqr.simps(2)
% 5.68/6.04 thf(fact_9683_sqr_Osimps_I1_J,axiom,
% 5.68/6.04 ( ( sqr @ one )
% 5.68/6.04 = one ) ).
% 5.68/6.04
% 5.68/6.04 % sqr.simps(1)
% 5.68/6.04 thf(fact_9684_sqr__conv__mult,axiom,
% 5.68/6.04 ( sqr
% 5.68/6.04 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sqr_conv_mult
% 5.68/6.04 thf(fact_9685_pow_Osimps_I2_J,axiom,
% 5.68/6.04 ! [X: num,Y2: num] :
% 5.68/6.04 ( ( pow @ X @ ( bit0 @ Y2 ) )
% 5.68/6.04 = ( sqr @ ( pow @ X @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % pow.simps(2)
% 5.68/6.04 thf(fact_9686_sqr_Osimps_I3_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( sqr @ ( bit1 @ N ) )
% 5.68/6.04 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sqr.simps(3)
% 5.68/6.04 thf(fact_9687_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.68/6.04 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.68/6.04 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 5.68/6.04 = ( ( Deg = Deg4 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.simps(2)
% 5.68/6.04 thf(fact_9688_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.68/6.04 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( Xa2 != one_one_nat ) ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( ~ ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.elims(1)
% 5.68/6.04 thf(fact_9689_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.68/6.04 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 => ( ( ? [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( Xa2 != one_one_nat ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ~ ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X5: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.elims(2)
% 5.68/6.04 thf(fact_9690_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 5.68/6.04 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.68/6.04 => ( ! [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( Xa2 = one_one_nat ) )
% 5.68/6.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) ) ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) )
% 5.68/6.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.pelims(1)
% 5.68/6.04 thf(fact_9691_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.68/6.04 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.68/6.04 => ( ! [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) )
% 5.68/6.04 => ( Xa2 != one_one_nat ) ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.68/6.04 => ~ ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X5: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.pelims(2)
% 5.68/6.04 thf(fact_9692_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.68/6.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.68/6.04 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.68/6.04 => ( ! [Uu3: $o,Uv2: $o] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Leaf @ Uu3 @ Uv2 ) )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ Xa2 ) )
% 5.68/6.04 => ( Xa2 = one_one_nat ) ) )
% 5.68/6.04 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.68/6.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.68/6.04 => ( ( Deg2 = Xa2 )
% 5.68/6.04 & ! [X3: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.68/6.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 & ( case_o184042715313410164at_nat
% 5.68/6.04 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.68/6.04 & ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 @ ( produc6081775807080527818_nat_o
% 5.68/6.04 @ ^ [Mi3: nat,Ma3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.68/6.04 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 & ! [I3: nat] :
% 5.68/6.04 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.68/6.04 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 5.68/6.04 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.68/6.04 & ( ( Mi3 = Ma3 )
% 5.68/6.04 => ! [X2: vEBT_VEBT] :
% 5.68/6.04 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.68/6.04 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X6 ) ) )
% 5.68/6.04 & ( ( Mi3 != Ma3 )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.68/6.04 & ! [X2: nat] :
% 5.68/6.04 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.68/6.04 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.68/6.04 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.68/6.04 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.68/6.04 @ Mima ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % VEBT_internal.valid'.pelims(3)
% 5.68/6.04 thf(fact_9693_Sup__int__def,axiom,
% 5.68/6.04 ( complete_Sup_Sup_int
% 5.68/6.04 = ( ^ [X6: set_int] :
% 5.68/6.04 ( the_int
% 5.68/6.04 @ ^ [X2: int] :
% 5.68/6.04 ( ( member_int @ X2 @ X6 )
% 5.68/6.04 & ! [Y: int] :
% 5.68/6.04 ( ( member_int @ Y @ X6 )
% 5.68/6.04 => ( ord_less_eq_int @ Y @ X2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Sup_int_def
% 5.68/6.04 thf(fact_9694_take__bit__numeral__minus__numeral__int,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int
% 5.68/6.04 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.68/6.04 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_numeral_minus_numeral_int
% 5.68/6.04 thf(fact_9695_and__minus__numerals_I7_J,axiom,
% 5.68/6.04 ! [N: num,M: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_minus_numerals(7)
% 5.68/6.04 thf(fact_9696_take__bit__num__simps_I1_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(1)
% 5.68/6.04 thf(fact_9697_take__bit__num__simps_I2_J,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(2)
% 5.68/6.04 thf(fact_9698_take__bit__num__simps_I5_J,axiom,
% 5.68/6.04 ! [R2: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(5)
% 5.68/6.04 thf(fact_9699_take__bit__num__simps_I3_J,axiom,
% 5.68/6.04 ! [N: nat,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.68/6.04 = ( case_o6005452278849405969um_num @ none_num
% 5.68/6.04 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.68/6.04 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(3)
% 5.68/6.04 thf(fact_9700_take__bit__num__simps_I4_J,axiom,
% 5.68/6.04 ! [N: nat,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(4)
% 5.68/6.04 thf(fact_9701_take__bit__num__simps_I6_J,axiom,
% 5.68/6.04 ! [R2: num,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.68/6.04 = ( case_o6005452278849405969um_num @ none_num
% 5.68/6.04 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.68/6.04 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(6)
% 5.68/6.04 thf(fact_9702_take__bit__num__simps_I7_J,axiom,
% 5.68/6.04 ! [R2: num,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_simps(7)
% 5.68/6.04 thf(fact_9703_and__minus__numerals_I4_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_minus_numerals(4)
% 5.68/6.04 thf(fact_9704_and__minus__numerals_I8_J,axiom,
% 5.68/6.04 ! [N: num,M: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_minus_numerals(8)
% 5.68/6.04 thf(fact_9705_and__minus__numerals_I3_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_minus_numerals(3)
% 5.68/6.04 thf(fact_9706_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.68/6.04 ! [N: nat,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.68/6.04 = ( case_nat_option_num @ none_num
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( case_o6005452278849405969um_num @ none_num
% 5.68/6.04 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.68/6.04 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.68/6.04 @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.68/6.04 thf(fact_9707_and__not__num_Osimps_I1_J,axiom,
% 5.68/6.04 ( ( bit_and_not_num @ one @ one )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(1)
% 5.68/6.04 thf(fact_9708_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( bit_take_bit_num @ N @ one )
% 5.68/6.04 = ( case_nat_option_num @ none_num
% 5.68/6.04 @ ^ [N2: nat] : ( some_num @ one )
% 5.68/6.04 @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.68/6.04 thf(fact_9709_and__not__num_Osimps_I4_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.68/6.04 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(4)
% 5.68/6.04 thf(fact_9710_and__not__num_Osimps_I2_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(2)
% 5.68/6.04 thf(fact_9711_GreatestI__ex__nat,axiom,
% 5.68/6.04 ! [P: nat > $o,B: nat] :
% 5.68/6.04 ( ? [X_12: nat] : ( P @ X_12 )
% 5.68/6.04 => ( ! [Y3: nat] :
% 5.68/6.04 ( ( P @ Y3 )
% 5.68/6.04 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.68/6.04 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % GreatestI_ex_nat
% 5.68/6.04 thf(fact_9712_Greatest__le__nat,axiom,
% 5.68/6.04 ! [P: nat > $o,K: nat,B: nat] :
% 5.68/6.04 ( ( P @ K )
% 5.68/6.04 => ( ! [Y3: nat] :
% 5.68/6.04 ( ( P @ Y3 )
% 5.68/6.04 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.68/6.04 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Greatest_le_nat
% 5.68/6.04 thf(fact_9713_GreatestI__nat,axiom,
% 5.68/6.04 ! [P: nat > $o,K: nat,B: nat] :
% 5.68/6.04 ( ( P @ K )
% 5.68/6.04 => ( ! [Y3: nat] :
% 5.68/6.04 ( ( P @ Y3 )
% 5.68/6.04 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.68/6.04 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % GreatestI_nat
% 5.68/6.04 thf(fact_9714_and__not__num_Osimps_I3_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(3)
% 5.68/6.04 thf(fact_9715_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.68/6.04 ! [N: nat,M: num] :
% 5.68/6.04 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.68/6.04 = ( case_nat_option_num @ none_num
% 5.68/6.04 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.68/6.04 @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.68/6.04 thf(fact_9716_and__not__num_Osimps_I7_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.68/6.04 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(7)
% 5.68/6.04 thf(fact_9717_and__not__num__eq__Some__iff,axiom,
% 5.68/6.04 ! [M: num,N: num,Q2: num] :
% 5.68/6.04 ( ( ( bit_and_not_num @ M @ N )
% 5.68/6.04 = ( some_num @ Q2 ) )
% 5.68/6.04 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num_eq_Some_iff
% 5.68/6.04 thf(fact_9718_and__not__num_Osimps_I8_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(8)
% 5.68/6.04 thf(fact_9719_and__not__num__eq__None__iff,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( ( bit_and_not_num @ M @ N )
% 5.68/6.04 = none_num )
% 5.68/6.04 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = zero_zero_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num_eq_None_iff
% 5.68/6.04 thf(fact_9720_int__numeral__not__and__num,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % int_numeral_not_and_num
% 5.68/6.04 thf(fact_9721_int__numeral__and__not__num,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % int_numeral_and_not_num
% 5.68/6.04 thf(fact_9722_take__bit__num__def,axiom,
% 5.68/6.04 ( bit_take_bit_num
% 5.68/6.04 = ( ^ [N2: nat,M6: num] :
% 5.68/6.04 ( if_option_num
% 5.68/6.04 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 5.68/6.04 = zero_zero_nat )
% 5.68/6.04 @ none_num
% 5.68/6.04 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % take_bit_num_def
% 5.68/6.04 thf(fact_9723_Bit__Operations_Otake__bit__num__code,axiom,
% 5.68/6.04 ( bit_take_bit_num
% 5.68/6.04 = ( ^ [N2: nat,M6: num] :
% 5.68/6.04 ( produc478579273971653890on_num
% 5.68/6.04 @ ^ [A4: nat,X2: num] :
% 5.68/6.04 ( case_nat_option_num @ none_num
% 5.68/6.04 @ ^ [O: nat] :
% 5.68/6.04 ( case_num_option_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [P5: num] :
% 5.68/6.04 ( case_o6005452278849405969um_num @ none_num
% 5.68/6.04 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.68/6.04 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.68/6.04 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.68/6.04 @ X2 )
% 5.68/6.04 @ A4 )
% 5.68/6.04 @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Bit_Operations.take_bit_num_code
% 5.68/6.04 thf(fact_9724_Rats__eq__int__div__nat,axiom,
% 5.68/6.04 ( field_5140801741446780682s_real
% 5.68/6.04 = ( collect_real
% 5.68/6.04 @ ^ [Uu2: real] :
% 5.68/6.04 ? [I3: int,N2: nat] :
% 5.68/6.04 ( ( Uu2
% 5.68/6.04 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.68/6.04 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_eq_int_div_nat
% 5.68/6.04 thf(fact_9725_Rats__abs__iff,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 5.68/6.04 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_abs_iff
% 5.68/6.04 thf(fact_9726_Rats__no__bot__less,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ? [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.68/6.04 & ( ord_less_real @ X3 @ X ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_no_bot_less
% 5.68/6.04 thf(fact_9727_Rats__dense__in__real,axiom,
% 5.68/6.04 ! [X: real,Y2: real] :
% 5.68/6.04 ( ( ord_less_real @ X @ Y2 )
% 5.68/6.04 => ? [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.68/6.04 & ( ord_less_real @ X @ X3 )
% 5.68/6.04 & ( ord_less_real @ X3 @ Y2 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_dense_in_real
% 5.68/6.04 thf(fact_9728_Rats__no__top__le,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ? [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.68/6.04 & ( ord_less_eq_real @ X @ X3 ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_no_top_le
% 5.68/6.04 thf(fact_9729_Rats__eq__int__div__int,axiom,
% 5.68/6.04 ( field_5140801741446780682s_real
% 5.68/6.04 = ( collect_real
% 5.68/6.04 @ ^ [Uu2: real] :
% 5.68/6.04 ? [I3: int,J3: int] :
% 5.68/6.04 ( ( Uu2
% 5.68/6.04 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.68/6.04 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rats_eq_int_div_int
% 5.68/6.04 thf(fact_9730_and__not__num_Oelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2 != none_num ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ? [N3: num] :
% 5.68/6.04 ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ one ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ? [N3: num] :
% 5.68/6.04 ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2 != none_num ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.elims
% 5.68/6.04 thf(fact_9731_xor__num_Osimps_I8_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(8)
% 5.68/6.04 thf(fact_9732_xor__num_Osimps_I6_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(6)
% 5.68/6.04 thf(fact_9733_xor__num_Osimps_I9_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(9)
% 5.68/6.04 thf(fact_9734_xor__num_Osimps_I5_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(5)
% 5.68/6.04 thf(fact_9735_and__not__num_Osimps_I5_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(5)
% 5.68/6.04 thf(fact_9736_and__not__num_Osimps_I6_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(6)
% 5.68/6.04 thf(fact_9737_and__not__num_Osimps_I9_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.simps(9)
% 5.68/6.04 thf(fact_9738_xor__num_Osimps_I1_J,axiom,
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(1)
% 5.68/6.04 thf(fact_9739_xor__num_Oelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2 != none_num ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.elims
% 5.68/6.04 thf(fact_9740_xor__num_Osimps_I7_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.68/6.04 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(7)
% 5.68/6.04 thf(fact_9741_xor__num_Osimps_I4_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.68/6.04 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(4)
% 5.68/6.04 thf(fact_9742_xor__num_Osimps_I3_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.68/6.04 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(3)
% 5.68/6.04 thf(fact_9743_xor__num_Osimps_I2_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.68/6.04 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.simps(2)
% 5.68/6.04 thf(fact_9744_and__not__num_Opelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2 = none_num )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ one ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2 = none_num )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_not_num.pelims
% 5.68/6.04 thf(fact_9745_xor__num_Opelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2 = none_num )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit1 @ M5 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % xor_num.pelims
% 5.68/6.04 thf(fact_9746_and__num_Oelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ one ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ? [N3: num] :
% 5.68/6.04 ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2 != none_num ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ? [N3: num] :
% 5.68/6.04 ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ one ) ) ) )
% 5.68/6.04 => ( ( ? [M5: num] :
% 5.68/6.04 ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2 != none_num ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ( ( ? [M5: num] :
% 5.68/6.04 ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( some_num @ one ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( Y2
% 5.68/6.04 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.elims
% 5.68/6.04 thf(fact_9747_xor__num__rel__dict,axiom,
% 5.68/6.04 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.68/6.04
% 5.68/6.04 % xor_num_rel_dict
% 5.68/6.04 thf(fact_9748_xor__num__dict,axiom,
% 5.68/6.04 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.68/6.04
% 5.68/6.04 % xor_num_dict
% 5.68/6.04 thf(fact_9749_and__num_Osimps_I1_J,axiom,
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(1)
% 5.68/6.04 thf(fact_9750_and__num_Osimps_I5_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(5)
% 5.68/6.04 thf(fact_9751_and__num_Osimps_I7_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(7)
% 5.68/6.04 thf(fact_9752_and__num_Osimps_I3_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.68/6.04 = ( some_num @ one ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(3)
% 5.68/6.04 thf(fact_9753_and__num_Osimps_I4_J,axiom,
% 5.68/6.04 ! [M: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(4)
% 5.68/6.04 thf(fact_9754_and__num_Osimps_I2_J,axiom,
% 5.68/6.04 ! [N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.68/6.04 = none_num ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(2)
% 5.68/6.04 thf(fact_9755_and__num_Osimps_I6_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(6)
% 5.68/6.04 thf(fact_9756_and__num_Osimps_I8_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(8)
% 5.68/6.04 thf(fact_9757_and__num_Osimps_I9_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.68/6.04 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.simps(9)
% 5.68/6.04 thf(fact_9758_and__num_Opelims,axiom,
% 5.68/6.04 ! [X: num,Xa2: num,Y2: option_num] :
% 5.68/6.04 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ one ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2 = none_num )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ( ( X = one )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ one ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2 = none_num )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit0 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ( ( Xa2 = one )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( some_num @ one ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.68/6.04 => ( ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit0 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.68/6.04 => ~ ! [M5: num] :
% 5.68/6.04 ( ( X
% 5.68/6.04 = ( bit1 @ M5 ) )
% 5.68/6.04 => ! [N3: num] :
% 5.68/6.04 ( ( Xa2
% 5.68/6.04 = ( bit1 @ N3 ) )
% 5.68/6.04 => ( ( Y2
% 5.68/6.04 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.68/6.04 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.68/6.04 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.68/6.04 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % and_num.pelims
% 5.68/6.04 thf(fact_9759_and__num__dict,axiom,
% 5.68/6.04 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.68/6.04
% 5.68/6.04 % and_num_dict
% 5.68/6.04 thf(fact_9760_and__num__rel__dict,axiom,
% 5.68/6.04 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.68/6.04
% 5.68/6.04 % and_num_rel_dict
% 5.68/6.04 thf(fact_9761_rat__floor__lemma,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.68/6.04 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_floor_lemma
% 5.68/6.04 thf(fact_9762_mult__rat,axiom,
% 5.68/6.04 ! [A: int,B: int,C: int,D: int] :
% 5.68/6.04 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % mult_rat
% 5.68/6.04 thf(fact_9763_divide__rat,axiom,
% 5.68/6.04 ! [A: int,B: int,C: int,D: int] :
% 5.68/6.04 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % divide_rat
% 5.68/6.04 thf(fact_9764_less__rat,axiom,
% 5.68/6.04 ! [B: int,D: int,A: int,C: int] :
% 5.68/6.04 ( ( B != zero_zero_int )
% 5.68/6.04 => ( ( D != zero_zero_int )
% 5.68/6.04 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % less_rat
% 5.68/6.04 thf(fact_9765_add__rat,axiom,
% 5.68/6.04 ! [B: int,D: int,A: int,C: int] :
% 5.68/6.04 ( ( B != zero_zero_int )
% 5.68/6.04 => ( ( D != zero_zero_int )
% 5.68/6.04 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % add_rat
% 5.68/6.04 thf(fact_9766_le__rat,axiom,
% 5.68/6.04 ! [B: int,D: int,A: int,C: int] :
% 5.68/6.04 ( ( B != zero_zero_int )
% 5.68/6.04 => ( ( D != zero_zero_int )
% 5.68/6.04 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % le_rat
% 5.68/6.04 thf(fact_9767_diff__rat,axiom,
% 5.68/6.04 ! [B: int,D: int,A: int,C: int] :
% 5.68/6.04 ( ( B != zero_zero_int )
% 5.68/6.04 => ( ( D != zero_zero_int )
% 5.68/6.04 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.68/6.04 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % diff_rat
% 5.68/6.04 thf(fact_9768_sgn__rat,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.68/6.04 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sgn_rat
% 5.68/6.04 thf(fact_9769_eq__rat_I1_J,axiom,
% 5.68/6.04 ! [B: int,D: int,A: int,C: int] :
% 5.68/6.04 ( ( B != zero_zero_int )
% 5.68/6.04 => ( ( D != zero_zero_int )
% 5.68/6.04 => ( ( ( fract @ A @ B )
% 5.68/6.04 = ( fract @ C @ D ) )
% 5.68/6.04 = ( ( times_times_int @ A @ D )
% 5.68/6.04 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % eq_rat(1)
% 5.68/6.04 thf(fact_9770_mult__rat__cancel,axiom,
% 5.68/6.04 ! [C: int,A: int,B: int] :
% 5.68/6.04 ( ( C != zero_zero_int )
% 5.68/6.04 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.68/6.04 = ( fract @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % mult_rat_cancel
% 5.68/6.04 thf(fact_9771_quotient__of__eq,axiom,
% 5.68/6.04 ! [A: int,B: int,P4: int,Q2: int] :
% 5.68/6.04 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 5.68/6.04 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 => ( ( fract @ P4 @ Q2 )
% 5.68/6.04 = ( fract @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_eq
% 5.68/6.04 thf(fact_9772_normalize__eq,axiom,
% 5.68/6.04 ! [A: int,B: int,P4: int,Q2: int] :
% 5.68/6.04 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 5.68/6.04 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.68/6.04 => ( ( fract @ P4 @ Q2 )
% 5.68/6.04 = ( fract @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % normalize_eq
% 5.68/6.04 thf(fact_9773_rat__number__expand_I3_J,axiom,
% 5.68/6.04 ( numeral_numeral_rat
% 5.68/6.04 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_number_expand(3)
% 5.68/6.04 thf(fact_9774_rat__number__collapse_I3_J,axiom,
% 5.68/6.04 ! [W: num] :
% 5.68/6.04 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.68/6.04 = ( numeral_numeral_rat @ W ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_number_collapse(3)
% 5.68/6.04 thf(fact_9775_quotient__of__Fract,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( quotient_of @ ( fract @ A @ B ) )
% 5.68/6.04 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % quotient_of_Fract
% 5.68/6.04 thf(fact_9776_Fract__add__one,axiom,
% 5.68/6.04 ! [N: int,M: int] :
% 5.68/6.04 ( ( N != zero_zero_int )
% 5.68/6.04 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.68/6.04 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Fract_add_one
% 5.68/6.04 thf(fact_9777_Fract__le__zero__iff,axiom,
% 5.68/6.04 ! [B: int,A: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ B )
% 5.68/6.04 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.68/6.04 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Fract_le_zero_iff
% 5.68/6.04 thf(fact_9778_zero__le__Fract__iff,axiom,
% 5.68/6.04 ! [B: int,A: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ B )
% 5.68/6.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.68/6.04 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % zero_le_Fract_iff
% 5.68/6.04 thf(fact_9779_Fract__le__one__iff,axiom,
% 5.68/6.04 ! [B: int,A: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ B )
% 5.68/6.04 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.68/6.04 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Fract_le_one_iff
% 5.68/6.04 thf(fact_9780_one__le__Fract__iff,axiom,
% 5.68/6.04 ! [B: int,A: int] :
% 5.68/6.04 ( ( ord_less_int @ zero_zero_int @ B )
% 5.68/6.04 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.68/6.04 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % one_le_Fract_iff
% 5.68/6.04 thf(fact_9781_rat__number__expand_I5_J,axiom,
% 5.68/6.04 ! [K: num] :
% 5.68/6.04 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.68/6.04 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_number_expand(5)
% 5.68/6.04 thf(fact_9782_rat__number__collapse_I4_J,axiom,
% 5.68/6.04 ! [W: num] :
% 5.68/6.04 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.68/6.04 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % rat_number_collapse(4)
% 5.68/6.04 thf(fact_9783_image__minus__const__atLeastLessThan__nat,axiom,
% 5.68/6.04 ! [C: nat,Y2: nat,X: nat] :
% 5.68/6.04 ( ( ( ord_less_nat @ C @ Y2 )
% 5.68/6.04 => ( ( image_nat_nat
% 5.68/6.04 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.68/6.04 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 5.68/6.04 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_nat @ C @ Y2 )
% 5.68/6.04 => ( ( ( ord_less_nat @ X @ Y2 )
% 5.68/6.04 => ( ( image_nat_nat
% 5.68/6.04 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.68/6.04 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.68/6.04 & ( ~ ( ord_less_nat @ X @ Y2 )
% 5.68/6.04 => ( ( image_nat_nat
% 5.68/6.04 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.68/6.04 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 5.68/6.04 = bot_bot_set_nat ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_minus_const_atLeastLessThan_nat
% 5.68/6.04 thf(fact_9784_positive__rat,axiom,
% 5.68/6.04 ! [A: int,B: int] :
% 5.68/6.04 ( ( positive @ ( fract @ A @ B ) )
% 5.68/6.04 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % positive_rat
% 5.68/6.04 thf(fact_9785_bij__betw__Suc,axiom,
% 5.68/6.04 ! [M7: set_nat,N5: set_nat] :
% 5.68/6.04 ( ( bij_betw_nat_nat @ suc @ M7 @ N5 )
% 5.68/6.04 = ( ( image_nat_nat @ suc @ M7 )
% 5.68/6.04 = N5 ) ) ).
% 5.68/6.04
% 5.68/6.04 % bij_betw_Suc
% 5.68/6.04 thf(fact_9786_image__Suc__atLeastAtMost,axiom,
% 5.68/6.04 ! [I2: nat,J: nat] :
% 5.68/6.04 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.68/6.04 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_Suc_atLeastAtMost
% 5.68/6.04 thf(fact_9787_image__Suc__atLeastLessThan,axiom,
% 5.68/6.04 ! [I2: nat,J: nat] :
% 5.68/6.04 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.68/6.04 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_Suc_atLeastLessThan
% 5.68/6.04 thf(fact_9788_zero__notin__Suc__image,axiom,
% 5.68/6.04 ! [A2: set_nat] :
% 5.68/6.04 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % zero_notin_Suc_image
% 5.68/6.04 thf(fact_9789_Rat_Opositive__add,axiom,
% 5.68/6.04 ! [X: rat,Y2: rat] :
% 5.68/6.04 ( ( positive @ X )
% 5.68/6.04 => ( ( positive @ Y2 )
% 5.68/6.04 => ( positive @ ( plus_plus_rat @ X @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rat.positive_add
% 5.68/6.04 thf(fact_9790_Rat_Opositive__mult,axiom,
% 5.68/6.04 ! [X: rat,Y2: rat] :
% 5.68/6.04 ( ( positive @ X )
% 5.68/6.04 => ( ( positive @ Y2 )
% 5.68/6.04 => ( positive @ ( times_times_rat @ X @ Y2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rat.positive_mult
% 5.68/6.04 thf(fact_9791_image__Suc__lessThan,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_Suc_lessThan
% 5.68/6.04 thf(fact_9792_image__Suc__atMost,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.68/6.04 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_Suc_atMost
% 5.68/6.04 thf(fact_9793_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeast0_atMost_Suc_eq_insert_0
% 5.68/6.04 thf(fact_9794_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeast0_lessThan_Suc_eq_insert_0
% 5.68/6.04 thf(fact_9795_lessThan__Suc__eq__insert__0,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % lessThan_Suc_eq_insert_0
% 5.68/6.04 thf(fact_9796_atMost__Suc__eq__insert__0,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atMost_Suc_eq_insert_0
% 5.68/6.04 thf(fact_9797_Rat_Opositive_Orep__eq,axiom,
% 5.68/6.04 ( positive
% 5.68/6.04 = ( ^ [X2: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X2 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Rat.positive.rep_eq
% 5.68/6.04 thf(fact_9798_Inf__real__def,axiom,
% 5.68/6.04 ( comple4887499456419720421f_real
% 5.68/6.04 = ( ^ [X6: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X6 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Inf_real_def
% 5.68/6.04 thf(fact_9799_finite__int__iff__bounded__le,axiom,
% 5.68/6.04 ( finite_finite_int
% 5.68/6.04 = ( ^ [S4: set_int] :
% 5.68/6.04 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % finite_int_iff_bounded_le
% 5.68/6.04 thf(fact_9800_finite__int__iff__bounded,axiom,
% 5.68/6.04 ( finite_finite_int
% 5.68/6.04 = ( ^ [S4: set_int] :
% 5.68/6.04 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % finite_int_iff_bounded
% 5.68/6.04 thf(fact_9801_suminf__eq__SUP__real,axiom,
% 5.68/6.04 ! [X8: nat > real] :
% 5.68/6.04 ( ( summable_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 5.68/6.04 => ( ( suminf_real @ X8 )
% 5.68/6.04 = ( comple1385675409528146559p_real
% 5.68/6.04 @ ( image_nat_real
% 5.68/6.04 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 5.68/6.04 @ top_top_set_nat ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % suminf_eq_SUP_real
% 5.68/6.04 thf(fact_9802_image__add__int__atLeastLessThan,axiom,
% 5.68/6.04 ! [L2: int,U: int] :
% 5.68/6.04 ( ( image_int_int
% 5.68/6.04 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 5.68/6.04 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.68/6.04 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_add_int_atLeastLessThan
% 5.68/6.04 thf(fact_9803_range__mod,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( image_nat_nat
% 5.68/6.04 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 5.68/6.04 @ top_top_set_nat )
% 5.68/6.04 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % range_mod
% 5.68/6.04 thf(fact_9804_image__atLeastZeroLessThan__int,axiom,
% 5.68/6.04 ! [U: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.68/6.04 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.68/6.04 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % image_atLeastZeroLessThan_int
% 5.68/6.04 thf(fact_9805_UNIV__nat__eq,axiom,
% 5.68/6.04 ( top_top_set_nat
% 5.68/6.04 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % UNIV_nat_eq
% 5.68/6.04 thf(fact_9806_card__UNIV__bool,axiom,
% 5.68/6.04 ( ( finite_card_o @ top_top_set_o )
% 5.68/6.04 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_UNIV_bool
% 5.68/6.04 thf(fact_9807_range__mult,axiom,
% 5.68/6.04 ! [A: real] :
% 5.68/6.04 ( ( ( A = zero_zero_real )
% 5.68/6.04 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.68/6.04 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.68/6.04 & ( ( A != zero_zero_real )
% 5.68/6.04 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.68/6.04 = top_top_set_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % range_mult
% 5.68/6.04 thf(fact_9808_root__def,axiom,
% 5.68/6.04 ( root
% 5.68/6.04 = ( ^ [N2: nat,X2: real] :
% 5.68/6.04 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.68/6.04 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.68/6.04 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.68/6.04 @ X2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % root_def
% 5.68/6.04 thf(fact_9809_card__UNIV__char,axiom,
% 5.68/6.04 ( ( finite_card_char @ top_top_set_char )
% 5.68/6.04 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % card_UNIV_char
% 5.68/6.04 thf(fact_9810_UNIV__char__of__nat,axiom,
% 5.68/6.04 ( top_top_set_char
% 5.68/6.04 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % UNIV_char_of_nat
% 5.68/6.04 thf(fact_9811_char_Osize_I2_J,axiom,
% 5.68/6.04 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.68/6.04 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.68/6.04 = zero_zero_nat ) ).
% 5.68/6.04
% 5.68/6.04 % char.size(2)
% 5.68/6.04 thf(fact_9812_nat__of__char__less__256,axiom,
% 5.68/6.04 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nat_of_char_less_256
% 5.68/6.04 thf(fact_9813_range__nat__of__char,axiom,
% 5.68/6.04 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.68/6.04 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % range_nat_of_char
% 5.68/6.04 thf(fact_9814_integer__of__char__code,axiom,
% 5.68/6.04 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.68/6.04 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.68/6.04 = ( 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 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % integer_of_char_code
% 5.68/6.04 thf(fact_9815_String_Ochar__of__ascii__of,axiom,
% 5.68/6.04 ! [C: char] :
% 5.68/6.04 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.68/6.04 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % String.char_of_ascii_of
% 5.68/6.04 thf(fact_9816_DERIV__even__real__root,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.04 => ( 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 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_even_real_root
% 5.68/6.04 thf(fact_9817_DERIV__real__root__generic,axiom,
% 5.68/6.04 ! [N: nat,X: real,D4: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( X != zero_zero_real )
% 5.68/6.04 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( D4
% 5.68/6.04 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.68/6.04 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.04 => ( D4
% 5.68/6.04 = ( 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 ) ) ) ) ) ) ) ) )
% 5.68/6.04 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( D4
% 5.68/6.04 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_real_root_generic
% 5.68/6.04 thf(fact_9818_DERIV__neg__dec__right,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.68/6.04 => ? [D3: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.68/6.04 & ! [H4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.68/6.04 => ( ( ord_less_real @ H4 @ D3 )
% 5.68/6.04 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_neg_dec_right
% 5.68/6.04 thf(fact_9819_DERIV__pos__inc__right,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.68/6.04 => ? [D3: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.68/6.04 & ! [H4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.68/6.04 => ( ( ord_less_real @ H4 @ D3 )
% 5.68/6.04 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_pos_inc_right
% 5.68/6.04 thf(fact_9820_DERIV__pos__imp__increasing,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.68/6.04 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_pos_imp_increasing
% 5.68/6.04 thf(fact_9821_DERIV__neg__imp__decreasing,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.68/6.04 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_neg_imp_decreasing
% 5.68/6.04 thf(fact_9822_has__real__derivative__neg__dec__right,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.68/6.04 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.68/6.04 => ? [D3: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.68/6.04 & ! [H4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.68/6.04 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.68/6.04 => ( ( ord_less_real @ H4 @ D3 )
% 5.68/6.04 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % has_real_derivative_neg_dec_right
% 5.68/6.04 thf(fact_9823_has__real__derivative__pos__inc__right,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.68/6.04 => ? [D3: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.68/6.04 & ! [H4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.68/6.04 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.68/6.04 => ( ( ord_less_real @ H4 @ D3 )
% 5.68/6.04 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % has_real_derivative_pos_inc_right
% 5.68/6.04 thf(fact_9824_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.68/6.04 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_nonpos_imp_nonincreasing
% 5.68/6.04 thf(fact_9825_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.68/6.04 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_nonneg_imp_nondecreasing
% 5.68/6.04 thf(fact_9826_deriv__nonneg__imp__mono,axiom,
% 5.68/6.04 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.68/6.04 ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.68/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ A @ B )
% 5.68/6.04 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % deriv_nonneg_imp_mono
% 5.68/6.04 thf(fact_9827_DERIV__const__ratio__const,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real,K: real] :
% 5.68/6.04 ( ( A != B )
% 5.68/6.04 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.68/6.04 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_const_ratio_const
% 5.68/6.04 thf(fact_9828_MVT2,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.68/6.04 => ? [Z3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ Z3 )
% 5.68/6.04 & ( ord_less_real @ Z3 @ B )
% 5.68/6.04 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.68/6.04 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % MVT2
% 5.68/6.04 thf(fact_9829_DERIV__const__average,axiom,
% 5.68/6.04 ! [A: real,B: real,V: real > real,K: real] :
% 5.68/6.04 ( ( A != B )
% 5.68/6.04 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.68/6.04 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_const_average
% 5.68/6.04 thf(fact_9830_DERIV__local__min,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real,D: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.68/6.04 => ( ! [Y3: real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.68/6.04 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 5.68/6.04 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_local_min
% 5.68/6.04 thf(fact_9831_DERIV__local__max,axiom,
% 5.68/6.04 ! [F: real > real,L2: real,X: real,D: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.68/6.04 => ( ! [Y3: real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.68/6.04 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 5.68/6.04 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_local_max
% 5.68/6.04 thf(fact_9832_DERIV__pow,axiom,
% 5.68/6.04 ! [N: nat,X: real,S2: set_real] :
% 5.68/6.04 ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 5.68/6.04 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_pow
% 5.68/6.04 thf(fact_9833_DERIV__fun__pow,axiom,
% 5.68/6.04 ! [G: real > real,M: real,X: real,N: nat] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 5.68/6.04 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_fun_pow
% 5.68/6.04 thf(fact_9834_has__real__derivative__powr,axiom,
% 5.68/6.04 ! [Z: real,R2: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [Z2: real] : ( powr_real @ Z2 @ R2 )
% 5.68/6.04 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % has_real_derivative_powr
% 5.68/6.04 thf(fact_9835_DERIV__series_H,axiom,
% 5.68/6.04 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.68/6.04 ( ! [N3: nat] :
% 5.68/6.04 ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( F @ X2 @ N3 )
% 5.68/6.04 @ ( F4 @ X0 @ N3 )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.68/6.04 => ( summable_real @ ( F @ X3 ) ) )
% 5.68/6.04 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.68/6.04 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.68/6.04 => ( ( summable_real @ L5 )
% 5.68/6.04 => ( ! [N3: nat,X3: real,Y3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.68/6.04 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.68/6.04 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.68/6.04 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_series'
% 5.68/6.04 thf(fact_9836_DERIV__log,axiom,
% 5.68/6.04 ! [X: real,B: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( 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 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_log
% 5.68/6.04 thf(fact_9837_DERIV__fun__powr,axiom,
% 5.68/6.04 ! [G: real > real,M: real,X: real,R2: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 5.68/6.04 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_fun_powr
% 5.68/6.04 thf(fact_9838_DERIV__powr,axiom,
% 5.68/6.04 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.68/6.04 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.68/6.04 @ ( 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 ) ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_powr
% 5.68/6.04 thf(fact_9839_artanh__real__has__field__derivative,axiom,
% 5.68/6.04 ! [X: real,A2: set_real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.04 => ( 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 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % artanh_real_has_field_derivative
% 5.68/6.04 thf(fact_9840_DERIV__real__sqrt,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_real_sqrt
% 5.68/6.04 thf(fact_9841_DERIV__arctan,axiom,
% 5.68/6.04 ! [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 ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_arctan
% 5.68/6.04 thf(fact_9842_arsinh__real__has__field__derivative,axiom,
% 5.68/6.04 ! [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 ) ) ).
% 5.68/6.04
% 5.68/6.04 % arsinh_real_has_field_derivative
% 5.68/6.04 thf(fact_9843_DERIV__real__sqrt__generic,axiom,
% 5.68/6.04 ! [X: real,D4: real] :
% 5.68/6.04 ( ( X != zero_zero_real )
% 5.68/6.04 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( D4
% 5.68/6.04 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.68/6.04 => ( D4
% 5.68/6.04 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_real_sqrt_generic
% 5.68/6.04 thf(fact_9844_arcosh__real__has__field__derivative,axiom,
% 5.68/6.04 ! [X: real,A2: set_real] :
% 5.68/6.04 ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.04 => ( 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 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % arcosh_real_has_field_derivative
% 5.68/6.04 thf(fact_9845_DERIV__power__series_H,axiom,
% 5.68/6.04 ! [R: real,F: nat > real,X0: real] :
% 5.68/6.04 ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.68/6.04 => ( summable_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.68/6.04 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X2: real] :
% 5.68/6.04 ( suminf_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) )
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_power_series'
% 5.68/6.04 thf(fact_9846_DERIV__real__root,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.68/6.04 => ( 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 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_real_root
% 5.68/6.04 thf(fact_9847_DERIV__arccos,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.04 => ( ( ord_less_real @ X @ one_one_real )
% 5.68/6.04 => ( 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 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_arccos
% 5.68/6.04 thf(fact_9848_DERIV__arcsin,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.68/6.04 => ( ( ord_less_real @ X @ one_one_real )
% 5.68/6.04 => ( 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 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_arcsin
% 5.68/6.04 thf(fact_9849_Maclaurin__all__le__objl,axiom,
% 5.68/6.04 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.68/6.04 ( ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 & ! [M5: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.04 & ( ( F @ X )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_all_le_objl
% 5.68/6.04 thf(fact_9850_Maclaurin__all__le,axiom,
% 5.68/6.04 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.68/6.04 ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.04 & ( ( F @ X )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_all_le
% 5.68/6.04 thf(fact_9851_DERIV__odd__real__root,axiom,
% 5.68/6.04 ! [N: nat,X: real] :
% 5.68/6.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( ( X != zero_zero_real )
% 5.68/6.04 => ( 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 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_odd_real_root
% 5.68/6.04 thf(fact_9852_Maclaurin,axiom,
% 5.68/6.04 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ H2 )
% 5.68/6.04 & ( ( F @ H2 )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin
% 5.68/6.04 thf(fact_9853_Maclaurin2,axiom,
% 5.68/6.04 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ H2 )
% 5.68/6.04 & ( ( F @ H2 )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin2
% 5.68/6.04 thf(fact_9854_Maclaurin__minus,axiom,
% 5.68/6.04 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ H2 @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ zero_zero_real ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ H2 @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.68/6.04 & ( ( F @ H2 )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_minus
% 5.68/6.04 thf(fact_9855_Maclaurin__all__lt,axiom,
% 5.68/6.04 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.68/6.04 ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( X != zero_zero_real )
% 5.68/6.04 => ( ! [M5: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.68/6.04 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.04 & ( ( F @ X )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_all_lt
% 5.68/6.04 thf(fact_9856_Maclaurin__bi__le,axiom,
% 5.68/6.04 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.68/6.04 ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.68/6.04 & ( ( F @ X )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_bi_le
% 5.68/6.04 thf(fact_9857_Taylor,axiom,
% 5.68/6.04 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ A @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ B ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ A @ C )
% 5.68/6.04 => ( ( ord_less_eq_real @ C @ B )
% 5.68/6.04 => ( ( ord_less_eq_real @ A @ X )
% 5.68/6.04 => ( ( ord_less_eq_real @ X @ B )
% 5.68/6.04 => ( ( X != C )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ( ord_less_real @ X @ C )
% 5.68/6.04 => ( ( ord_less_real @ X @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ C ) ) )
% 5.68/6.04 & ( ~ ( ord_less_real @ X @ C )
% 5.68/6.04 => ( ( ord_less_real @ C @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ X ) ) )
% 5.68/6.04 & ( ( F @ X )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Taylor
% 5.68/6.04 thf(fact_9858_Taylor__up,axiom,
% 5.68/6.04 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ A @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ B ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ A @ C )
% 5.68/6.04 => ( ( ord_less_real @ C @ B )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ C @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ B )
% 5.68/6.04 & ( ( F @ B )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Taylor_up
% 5.68/6.04 thf(fact_9859_Taylor__down,axiom,
% 5.68/6.04 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( ( Diff @ zero_zero_nat )
% 5.68/6.04 = F )
% 5.68/6.04 => ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ A @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ B ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ( ord_less_real @ A @ C )
% 5.68/6.04 => ( ( ord_less_eq_real @ C @ B )
% 5.68/6.04 => ? [T4: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ T4 )
% 5.68/6.04 & ( ord_less_real @ T4 @ C )
% 5.68/6.04 & ( ( F @ A )
% 5.68/6.04 = ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ N ) )
% 5.68/6.04 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Taylor_down
% 5.68/6.04 thf(fact_9860_Maclaurin__lemma2,axiom,
% 5.68/6.04 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.68/6.04 ( ! [M5: nat,T4: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M5 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.68/6.04 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ( N
% 5.68/6.04 = ( suc @ K ) )
% 5.68/6.04 => ! [M2: nat,T5: real] :
% 5.68/6.04 ( ( ( ord_less_nat @ M2 @ N )
% 5.68/6.04 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.68/6.04 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [U2: real] :
% 5.68/6.04 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.68/6.04 @ ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.68/6.04 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.68/6.04 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T5 )
% 5.68/6.04 @ ( plus_plus_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T5 @ P5 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.68/6.04 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T5 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Maclaurin_lemma2
% 5.68/6.04 thf(fact_9861_DERIV__arctan__series,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.04 => ( has_fi5821293074295781190e_real
% 5.68/6.04 @ ^ [X9: real] :
% 5.68/6.04 ( suminf_real
% 5.68/6.04 @ ^ [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 @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [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 ) ) ) ) ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_arctan_series
% 5.68/6.04 thf(fact_9862_isCont__Lb__Ub,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_eq_real @ X3 @ B ) )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.68/6.04 => ? [L6: real,M8: real] :
% 5.68/6.04 ( ! [X5: real] :
% 5.68/6.04 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.68/6.04 & ( ord_less_eq_real @ X5 @ B ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 5.68/6.04 & ( ord_less_eq_real @ ( F @ X5 ) @ M8 ) ) )
% 5.68/6.04 & ! [Y4: real] :
% 5.68/6.04 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 5.68/6.04 & ( ord_less_eq_real @ Y4 @ M8 ) )
% 5.68/6.04 => ? [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 & ( ( F @ X3 )
% 5.68/6.04 = Y4 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % isCont_Lb_Ub
% 5.68/6.04 thf(fact_9863_isCont__real__sqrt,axiom,
% 5.68/6.04 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.68/6.04
% 5.68/6.04 % isCont_real_sqrt
% 5.68/6.04 thf(fact_9864_isCont__real__root,axiom,
% 5.68/6.04 ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.68/6.04
% 5.68/6.04 % isCont_real_root
% 5.68/6.04 thf(fact_9865_isCont__inverse__function2,axiom,
% 5.68/6.04 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ X )
% 5.68/6.04 => ( ( ord_less_real @ X @ B )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.68/6.04 => ( ( G @ ( F @ Z3 ) )
% 5.68/6.04 = Z3 ) ) )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % isCont_inverse_function2
% 5.68/6.04 thf(fact_9866_LIM__less__bound,axiom,
% 5.68/6.04 ! [B: real,X: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ B @ X )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.68/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.68/6.04 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.68/6.04 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIM_less_bound
% 5.68/6.04 thf(fact_9867_isCont__inverse__function,axiom,
% 5.68/6.04 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ D )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 5.68/6.04 => ( ( G @ ( F @ Z3 ) )
% 5.68/6.04 = Z3 ) )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % isCont_inverse_function
% 5.68/6.04 thf(fact_9868_GMVT_H,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_real @ Z3 @ B )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.68/6.04 => ( ! [Z3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ Z3 )
% 5.68/6.04 => ( ( ord_less_real @ Z3 @ B )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.68/6.04 => ? [C2: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ C2 )
% 5.68/6.04 & ( ord_less_real @ C2 @ B )
% 5.68/6.04 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.68/6.04 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % GMVT'
% 5.68/6.04 thf(fact_9869_LIM__cos__div__sin,axiom,
% 5.68/6.04 ( filterlim_real_real
% 5.68/6.04 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIM_cos_div_sin
% 5.68/6.04 thf(fact_9870_summable__Leibniz_I3_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ( topolo6980174941875973593q_real @ A )
% 5.68/6.04 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.68/6.04 => ! [N7: nat] :
% 5.68/6.04 ( member_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.68/6.04 @ ( set_or1222579329274155063t_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz(3)
% 5.68/6.04 thf(fact_9871_summable__Leibniz_I2_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ( topolo6980174941875973593q_real @ A )
% 5.68/6.04 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.68/6.04 => ! [N7: nat] :
% 5.68/6.04 ( member_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.68/6.04 @ ( set_or1222579329274155063t_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz(2)
% 5.68/6.04 thf(fact_9872_filterlim__Suc,axiom,
% 5.68/6.04 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.68/6.04
% 5.68/6.04 % filterlim_Suc
% 5.68/6.04 thf(fact_9873_mult__nat__right__at__top,axiom,
% 5.68/6.04 ! [C: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.68/6.04 => ( filterlim_nat_nat
% 5.68/6.04 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.68/6.04 @ at_top_nat
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % mult_nat_right_at_top
% 5.68/6.04 thf(fact_9874_mult__nat__left__at__top,axiom,
% 5.68/6.04 ! [C: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.68/6.04 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % mult_nat_left_at_top
% 5.68/6.04 thf(fact_9875_monoseq__convergent,axiom,
% 5.68/6.04 ! [X8: nat > real,B4: real] :
% 5.68/6.04 ( ( topolo6980174941875973593q_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B4 )
% 5.68/6.04 => ~ ! [L6: real] :
% 5.68/6.04 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % monoseq_convergent
% 5.68/6.04 thf(fact_9876_LIMSEQ__root,axiom,
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_root
% 5.68/6.04 thf(fact_9877_nested__sequence__unique,axiom,
% 5.68/6.04 ! [F: nat > real,G: nat > real] :
% 5.68/6.04 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.68/6.04 => ( ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 => ? [L4: real] :
% 5.68/6.04 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 5.68/6.04 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.68/6.04 & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 5.68/6.04 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nested_sequence_unique
% 5.68/6.04 thf(fact_9878_LIMSEQ__inverse__zero,axiom,
% 5.68/6.04 ! [X8: nat > real] :
% 5.68/6.04 ( ! [R3: real] :
% 5.68/6.04 ? [N8: nat] :
% 5.68/6.04 ! [N3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.68/6.04 => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_zero
% 5.68/6.04 thf(fact_9879_LIMSEQ__root__const,axiom,
% 5.68/6.04 ! [C: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ C )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_root_const
% 5.68/6.04 thf(fact_9880_LIMSEQ__inverse__real__of__nat,axiom,
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_real_of_nat
% 5.68/6.04 thf(fact_9881_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.68/6.04 ! [R2: real] :
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ R2 )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_real_of_nat_add
% 5.68/6.04 thf(fact_9882_increasing__LIMSEQ,axiom,
% 5.68/6.04 ! [F: nat > real,L2: real] :
% 5.68/6.04 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.68/6.04 => ( ! [E2: real] :
% 5.68/6.04 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.68/6.04 => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 5.68/6.04 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % increasing_LIMSEQ
% 5.68/6.04 thf(fact_9883_LIMSEQ__realpow__zero,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( ord_less_real @ X @ one_one_real )
% 5.68/6.04 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_realpow_zero
% 5.68/6.04 thf(fact_9884_LIMSEQ__divide__realpow__zero,axiom,
% 5.68/6.04 ! [X: real,A: real] :
% 5.68/6.04 ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_divide_realpow_zero
% 5.68/6.04 thf(fact_9885_LIMSEQ__abs__realpow__zero2,axiom,
% 5.68/6.04 ! [C: real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.68/6.04 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_abs_realpow_zero2
% 5.68/6.04 thf(fact_9886_LIMSEQ__abs__realpow__zero,axiom,
% 5.68/6.04 ! [C: real] :
% 5.68/6.04 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.68/6.04 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_abs_realpow_zero
% 5.68/6.04 thf(fact_9887_LIMSEQ__inverse__realpow__zero,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_real @ one_one_real @ X )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_realpow_zero
% 5.68/6.04 thf(fact_9888_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.68/6.04 ! [R2: real] :
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ R2 )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.68/6.04 thf(fact_9889_tendsto__exp__limit__sequentially,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % tendsto_exp_limit_sequentially
% 5.68/6.04 thf(fact_9890_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.68/6.04 ! [R2: real] :
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ R2 )
% 5.68/6.04 @ at_top_nat ) ).
% 5.68/6.04
% 5.68/6.04 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.68/6.04 thf(fact_9891_summable__Leibniz_I1_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ( topolo6980174941875973593q_real @ A )
% 5.68/6.04 => ( summable_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz(1)
% 5.68/6.04 thf(fact_9892_summable,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( summable_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable
% 5.68/6.04 thf(fact_9893_cos__diff__limit__1,axiom,
% 5.68/6.04 ! [Theta: nat > real,Theta2: real] :
% 5.68/6.04 ( ( filterlim_nat_real
% 5.68/6.04 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 => ~ ! [K2: nat > int] :
% 5.68/6.04 ~ ( filterlim_nat_real
% 5.68/6.04 @ ^ [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 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % cos_diff_limit_1
% 5.68/6.04 thf(fact_9894_cos__limit__1,axiom,
% 5.68/6.04 ! [Theta: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real
% 5.68/6.04 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 => ? [K2: nat > int] :
% 5.68/6.04 ( filterlim_nat_real
% 5.68/6.04 @ ^ [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 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % cos_limit_1
% 5.68/6.04 thf(fact_9895_summable__Leibniz_I4_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ( topolo6980174941875973593q_real @ A )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.68/6.04 @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz(4)
% 5.68/6.04 thf(fact_9896_zeroseq__arctan__series,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % zeroseq_arctan_series
% 5.68/6.04 thf(fact_9897_summable__Leibniz_H_I2_J,axiom,
% 5.68/6.04 ! [A: nat > real,N: nat] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( ord_less_eq_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz'(2)
% 5.68/6.04 thf(fact_9898_summable__Leibniz_H_I3_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.68/6.04 @ at_top_nat ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz'(3)
% 5.68/6.04 thf(fact_9899_sums__alternating__upper__lower,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ? [L4: real] :
% 5.68/6.04 ( ! [N7: nat] :
% 5.68/6.04 ( ord_less_eq_real
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.68/6.04 @ L4 )
% 5.68/6.04 & ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ L4 )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 & ! [N7: nat] :
% 5.68/6.04 ( ord_less_eq_real @ L4
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 5.68/6.04 & ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ L4 )
% 5.68/6.04 @ at_top_nat ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % sums_alternating_upper_lower
% 5.68/6.04 thf(fact_9900_summable__Leibniz_I5_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ( topolo6980174941875973593q_real @ A )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.68/6.04 @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz(5)
% 5.68/6.04 thf(fact_9901_summable__Leibniz_H_I4_J,axiom,
% 5.68/6.04 ! [A: nat > real,N: nat] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( ord_less_eq_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.68/6.04 @ ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz'(4)
% 5.68/6.04 thf(fact_9902_summable__Leibniz_H_I5_J,axiom,
% 5.68/6.04 ! [A: nat > real] :
% 5.68/6.04 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.68/6.04 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.68/6.04 => ( filterlim_nat_real
% 5.68/6.04 @ ^ [N2: nat] :
% 5.68/6.04 ( groups6591440286371151544t_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.68/6.04 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real
% 5.68/6.04 @ ( suminf_real
% 5.68/6.04 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.68/6.04 @ at_top_nat ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_Leibniz'(5)
% 5.68/6.04 thf(fact_9903_eventually__sequentially__Suc,axiom,
% 5.68/6.04 ! [P: nat > $o] :
% 5.68/6.04 ( ( eventually_nat
% 5.68/6.04 @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % eventually_sequentially_Suc
% 5.68/6.04 thf(fact_9904_eventually__sequentially__seg,axiom,
% 5.68/6.04 ! [P: nat > $o,K: nat] :
% 5.68/6.04 ( ( eventually_nat
% 5.68/6.04 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % eventually_sequentially_seg
% 5.68/6.04 thf(fact_9905_sequentially__offset,axiom,
% 5.68/6.04 ! [P: nat > $o,K: nat] :
% 5.68/6.04 ( ( eventually_nat @ P @ at_top_nat )
% 5.68/6.04 => ( eventually_nat
% 5.68/6.04 @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 5.68/6.04 @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % sequentially_offset
% 5.68/6.04 thf(fact_9906_le__sequentially,axiom,
% 5.68/6.04 ! [F5: filter_nat] :
% 5.68/6.04 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.68/6.04 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % le_sequentially
% 5.68/6.04 thf(fact_9907_eventually__sequentiallyI,axiom,
% 5.68/6.04 ! [C: nat,P: nat > $o] :
% 5.68/6.04 ( ! [X3: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ C @ X3 )
% 5.68/6.04 => ( P @ X3 ) )
% 5.68/6.04 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % eventually_sequentiallyI
% 5.68/6.04 thf(fact_9908_eventually__sequentially,axiom,
% 5.68/6.04 ! [P: nat > $o] :
% 5.68/6.04 ( ( eventually_nat @ P @ at_top_nat )
% 5.68/6.04 = ( ? [N6: nat] :
% 5.68/6.04 ! [N2: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.68/6.04 => ( P @ N2 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % eventually_sequentially
% 5.68/6.04 thf(fact_9909_real__bounded__linear,axiom,
% 5.68/6.04 ( real_V5970128139526366754l_real
% 5.68/6.04 = ( ^ [F3: real > real] :
% 5.68/6.04 ? [C3: real] :
% 5.68/6.04 ( F3
% 5.68/6.04 = ( ^ [X2: real] : ( times_times_real @ X2 @ C3 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % real_bounded_linear
% 5.68/6.04 thf(fact_9910_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.68/6.04 ! [L2: nat,U: nat] :
% 5.68/6.04 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.68/6.04 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastSucAtMost_greaterThanAtMost
% 5.68/6.04 thf(fact_9911_sqrt__at__top,axiom,
% 5.68/6.04 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.68/6.04
% 5.68/6.04 % sqrt_at_top
% 5.68/6.04 thf(fact_9912_tendsto__power__div__exp__0,axiom,
% 5.68/6.04 ! [K: nat] :
% 5.68/6.04 ( filterlim_real_real
% 5.68/6.04 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.68/6.04 @ at_top_real ) ).
% 5.68/6.04
% 5.68/6.04 % tendsto_power_div_exp_0
% 5.68/6.04 thf(fact_9913_tendsto__exp__limit__at__top,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( filterlim_real_real
% 5.68/6.04 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y ) ) @ Y )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.68/6.04 @ at_top_real ) ).
% 5.68/6.04
% 5.68/6.04 % tendsto_exp_limit_at_top
% 5.68/6.04 thf(fact_9914_filterlim__tan__at__left,axiom,
% 5.68/6.04 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 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % filterlim_tan_at_left
% 5.68/6.04 thf(fact_9915_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.68/6.04 ! [B: real,F: real > real,Flim: real] :
% 5.68/6.04 ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ B @ X3 )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.68/6.04 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.68/6.04 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_neg_imp_decreasing_at_top
% 5.68/6.04 thf(fact_9916_tendsto__arctan__at__top,axiom,
% 5.68/6.04 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.68/6.04
% 5.68/6.04 % tendsto_arctan_at_top
% 5.68/6.04 thf(fact_9917_at__top__le__at__infinity,axiom,
% 5.68/6.04 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.68/6.04
% 5.68/6.04 % at_top_le_at_infinity
% 5.68/6.04 thf(fact_9918_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.68/6.04 ! [L2: int,U: int] :
% 5.68/6.04 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.68/6.04 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.68/6.04 thf(fact_9919_filterlim__pow__at__bot__even,axiom,
% 5.68/6.04 ! [N: nat,F: real > real,F5: filter_real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.68/6.04 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( filterlim_real_real
% 5.68/6.04 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.68/6.04 @ at_top_real
% 5.68/6.04 @ F5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % filterlim_pow_at_bot_even
% 5.68/6.04 thf(fact_9920_at__bot__le__at__infinity,axiom,
% 5.68/6.04 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.68/6.04
% 5.68/6.04 % at_bot_le_at_infinity
% 5.68/6.04 thf(fact_9921_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.68/6.04 ! [B: real,F: real > real,Flim: real] :
% 5.68/6.04 ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ X3 @ B )
% 5.68/6.04 => ? [Y4: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.68/6.04 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.68/6.04 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_pos_imp_increasing_at_bot
% 5.68/6.04 thf(fact_9922_filterlim__pow__at__bot__odd,axiom,
% 5.68/6.04 ! [N: nat,F: real > real,F5: filter_real] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.68/6.04 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.68/6.04 => ( filterlim_real_real
% 5.68/6.04 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.68/6.04 @ at_bot_real
% 5.68/6.04 @ F5 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % filterlim_pow_at_bot_odd
% 5.68/6.04 thf(fact_9923_tendsto__arctan__at__bot,axiom,
% 5.68/6.04 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.68/6.04
% 5.68/6.04 % tendsto_arctan_at_bot
% 5.68/6.04 thf(fact_9924_Bseq__eq__bounded,axiom,
% 5.68/6.04 ! [F: nat > real,A: real,B: real] :
% 5.68/6.04 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.68/6.04 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % Bseq_eq_bounded
% 5.68/6.04 thf(fact_9925_Bseq__realpow,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.68/6.04 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % Bseq_realpow
% 5.68/6.04 thf(fact_9926_tendsto__exp__limit__at__right,axiom,
% 5.68/6.04 ! [X: real] :
% 5.68/6.04 ( filterlim_real_real
% 5.68/6.04 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.68/6.04 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % tendsto_exp_limit_at_right
% 5.68/6.04 thf(fact_9927_filterlim__tan__at__right,axiom,
% 5.68/6.04 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 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % filterlim_tan_at_right
% 5.68/6.04 thf(fact_9928_eventually__at__right__to__0,axiom,
% 5.68/6.04 ! [P: real > $o,A: real] :
% 5.68/6.04 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.68/6.04 = ( eventually_real
% 5.68/6.04 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.68/6.04 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % eventually_at_right_to_0
% 5.68/6.04 thf(fact_9929_atLeast__Suc__greaterThan,axiom,
% 5.68/6.04 ! [K: nat] :
% 5.68/6.04 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.68/6.04 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeast_Suc_greaterThan
% 5.68/6.04 thf(fact_9930_decseq__bounded,axiom,
% 5.68/6.04 ! [X8: nat > real,B4: real] :
% 5.68/6.04 ( ( order_9091379641038594480t_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ B4 @ ( X8 @ I4 ) )
% 5.68/6.04 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % decseq_bounded
% 5.68/6.04 thf(fact_9931_greaterThan__0,axiom,
% 5.68/6.04 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.68/6.04 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.68/6.04
% 5.68/6.04 % greaterThan_0
% 5.68/6.04 thf(fact_9932_greaterThan__Suc,axiom,
% 5.68/6.04 ! [K: nat] :
% 5.68/6.04 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.68/6.04 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % greaterThan_Suc
% 5.68/6.04 thf(fact_9933_decseq__convergent,axiom,
% 5.68/6.04 ! [X8: nat > real,B4: real] :
% 5.68/6.04 ( ( order_9091379641038594480t_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ B4 @ ( X8 @ I4 ) )
% 5.68/6.04 => ~ ! [L6: real] :
% 5.68/6.04 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.68/6.04 => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % decseq_convergent
% 5.68/6.04 thf(fact_9934_atLeast__Suc,axiom,
% 5.68/6.04 ! [K: nat] :
% 5.68/6.04 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.68/6.04 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeast_Suc
% 5.68/6.04 thf(fact_9935_GMVT,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_eq_real @ X3 @ B ) )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ( ord_less_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_real @ X3 @ B ) )
% 5.68/6.04 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_eq_real @ X3 @ B ) )
% 5.68/6.04 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ( ord_less_real @ A @ X3 )
% 5.68/6.04 & ( ord_less_real @ X3 @ B ) )
% 5.68/6.04 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.68/6.04 => ? [G_c: real,F_c: real,C2: real] :
% 5.68/6.04 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.68/6.04 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.68/6.04 & ( ord_less_real @ A @ C2 )
% 5.68/6.04 & ( ord_less_real @ C2 @ B )
% 5.68/6.04 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.68/6.04 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % GMVT
% 5.68/6.04 thf(fact_9936_MVT,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_real @ X3 @ B )
% 5.68/6.04 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.68/6.04 => ? [L4: real,Z3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ Z3 )
% 5.68/6.04 & ( ord_less_real @ Z3 @ B )
% 5.68/6.04 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 5.68/6.04 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.68/6.04 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % MVT
% 5.68/6.04 thf(fact_9937_continuous__on__arcosh_H,axiom,
% 5.68/6.04 ! [A2: set_real,F: real > real] :
% 5.68/6.04 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( member_real @ X3 @ A2 )
% 5.68/6.04 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.68/6.04 => ( topolo5044208981011980120l_real @ A2
% 5.68/6.04 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % continuous_on_arcosh'
% 5.68/6.04 thf(fact_9938_continuous__image__closed__interval,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real] :
% 5.68/6.04 ( ( ord_less_eq_real @ A @ B )
% 5.68/6.04 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.68/6.04 => ? [C2: real,D3: real] :
% 5.68/6.04 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.68/6.04 = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 5.68/6.04 & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % continuous_image_closed_interval
% 5.68/6.04 thf(fact_9939_continuous__on__arcosh,axiom,
% 5.68/6.04 ! [A2: set_real] :
% 5.68/6.04 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.68/6.04 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % continuous_on_arcosh
% 5.68/6.04 thf(fact_9940_continuous__on__artanh,axiom,
% 5.68/6.04 ! [A2: set_real] :
% 5.68/6.04 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.68/6.04 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % continuous_on_artanh
% 5.68/6.04 thf(fact_9941_DERIV__isconst2,axiom,
% 5.68/6.04 ! [A: real,B: real,F: real > real,X: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ B )
% 5.68/6.04 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.68/6.04 => ( ! [X3: real] :
% 5.68/6.04 ( ( ord_less_real @ A @ X3 )
% 5.68/6.04 => ( ( ord_less_real @ X3 @ B )
% 5.68/6.04 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.68/6.04 => ( ( ord_less_eq_real @ A @ X )
% 5.68/6.04 => ( ( ord_less_eq_real @ X @ B )
% 5.68/6.04 => ( ( F @ X )
% 5.68/6.04 = ( F @ A ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % DERIV_isconst2
% 5.68/6.04 thf(fact_9942_upto_Opelims,axiom,
% 5.68/6.04 ! [X: int,Xa2: int,Y2: list_int] :
% 5.68/6.04 ( ( ( upto @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.68/6.04 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.68/6.04 => ( Y2 = nil_int ) ) )
% 5.68/6.04 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto.pelims
% 5.68/6.04 thf(fact_9943_nth__upto,axiom,
% 5.68/6.04 ! [I2: int,K: nat,J: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.68/6.04 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.68/6.04 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nth_upto
% 5.68/6.04 thf(fact_9944_length__upto,axiom,
% 5.68/6.04 ! [I2: int,J: int] :
% 5.68/6.04 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 5.68/6.04 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % length_upto
% 5.68/6.04 thf(fact_9945_upto__rec__numeral_I1_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = nil_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec_numeral(1)
% 5.68/6.04 thf(fact_9946_upto__rec__numeral_I4_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( 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 ) ) ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = nil_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec_numeral(4)
% 5.68/6.04 thf(fact_9947_upto__rec__numeral_I3_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = ( 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 ) ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.68/6.04 = nil_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec_numeral(3)
% 5.68/6.04 thf(fact_9948_upto__rec__numeral_I2_J,axiom,
% 5.68/6.04 ! [M: num,N: num] :
% 5.68/6.04 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.68/6.04 = nil_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec_numeral(2)
% 5.68/6.04 thf(fact_9949_atLeastAtMost__upto,axiom,
% 5.68/6.04 ( set_or1266510415728281911st_int
% 5.68/6.04 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastAtMost_upto
% 5.68/6.04 thf(fact_9950_upto__split2,axiom,
% 5.68/6.04 ! [I2: int,J: int,K: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( ord_less_eq_int @ J @ K )
% 5.68/6.04 => ( ( upto @ I2 @ K )
% 5.68/6.04 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_split2
% 5.68/6.04 thf(fact_9951_upto__rec1,axiom,
% 5.68/6.04 ! [I2: int,J: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( upto @ I2 @ J )
% 5.68/6.04 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec1
% 5.68/6.04 thf(fact_9952_upto_Osimps,axiom,
% 5.68/6.04 ( upto
% 5.68/6.04 = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto.simps
% 5.68/6.04 thf(fact_9953_upto_Oelims,axiom,
% 5.68/6.04 ! [X: int,Xa2: int,Y2: list_int] :
% 5.68/6.04 ( ( ( upto @ X @ Xa2 )
% 5.68/6.04 = Y2 )
% 5.68/6.04 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.68/6.04 => ( Y2
% 5.68/6.04 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.68/6.04 => ( Y2 = nil_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto.elims
% 5.68/6.04 thf(fact_9954_upto__split1,axiom,
% 5.68/6.04 ! [I2: int,J: int,K: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( ord_less_eq_int @ J @ K )
% 5.68/6.04 => ( ( upto @ I2 @ K )
% 5.68/6.04 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_split1
% 5.68/6.04 thf(fact_9955_upto__rec2,axiom,
% 5.68/6.04 ! [I2: int,J: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( upto @ I2 @ J )
% 5.68/6.04 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_rec2
% 5.68/6.04 thf(fact_9956_atLeastLessThan__upto,axiom,
% 5.68/6.04 ( set_or4662586982721622107an_int
% 5.68/6.04 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % atLeastLessThan_upto
% 5.68/6.04 thf(fact_9957_greaterThanAtMost__upto,axiom,
% 5.68/6.04 ( set_or6656581121297822940st_int
% 5.68/6.04 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % greaterThanAtMost_upto
% 5.68/6.04 thf(fact_9958_upto__split3,axiom,
% 5.68/6.04 ! [I2: int,J: int,K: int] :
% 5.68/6.04 ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( ord_less_eq_int @ J @ K )
% 5.68/6.04 => ( ( upto @ I2 @ K )
% 5.68/6.04 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto_split3
% 5.68/6.04 thf(fact_9959_greaterThanLessThan__upto,axiom,
% 5.68/6.04 ( set_or5832277885323065728an_int
% 5.68/6.04 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % greaterThanLessThan_upto
% 5.68/6.04 thf(fact_9960_upto_Opsimps,axiom,
% 5.68/6.04 ! [I2: int,J: int] :
% 5.68/6.04 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.68/6.04 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( upto @ I2 @ J )
% 5.68/6.04 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.68/6.04 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.68/6.04 => ( ( upto @ I2 @ J )
% 5.68/6.04 = nil_int ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % upto.psimps
% 5.68/6.04 thf(fact_9961_mono__Suc,axiom,
% 5.68/6.04 order_mono_nat_nat @ suc ).
% 5.68/6.04
% 5.68/6.04 % mono_Suc
% 5.68/6.04 thf(fact_9962_mono__times__nat,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % mono_times_nat
% 5.68/6.04 thf(fact_9963_incseq__bounded,axiom,
% 5.68/6.04 ! [X8: nat > real,B4: real] :
% 5.68/6.04 ( ( order_mono_nat_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B4 )
% 5.68/6.04 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % incseq_bounded
% 5.68/6.04 thf(fact_9964_incseq__convergent,axiom,
% 5.68/6.04 ! [X8: nat > real,B4: real] :
% 5.68/6.04 ( ( order_mono_nat_real @ X8 )
% 5.68/6.04 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B4 )
% 5.68/6.04 => ~ ! [L6: real] :
% 5.68/6.04 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.68/6.04 => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % incseq_convergent
% 5.68/6.04 thf(fact_9965_mono__ge2__power__minus__self,axiom,
% 5.68/6.04 ! [K: nat] :
% 5.68/6.04 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.68/6.04 => ( order_mono_nat_nat
% 5.68/6.04 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % mono_ge2_power_minus_self
% 5.68/6.04 thf(fact_9966_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.68/6.04 ! [F: nat > real,G: nat > nat] :
% 5.68/6.04 ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.04 => ( ( order_mono_nat_real @ F )
% 5.68/6.04 => ( ( order_5726023648592871131at_nat @ G )
% 5.68/6.04 => ( ( bfun_nat_real
% 5.68/6.04 @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 5.68/6.04 @ at_top_nat )
% 5.68/6.04 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % nonneg_incseq_Bseq_subseq_iff
% 5.68/6.04 thf(fact_9967_strict__mono__imp__increasing,axiom,
% 5.68/6.04 ! [F: nat > nat,N: nat] :
% 5.68/6.04 ( ( order_5726023648592871131at_nat @ F )
% 5.68/6.04 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % strict_mono_imp_increasing
% 5.68/6.04 thf(fact_9968_inj__sgn__power,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.04 => ( inj_on_real_real
% 5.68/6.04 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.68/6.04 @ top_top_set_real ) ) ).
% 5.68/6.04
% 5.68/6.04 % inj_sgn_power
% 5.68/6.04 thf(fact_9969_inj__on__diff__nat,axiom,
% 5.68/6.04 ! [N5: set_nat,K: nat] :
% 5.68/6.04 ( ! [N3: nat] :
% 5.68/6.04 ( ( member_nat @ N3 @ N5 )
% 5.68/6.04 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.68/6.04 => ( inj_on_nat_nat
% 5.68/6.04 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.68/6.04 @ N5 ) ) ).
% 5.68/6.04
% 5.68/6.04 % inj_on_diff_nat
% 5.68/6.04 thf(fact_9970_inj__Suc,axiom,
% 5.68/6.04 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.68/6.04
% 5.68/6.04 % inj_Suc
% 5.68/6.04 thf(fact_9971_summable__reindex,axiom,
% 5.68/6.04 ! [F: nat > real,G: nat > nat] :
% 5.68/6.04 ( ( summable_real @ F )
% 5.68/6.04 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.68/6.04 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.04 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % summable_reindex
% 5.68/6.04 thf(fact_9972_suminf__reindex__mono,axiom,
% 5.68/6.04 ! [F: nat > real,G: nat > nat] :
% 5.68/6.04 ( ( summable_real @ F )
% 5.68/6.04 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.68/6.04 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.04 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % suminf_reindex_mono
% 5.68/6.04 thf(fact_9973_inj__on__char__of__nat,axiom,
% 5.68/6.04 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % inj_on_char_of_nat
% 5.68/6.04 thf(fact_9974_suminf__reindex,axiom,
% 5.68/6.04 ! [F: nat > real,G: nat > nat] :
% 5.68/6.04 ( ( summable_real @ F )
% 5.68/6.04 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.68/6.04 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.68/6.04 => ( ! [X3: nat] :
% 5.68/6.04 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.68/6.04 => ( ( F @ X3 )
% 5.68/6.04 = zero_zero_real ) )
% 5.68/6.04 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.68/6.04 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % suminf_reindex
% 5.68/6.04 thf(fact_9975_powr__real__of__int_H,axiom,
% 5.68/6.04 ! [X: real,N: int] :
% 5.68/6.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.68/6.04 => ( ( ( X != zero_zero_real )
% 5.68/6.04 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.68/6.04 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.68/6.04 = ( power_int_real @ X @ N ) ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % powr_real_of_int'
% 5.68/6.04 thf(fact_9976_min__Suc__Suc,axiom,
% 5.68/6.04 ! [M: nat,N: nat] :
% 5.68/6.04 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.68/6.04 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.68/6.04
% 5.68/6.04 % min_Suc_Suc
% 5.68/6.04 thf(fact_9977_min__0R,axiom,
% 5.68/6.04 ! [N: nat] :
% 5.68/6.04 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.68/6.05 = zero_zero_nat ) ).
% 5.68/6.05
% 5.68/6.05 % min_0R
% 5.68/6.05 thf(fact_9978_min__0L,axiom,
% 5.68/6.05 ! [N: nat] :
% 5.68/6.05 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.68/6.05 = zero_zero_nat ) ).
% 5.68/6.05
% 5.68/6.05 % min_0L
% 5.68/6.05 thf(fact_9979_min__numeral__Suc,axiom,
% 5.68/6.05 ! [K: num,N: nat] :
% 5.68/6.05 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.68/6.05 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % min_numeral_Suc
% 5.68/6.05 thf(fact_9980_min__Suc__numeral,axiom,
% 5.68/6.05 ! [N: nat,K: num] :
% 5.68/6.05 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.68/6.05 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % min_Suc_numeral
% 5.68/6.05 thf(fact_9981_nat__mult__min__right,axiom,
% 5.68/6.05 ! [M: nat,N: nat,Q2: nat] :
% 5.68/6.05 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.68/6.05 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % nat_mult_min_right
% 5.68/6.05 thf(fact_9982_nat__mult__min__left,axiom,
% 5.68/6.05 ! [M: nat,N: nat,Q2: nat] :
% 5.68/6.05 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.68/6.05 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % nat_mult_min_left
% 5.68/6.05 thf(fact_9983_min__diff,axiom,
% 5.68/6.05 ! [M: nat,I2: nat,N: nat] :
% 5.68/6.05 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 5.68/6.05 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I2 ) ) ).
% 5.68/6.05
% 5.68/6.05 % min_diff
% 5.68/6.05 thf(fact_9984_inf__nat__def,axiom,
% 5.68/6.05 inf_inf_nat = ord_min_nat ).
% 5.68/6.05
% 5.68/6.05 % inf_nat_def
% 5.68/6.05 thf(fact_9985_concat__bit__assoc__sym,axiom,
% 5.68/6.05 ! [M: nat,N: nat,K: int,L2: int,R2: int] :
% 5.68/6.05 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 )
% 5.68/6.05 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % concat_bit_assoc_sym
% 5.68/6.05 thf(fact_9986_take__bit__concat__bit__eq,axiom,
% 5.68/6.05 ! [M: nat,N: nat,K: int,L2: int] :
% 5.68/6.05 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.68/6.05 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % take_bit_concat_bit_eq
% 5.68/6.05 thf(fact_9987_min__Suc1,axiom,
% 5.68/6.05 ! [N: nat,M: nat] :
% 5.68/6.05 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.68/6.05 = ( case_nat_nat @ zero_zero_nat
% 5.68/6.05 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N @ M3 ) )
% 5.68/6.05 @ M ) ) ).
% 5.68/6.05
% 5.68/6.05 % min_Suc1
% 5.68/6.05 thf(fact_9988_min__Suc2,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.68/6.05 = ( case_nat_nat @ zero_zero_nat
% 5.68/6.05 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N ) )
% 5.68/6.05 @ M ) ) ).
% 5.68/6.05
% 5.68/6.05 % min_Suc2
% 5.68/6.05 thf(fact_9989_min__enat__simps_I2_J,axiom,
% 5.68/6.05 ! [Q2: extended_enat] :
% 5.68/6.05 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.68/6.05 = zero_z5237406670263579293d_enat ) ).
% 5.68/6.05
% 5.68/6.05 % min_enat_simps(2)
% 5.68/6.05 thf(fact_9990_min__enat__simps_I3_J,axiom,
% 5.68/6.05 ! [Q2: extended_enat] :
% 5.68/6.05 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.68/6.05 = zero_z5237406670263579293d_enat ) ).
% 5.68/6.05
% 5.68/6.05 % min_enat_simps(3)
% 5.68/6.05 thf(fact_9991_inf__enat__def,axiom,
% 5.68/6.05 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.68/6.05
% 5.68/6.05 % inf_enat_def
% 5.68/6.05 thf(fact_9992_hd__upt,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_nat @ I2 @ J )
% 5.68/6.05 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 5.68/6.05 = I2 ) ) ).
% 5.68/6.05
% 5.68/6.05 % hd_upt
% 5.68/6.05 thf(fact_9993_upt__conv__Nil,axiom,
% 5.68/6.05 ! [J: nat,I2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ J @ I2 )
% 5.68/6.05 => ( ( upt @ I2 @ J )
% 5.68/6.05 = nil_nat ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_conv_Nil
% 5.68/6.05 thf(fact_9994_drop__upt,axiom,
% 5.68/6.05 ! [M: nat,I2: nat,J: nat] :
% 5.68/6.05 ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 5.68/6.05 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 5.68/6.05
% 5.68/6.05 % drop_upt
% 5.68/6.05 thf(fact_9995_length__upt,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 5.68/6.05 = ( minus_minus_nat @ J @ I2 ) ) ).
% 5.68/6.05
% 5.68/6.05 % length_upt
% 5.68/6.05 thf(fact_9996_upt__eq__Nil__conv,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ( upt @ I2 @ J )
% 5.68/6.05 = nil_nat )
% 5.68/6.05 = ( ( J = zero_zero_nat )
% 5.68/6.05 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_eq_Nil_conv
% 5.68/6.05 thf(fact_9997_nth__upt,axiom,
% 5.68/6.05 ! [I2: nat,K: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 5.68/6.05 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 5.68/6.05 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % nth_upt
% 5.68/6.05 thf(fact_9998_take__upt,axiom,
% 5.68/6.05 ! [I2: nat,M: nat,N: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 5.68/6.05 => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 5.68/6.05 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % take_upt
% 5.68/6.05 thf(fact_9999_upt__rec__numeral,axiom,
% 5.68/6.05 ! [M: num,N: num] :
% 5.68/6.05 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.05 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.05 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.68/6.05 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.05 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.68/6.05 = nil_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_rec_numeral
% 5.68/6.05 thf(fact_10000_map__add__upt,axiom,
% 5.68/6.05 ! [N: nat,M: nat] :
% 5.68/6.05 ( ( map_nat_nat
% 5.68/6.05 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 5.68/6.05 @ ( upt @ zero_zero_nat @ M ) )
% 5.68/6.05 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % map_add_upt
% 5.68/6.05 thf(fact_10001_map__Suc__upt,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.68/6.05 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % map_Suc_upt
% 5.68/6.05 thf(fact_10002_upt__Suc,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.05 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.68/6.05 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.68/6.05 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.05 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.68/6.05 = nil_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_Suc
% 5.68/6.05 thf(fact_10003_upt__Suc__append,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.05 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.68/6.05 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_Suc_append
% 5.68/6.05 thf(fact_10004_upt__rec,axiom,
% 5.68/6.05 ( upt
% 5.68/6.05 = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_rec
% 5.68/6.05 thf(fact_10005_upt__conv__Cons,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_nat @ I2 @ J )
% 5.68/6.05 => ( ( upt @ I2 @ J )
% 5.68/6.05 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_conv_Cons
% 5.68/6.05 thf(fact_10006_upt__conv__Cons__Cons,axiom,
% 5.68/6.05 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.68/6.05 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.68/6.05 = ( upt @ M @ Q2 ) )
% 5.68/6.05 = ( ( cons_nat @ N @ Ns )
% 5.68/6.05 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_conv_Cons_Cons
% 5.68/6.05 thf(fact_10007_upt__add__eq__append,axiom,
% 5.68/6.05 ! [I2: nat,J: nat,K: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.05 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.68/6.05 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_add_eq_append
% 5.68/6.05 thf(fact_10008_greaterThanLessThan__upt,axiom,
% 5.68/6.05 ( set_or5834768355832116004an_nat
% 5.68/6.05 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % greaterThanLessThan_upt
% 5.68/6.05 thf(fact_10009_greaterThanAtMost__upt,axiom,
% 5.68/6.05 ( set_or6659071591806873216st_nat
% 5.68/6.05 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % greaterThanAtMost_upt
% 5.68/6.05 thf(fact_10010_atLeastLessThan__upt,axiom,
% 5.68/6.05 ( set_or4665077453230672383an_nat
% 5.68/6.05 = ( ^ [I3: nat,J3: nat] : ( set_nat2 @ ( upt @ I3 @ J3 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % atLeastLessThan_upt
% 5.68/6.05 thf(fact_10011_atLeastAtMost__upt,axiom,
% 5.68/6.05 ( set_or1269000886237332187st_nat
% 5.68/6.05 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % atLeastAtMost_upt
% 5.68/6.05 thf(fact_10012_atLeast__upt,axiom,
% 5.68/6.05 ( set_ord_lessThan_nat
% 5.68/6.05 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % atLeast_upt
% 5.68/6.05 thf(fact_10013_upt__eq__Cons__conv,axiom,
% 5.68/6.05 ! [I2: nat,J: nat,X: nat,Xs2: list_nat] :
% 5.68/6.05 ( ( ( upt @ I2 @ J )
% 5.68/6.05 = ( cons_nat @ X @ Xs2 ) )
% 5.68/6.05 = ( ( ord_less_nat @ I2 @ J )
% 5.68/6.05 & ( I2 = X )
% 5.68/6.05 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 5.68/6.05 = Xs2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % upt_eq_Cons_conv
% 5.68/6.05 thf(fact_10014_atMost__upto,axiom,
% 5.68/6.05 ( set_ord_atMost_nat
% 5.68/6.05 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % atMost_upto
% 5.68/6.05 thf(fact_10015_map__decr__upt,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( map_nat_nat
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.68/6.05 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.68/6.05 = ( upt @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % map_decr_upt
% 5.68/6.05 thf(fact_10016_sorted__list__of__set__atMost__Suc,axiom,
% 5.68/6.05 ! [K: nat] :
% 5.68/6.05 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.68/6.05 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_list_of_set_atMost_Suc
% 5.68/6.05 thf(fact_10017_sorted__list__of__set__lessThan__Suc,axiom,
% 5.68/6.05 ! [K: nat] :
% 5.68/6.05 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.68/6.05 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_list_of_set_lessThan_Suc
% 5.68/6.05 thf(fact_10018_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.68/6.05 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.68/6.05 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_list_of_set_greaterThanAtMost
% 5.68/6.05 thf(fact_10019_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.68/6.05 ! [I2: nat,J: nat] :
% 5.68/6.05 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.68/6.05 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.68/6.05 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_list_of_set_greaterThanLessThan
% 5.68/6.05 thf(fact_10020_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.68/6.05 ! [N: nat,J: nat,I2: nat] :
% 5.68/6.05 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 5.68/6.05 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 5.68/6.05 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % nth_sorted_list_of_set_greaterThanAtMost
% 5.68/6.05 thf(fact_10021_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.68/6.05 ! [N: nat,J: nat,I2: nat] :
% 5.68/6.05 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.68/6.05 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 5.68/6.05 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % nth_sorted_list_of_set_greaterThanLessThan
% 5.68/6.05 thf(fact_10022_sum__list__upt,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ M @ N )
% 5.68/6.05 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.68/6.05 = ( groups3542108847815614940at_nat
% 5.68/6.05 @ ^ [X2: nat] : X2
% 5.68/6.05 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sum_list_upt
% 5.68/6.05 thf(fact_10023_card__length__sum__list__rec,axiom,
% 5.68/6.05 ! [M: nat,N5: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.68/6.05 => ( ( finite_card_list_nat
% 5.68/6.05 @ ( collect_list_nat
% 5.68/6.05 @ ^ [L: list_nat] :
% 5.68/6.05 ( ( ( size_size_list_nat @ L )
% 5.68/6.05 = M )
% 5.68/6.05 & ( ( groups4561878855575611511st_nat @ L )
% 5.68/6.05 = N5 ) ) ) )
% 5.68/6.05 = ( plus_plus_nat
% 5.68/6.05 @ ( finite_card_list_nat
% 5.68/6.05 @ ( collect_list_nat
% 5.68/6.05 @ ^ [L: list_nat] :
% 5.68/6.05 ( ( ( size_size_list_nat @ L )
% 5.68/6.05 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.68/6.05 & ( ( groups4561878855575611511st_nat @ L )
% 5.68/6.05 = N5 ) ) ) )
% 5.68/6.05 @ ( finite_card_list_nat
% 5.68/6.05 @ ( collect_list_nat
% 5.68/6.05 @ ^ [L: list_nat] :
% 5.68/6.05 ( ( ( size_size_list_nat @ L )
% 5.68/6.05 = M )
% 5.68/6.05 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.68/6.05 = N5 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % card_length_sum_list_rec
% 5.68/6.05 thf(fact_10024_card__length__sum__list,axiom,
% 5.68/6.05 ! [M: nat,N5: nat] :
% 5.68/6.05 ( ( finite_card_list_nat
% 5.68/6.05 @ ( collect_list_nat
% 5.68/6.05 @ ^ [L: list_nat] :
% 5.68/6.05 ( ( ( size_size_list_nat @ L )
% 5.68/6.05 = M )
% 5.68/6.05 & ( ( groups4561878855575611511st_nat @ L )
% 5.68/6.05 = N5 ) ) ) )
% 5.68/6.05 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 5.68/6.05
% 5.68/6.05 % card_length_sum_list
% 5.68/6.05 thf(fact_10025_sorted__upt,axiom,
% 5.68/6.05 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_upt
% 5.68/6.05 thf(fact_10026_sorted__wrt__upt,axiom,
% 5.68/6.05 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_wrt_upt
% 5.68/6.05 thf(fact_10027_sorted__wrt__less__idx,axiom,
% 5.68/6.05 ! [Ns: list_nat,I2: nat] :
% 5.68/6.05 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.68/6.05 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.68/6.05 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_wrt_less_idx
% 5.68/6.05 thf(fact_10028_sorted__upto,axiom,
% 5.68/6.05 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % sorted_upto
% 5.68/6.05 thf(fact_10029_card__le__Suc__Max,axiom,
% 5.68/6.05 ! [S3: set_nat] :
% 5.68/6.05 ( ( finite_finite_nat @ S3 )
% 5.68/6.05 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % card_le_Suc_Max
% 5.68/6.05 thf(fact_10030_divide__nat__def,axiom,
% 5.68/6.05 ( divide_divide_nat
% 5.68/6.05 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.05 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.68/6.05 @ ( lattic8265883725875713057ax_nat
% 5.68/6.05 @ ( collect_nat
% 5.68/6.05 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % divide_nat_def
% 5.68/6.05 thf(fact_10031_gcd__is__Max__divisors__nat,axiom,
% 5.68/6.05 ! [N: nat,M: nat] :
% 5.68/6.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.68/6.05 => ( ( gcd_gcd_nat @ M @ N )
% 5.68/6.05 = ( lattic8265883725875713057ax_nat
% 5.68/6.05 @ ( collect_nat
% 5.68/6.05 @ ^ [D2: nat] :
% 5.68/6.05 ( ( dvd_dvd_nat @ D2 @ M )
% 5.68/6.05 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % gcd_is_Max_divisors_nat
% 5.68/6.05 thf(fact_10032_sup__enat__def,axiom,
% 5.68/6.05 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.68/6.05
% 5.68/6.05 % sup_enat_def
% 5.68/6.05 thf(fact_10033_sup__nat__def,axiom,
% 5.68/6.05 sup_sup_nat = ord_max_nat ).
% 5.68/6.05
% 5.68/6.05 % sup_nat_def
% 5.68/6.05 thf(fact_10034_atLeastLessThan__add__Un,axiom,
% 5.68/6.05 ! [I2: nat,J: nat,K: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ I2 @ J )
% 5.68/6.05 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.68/6.05 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % atLeastLessThan_add_Un
% 5.68/6.05 thf(fact_10035_less__eq,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.68/6.05 = ( ord_less_nat @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % less_eq
% 5.68/6.05 thf(fact_10036_pred__nat__trancl__eq__le,axiom,
% 5.68/6.05 ! [M: nat,N: nat] :
% 5.68/6.05 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.68/6.05 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % pred_nat_trancl_eq_le
% 5.68/6.05 thf(fact_10037_Field__natLeq__on,axiom,
% 5.68/6.05 ! [N: nat] :
% 5.68/6.05 ( ( field_nat
% 5.68/6.05 @ ( collec3392354462482085612at_nat
% 5.68/6.05 @ ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( ( ord_less_nat @ X2 @ N )
% 5.68/6.05 & ( ord_less_nat @ Y @ N )
% 5.68/6.05 & ( ord_less_eq_nat @ X2 @ Y ) ) ) ) )
% 5.68/6.05 = ( collect_nat
% 5.68/6.05 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Field_natLeq_on
% 5.68/6.05 thf(fact_10038_natLess__def,axiom,
% 5.68/6.05 ( bNF_Ca8459412986667044542atLess
% 5.68/6.05 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % natLess_def
% 5.68/6.05 thf(fact_10039_wf__less,axiom,
% 5.68/6.05 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.68/6.05
% 5.68/6.05 % wf_less
% 5.68/6.05 thf(fact_10040_prod__encode__prod__decode__aux,axiom,
% 5.68/6.05 ! [K: nat,M: nat] :
% 5.68/6.05 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.68/6.05 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.68/6.05
% 5.68/6.05 % prod_encode_prod_decode_aux
% 5.68/6.05 thf(fact_10041_le__prod__encode__2,axiom,
% 5.68/6.05 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % le_prod_encode_2
% 5.68/6.05 thf(fact_10042_le__prod__encode__1,axiom,
% 5.68/6.05 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % le_prod_encode_1
% 5.68/6.05 thf(fact_10043_prod__encode__def,axiom,
% 5.68/6.05 ( nat_prod_encode
% 5.68/6.05 = ( produc6842872674320459806at_nat
% 5.68/6.05 @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % prod_encode_def
% 5.68/6.05 thf(fact_10044_list__encode_Oelims,axiom,
% 5.68/6.05 ! [X: list_nat,Y2: nat] :
% 5.68/6.05 ( ( ( nat_list_encode @ X )
% 5.68/6.05 = Y2 )
% 5.68/6.05 => ( ( ( X = nil_nat )
% 5.68/6.05 => ( Y2 != zero_zero_nat ) )
% 5.68/6.05 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.68/6.05 ( ( X
% 5.68/6.05 = ( cons_nat @ X3 @ Xs3 ) )
% 5.68/6.05 => ( Y2
% 5.68/6.05 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % list_encode.elims
% 5.68/6.05 thf(fact_10045_list__encode_Osimps_I2_J,axiom,
% 5.68/6.05 ! [X: nat,Xs2: list_nat] :
% 5.68/6.05 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.68/6.05 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % list_encode.simps(2)
% 5.68/6.05 thf(fact_10046_list__encode_Opelims,axiom,
% 5.68/6.05 ! [X: list_nat,Y2: nat] :
% 5.68/6.05 ( ( ( nat_list_encode @ X )
% 5.68/6.05 = Y2 )
% 5.68/6.05 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.68/6.05 => ( ( ( X = nil_nat )
% 5.68/6.05 => ( ( Y2 = zero_zero_nat )
% 5.68/6.05 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.68/6.05 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.68/6.05 ( ( X
% 5.68/6.05 = ( cons_nat @ X3 @ Xs3 ) )
% 5.68/6.05 => ( ( Y2
% 5.68/6.05 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.68/6.05 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % list_encode.pelims
% 5.68/6.05 thf(fact_10047_Gcd__int__greater__eq__0,axiom,
% 5.68/6.05 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.68/6.05
% 5.68/6.05 % Gcd_int_greater_eq_0
% 5.68/6.05 thf(fact_10048_Gcd__nat__set__eq__fold,axiom,
% 5.68/6.05 ! [Xs2: list_nat] :
% 5.68/6.05 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 5.68/6.05 = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 5.68/6.05
% 5.68/6.05 % Gcd_nat_set_eq_fold
% 5.68/6.05 thf(fact_10049_Gcd__int__set__eq__fold,axiom,
% 5.68/6.05 ! [Xs2: list_int] :
% 5.68/6.05 ( ( gcd_Gcd_int @ ( set_int2 @ Xs2 ) )
% 5.68/6.05 = ( fold_int_int @ gcd_gcd_int @ Xs2 @ zero_zero_int ) ) ).
% 5.68/6.05
% 5.68/6.05 % Gcd_int_set_eq_fold
% 5.68/6.05 thf(fact_10050_vanishes__mult__bounded,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ? [A7: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 5.68/6.05 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A7 ) )
% 5.68/6.05 => ( ( vanishes @ Y6 )
% 5.68/6.05 => ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_mult_bounded
% 5.68/6.05 thf(fact_10051_vanishes__const,axiom,
% 5.68/6.05 ! [C: rat] :
% 5.68/6.05 ( ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : C )
% 5.68/6.05 = ( C = zero_zero_rat ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_const
% 5.68/6.05 thf(fact_10052_vanishes__diff,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( vanishes @ X8 )
% 5.68/6.05 => ( ( vanishes @ Y6 )
% 5.68/6.05 => ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_diff
% 5.68/6.05 thf(fact_10053_vanishes__minus,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( vanishes @ X8 )
% 5.68/6.05 => ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_minus
% 5.68/6.05 thf(fact_10054_vanishes__add,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( vanishes @ X8 )
% 5.68/6.05 => ( ( vanishes @ Y6 )
% 5.68/6.05 => ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_add
% 5.68/6.05 thf(fact_10055_vanishesD,axiom,
% 5.68/6.05 ! [X8: nat > rat,R2: rat] :
% 5.68/6.05 ( ( vanishes @ X8 )
% 5.68/6.05 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.68/6.05 => ? [K2: nat] :
% 5.68/6.05 ! [N7: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ N7 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N7 ) ) @ R2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishesD
% 5.68/6.05 thf(fact_10056_vanishesI,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ! [R3: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.68/6.05 => ? [K4: nat] :
% 5.68/6.05 ! [N3: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R3 ) ) )
% 5.68/6.05 => ( vanishes @ X8 ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishesI
% 5.68/6.05 thf(fact_10057_vanishes__def,axiom,
% 5.68/6.05 ( vanishes
% 5.68/6.05 = ( ^ [X6: nat > rat] :
% 5.68/6.05 ! [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 => ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_def
% 5.68/6.05 thf(fact_10058_cauchy__def,axiom,
% 5.68/6.05 ( cauchy
% 5.68/6.05 = ( ^ [X6: nat > rat] :
% 5.68/6.05 ! [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 => ? [K3: nat] :
% 5.68/6.05 ! [M6: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ M6 )
% 5.68/6.05 => ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_def
% 5.68/6.05 thf(fact_10059_cauchy__inverse,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ~ ( vanishes @ X8 )
% 5.68/6.05 => ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X8 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_inverse
% 5.68/6.05 thf(fact_10060_cauchy__mult,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_mult
% 5.68/6.05 thf(fact_10061_cauchy__minus,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_minus
% 5.68/6.05 thf(fact_10062_cauchy__const,axiom,
% 5.68/6.05 ! [X: rat] :
% 5.68/6.05 ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : X ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_const
% 5.68/6.05 thf(fact_10063_cauchy__add,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_add
% 5.68/6.05 thf(fact_10064_cauchy__diff,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( cauchy
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_diff
% 5.68/6.05 thf(fact_10065_cauchy__imp__bounded,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ? [B2: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.68/6.05 & ! [N7: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N7 ) ) @ B2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_imp_bounded
% 5.68/6.05 thf(fact_10066_vanishes__diff__inverse,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ~ ( vanishes @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ~ ( vanishes @ Y6 )
% 5.68/6.05 => ( ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) )
% 5.68/6.05 => ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X8 @ N2 ) ) @ ( inverse_inverse_rat @ ( Y6 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % vanishes_diff_inverse
% 5.68/6.05 thf(fact_10067_cauchy__not__vanishes__cases,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ~ ( vanishes @ X8 )
% 5.68/6.05 => ? [B2: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.68/6.05 & ? [K2: nat] :
% 5.68/6.05 ( ! [N7: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ N7 )
% 5.68/6.05 => ( ord_less_rat @ B2 @ ( uminus_uminus_rat @ ( X8 @ N7 ) ) ) )
% 5.68/6.05 | ! [N7: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ N7 )
% 5.68/6.05 => ( ord_less_rat @ B2 @ ( X8 @ N7 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_not_vanishes_cases
% 5.68/6.05 thf(fact_10068_cauchy__not__vanishes,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ~ ( vanishes @ X8 )
% 5.68/6.05 => ? [B2: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.68/6.05 & ? [K2: nat] :
% 5.68/6.05 ! [N7: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ N7 )
% 5.68/6.05 => ( ord_less_rat @ B2 @ ( abs_abs_rat @ ( X8 @ N7 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchy_not_vanishes
% 5.68/6.05 thf(fact_10069_cauchyD,axiom,
% 5.68/6.05 ! [X8: nat > rat,R2: rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.68/6.05 => ? [K2: nat] :
% 5.68/6.05 ! [M2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.68/6.05 => ! [N7: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K2 @ N7 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M2 ) @ ( X8 @ N7 ) ) ) @ R2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchyD
% 5.68/6.05 thf(fact_10070_cauchyI,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ! [R3: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.68/6.05 => ? [K4: nat] :
% 5.68/6.05 ! [M5: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K4 @ M5 )
% 5.68/6.05 => ! [N3: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.68/6.05 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ R3 ) ) ) )
% 5.68/6.05 => ( cauchy @ X8 ) ) ).
% 5.68/6.05
% 5.68/6.05 % cauchyI
% 5.68/6.05 thf(fact_10071_le__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.68/6.05 = ( ! [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 => ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( plus_plus_rat @ ( Y6 @ N2 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % le_Real
% 5.68/6.05 thf(fact_10072_Real__induct,axiom,
% 5.68/6.05 ! [P: real > $o,X: real] :
% 5.68/6.05 ( ! [X10: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X10 )
% 5.68/6.05 => ( P @ ( real2 @ X10 ) ) )
% 5.68/6.05 => ( P @ X ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real_induct
% 5.68/6.05 thf(fact_10073_of__int__Real,axiom,
% 5.68/6.05 ( ring_1_of_int_real
% 5.68/6.05 = ( ^ [X2: int] :
% 5.68/6.05 ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( ring_1_of_int_rat @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % of_int_Real
% 5.68/6.05 thf(fact_10074_of__nat__Real,axiom,
% 5.68/6.05 ( semiri5074537144036343181t_real
% 5.68/6.05 = ( ^ [X2: nat] :
% 5.68/6.05 ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( semiri681578069525770553at_rat @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % of_nat_Real
% 5.68/6.05 thf(fact_10075_zero__real__def,axiom,
% 5.68/6.05 ( zero_zero_real
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat ) ) ).
% 5.68/6.05
% 5.68/6.05 % zero_real_def
% 5.68/6.05 thf(fact_10076_one__real__def,axiom,
% 5.68/6.05 ( one_one_real
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : one_one_rat ) ) ).
% 5.68/6.05
% 5.68/6.05 % one_real_def
% 5.68/6.05 thf(fact_10077_minus__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( uminus_uminus_real @ ( real2 @ X8 ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % minus_Real
% 5.68/6.05 thf(fact_10078_add__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( plus_plus_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % add_Real
% 5.68/6.05 thf(fact_10079_mult__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % mult_Real
% 5.68/6.05 thf(fact_10080_diff__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( minus_minus_real @ ( real2 @ X8 ) @ ( real2 @ Y6 ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % diff_Real
% 5.68/6.05 thf(fact_10081_eq__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( ( real2 @ X8 )
% 5.68/6.05 = ( real2 @ Y6 ) )
% 5.68/6.05 = ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % eq_Real
% 5.68/6.05 thf(fact_10082_inverse__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( ( vanishes @ X8 )
% 5.68/6.05 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.68/6.05 = zero_zero_real ) )
% 5.68/6.05 & ( ~ ( vanishes @ X8 )
% 5.68/6.05 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X8 @ N2 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_Real
% 5.68/6.05 thf(fact_10083_not__positive__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 5.68/6.05 = ( ! [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 => ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ R5 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % not_positive_Real
% 5.68/6.05 thf(fact_10084_Real_Opositive__minus,axiom,
% 5.68/6.05 ! [X: real] :
% 5.68/6.05 ( ~ ( positive2 @ X )
% 5.68/6.05 => ( ( X != zero_zero_real )
% 5.68/6.05 => ( positive2 @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive_minus
% 5.68/6.05 thf(fact_10085_Real_Opositive__add,axiom,
% 5.68/6.05 ! [X: real,Y2: real] :
% 5.68/6.05 ( ( positive2 @ X )
% 5.68/6.05 => ( ( positive2 @ Y2 )
% 5.68/6.05 => ( positive2 @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive_add
% 5.68/6.05 thf(fact_10086_Real_Opositive__mult,axiom,
% 5.68/6.05 ! [X: real,Y2: real] :
% 5.68/6.05 ( ( positive2 @ X )
% 5.68/6.05 => ( ( positive2 @ Y2 )
% 5.68/6.05 => ( positive2 @ ( times_times_real @ X @ Y2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive_mult
% 5.68/6.05 thf(fact_10087_Real_Opositive__zero,axiom,
% 5.68/6.05 ~ ( positive2 @ zero_zero_real ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive_zero
% 5.68/6.05 thf(fact_10088_less__real__def,axiom,
% 5.68/6.05 ( ord_less_real
% 5.68/6.05 = ( ^ [X2: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % less_real_def
% 5.68/6.05 thf(fact_10089_positive__Real,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( positive2 @ ( real2 @ X8 ) )
% 5.68/6.05 = ( ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % positive_Real
% 5.68/6.05 thf(fact_10090_Real_Opositive_Orep__eq,axiom,
% 5.68/6.05 ( positive2
% 5.68/6.05 = ( ^ [X2: real] :
% 5.68/6.05 ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( rep_real @ X2 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive.rep_eq
% 5.68/6.05 thf(fact_10091_inverse__real_Oabs__eq,axiom,
% 5.68/6.05 ! [X: nat > rat] :
% 5.68/6.05 ( ( realrel @ X @ X )
% 5.68/6.05 => ( ( inverse_inverse_real @ ( real2 @ X ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ( if_nat_rat @ ( vanishes @ X )
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_real.abs_eq
% 5.68/6.05 thf(fact_10092_realrel__refl,axiom,
% 5.68/6.05 ! [X8: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( realrel @ X8 @ X8 ) ) ).
% 5.68/6.05
% 5.68/6.05 % realrel_refl
% 5.68/6.05 thf(fact_10093_zero__real_Orsp,axiom,
% 5.68/6.05 ( realrel
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat ) ).
% 5.68/6.05
% 5.68/6.05 % zero_real.rsp
% 5.68/6.05 thf(fact_10094_one__real_Orsp,axiom,
% 5.68/6.05 ( realrel
% 5.68/6.05 @ ^ [N2: nat] : one_one_rat
% 5.68/6.05 @ ^ [N2: nat] : one_one_rat ) ).
% 5.68/6.05
% 5.68/6.05 % one_real.rsp
% 5.68/6.05 thf(fact_10095_real_Oabs__induct,axiom,
% 5.68/6.05 ! [P: real > $o,X: real] :
% 5.68/6.05 ( ! [Y3: nat > rat] :
% 5.68/6.05 ( ( realrel @ Y3 @ Y3 )
% 5.68/6.05 => ( P @ ( real2 @ Y3 ) ) )
% 5.68/6.05 => ( P @ X ) ) ).
% 5.68/6.05
% 5.68/6.05 % real.abs_induct
% 5.68/6.05 thf(fact_10096_uminus__real_Oabs__eq,axiom,
% 5.68/6.05 ! [X: nat > rat] :
% 5.68/6.05 ( ( realrel @ X @ X )
% 5.68/6.05 => ( ( uminus_uminus_real @ ( real2 @ X ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_real.abs_eq
% 5.68/6.05 thf(fact_10097_plus__real_Oabs__eq,axiom,
% 5.68/6.05 ! [Xa2: nat > rat,X: nat > rat] :
% 5.68/6.05 ( ( realrel @ Xa2 @ Xa2 )
% 5.68/6.05 => ( ( realrel @ X @ X )
% 5.68/6.05 => ( ( plus_plus_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( plus_plus_rat @ ( Xa2 @ N2 ) @ ( X @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_real.abs_eq
% 5.68/6.05 thf(fact_10098_times__real_Oabs__eq,axiom,
% 5.68/6.05 ! [Xa2: nat > rat,X: nat > rat] :
% 5.68/6.05 ( ( realrel @ Xa2 @ Xa2 )
% 5.68/6.05 => ( ( realrel @ X @ X )
% 5.68/6.05 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 5.68/6.05 = ( real2
% 5.68/6.05 @ ^ [N2: nat] : ( times_times_rat @ ( Xa2 @ N2 ) @ ( X @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_real.abs_eq
% 5.68/6.05 thf(fact_10099_realrelI,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y6: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y6 @ N2 ) ) )
% 5.68/6.05 => ( realrel @ X8 @ Y6 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % realrelI
% 5.68/6.05 thf(fact_10100_realrel__def,axiom,
% 5.68/6.05 ( realrel
% 5.68/6.05 = ( ^ [X6: nat > rat,Y7: nat > rat] :
% 5.68/6.05 ( ( cauchy @ X6 )
% 5.68/6.05 & ( cauchy @ Y7 )
% 5.68/6.05 & ( vanishes
% 5.68/6.05 @ ^ [N2: nat] : ( minus_minus_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % realrel_def
% 5.68/6.05 thf(fact_10101_Real_Opositive_Oabs__eq,axiom,
% 5.68/6.05 ! [X: nat > rat] :
% 5.68/6.05 ( ( realrel @ X @ X )
% 5.68/6.05 => ( ( positive2 @ ( real2 @ X ) )
% 5.68/6.05 = ( ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( X @ N2 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive.abs_eq
% 5.68/6.05 thf(fact_10102_inverse__real__def,axiom,
% 5.68/6.05 ( inverse_inverse_real
% 5.68/6.05 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ( if_nat_rat @ ( vanishes @ X6 )
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_real_def
% 5.68/6.05 thf(fact_10103_cr__real__def,axiom,
% 5.68/6.05 ( cr_real
% 5.68/6.05 = ( ^ [X2: nat > rat,Y: real] :
% 5.68/6.05 ( ( realrel @ X2 @ X2 )
% 5.68/6.05 & ( ( real2 @ X2 )
% 5.68/6.05 = Y ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cr_real_def
% 5.68/6.05 thf(fact_10104_uminus__real__def,axiom,
% 5.68/6.05 ( uminus_uminus_real
% 5.68/6.05 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.68/6.05 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_real_def
% 5.68/6.05 thf(fact_10105_times__real__def,axiom,
% 5.68/6.05 ( times_times_real
% 5.68/6.05 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_real_def
% 5.68/6.05 thf(fact_10106_plus__real__def,axiom,
% 5.68/6.05 ( plus_plus_real
% 5.68/6.05 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_real_def
% 5.68/6.05 thf(fact_10107_Real_Opositive_Orsp,axiom,
% 5.68/6.05 ( bNF_re728719798268516973at_o_o @ realrel
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive.rsp
% 5.68/6.05 thf(fact_10108_plus__real_Orsp,axiom,
% 5.68/6.05 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_real.rsp
% 5.68/6.05 thf(fact_10109_uminus__real_Orsp,axiom,
% 5.68/6.05 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.68/6.05 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) )
% 5.68/6.05 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_real.rsp
% 5.68/6.05 thf(fact_10110_times__real_Orsp,axiom,
% 5.68/6.05 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_real.rsp
% 5.68/6.05 thf(fact_10111_less__natural_Orsp,axiom,
% 5.68/6.05 ( bNF_re578469030762574527_nat_o
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re4705727531993890431at_o_o
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ord_less_nat
% 5.68/6.05 @ ord_less_nat ) ).
% 5.68/6.05
% 5.68/6.05 % less_natural.rsp
% 5.68/6.05 thf(fact_10112_divide__natural_Orsp,axiom,
% 5.68/6.05 ( bNF_re1345281282404953727at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re5653821019739307937at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/6.05 @ divide_divide_nat
% 5.68/6.05 @ divide_divide_nat ) ).
% 5.68/6.05
% 5.68/6.05 % divide_natural.rsp
% 5.68/6.05 thf(fact_10113_times__integer_Orsp,axiom,
% 5.68/6.05 ( bNF_re711492959462206631nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re4712519889275205905nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/6.05 @ times_times_int
% 5.68/6.05 @ times_times_int ) ).
% 5.68/6.05
% 5.68/6.05 % times_integer.rsp
% 5.68/6.05 thf(fact_10114_times__natural_Orsp,axiom,
% 5.68/6.05 ( bNF_re1345281282404953727at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re5653821019739307937at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/6.05 @ times_times_nat
% 5.68/6.05 @ times_times_nat ) ).
% 5.68/6.05
% 5.68/6.05 % times_natural.rsp
% 5.68/6.05 thf(fact_10115_Suc_Orsp,axiom,
% 5.68/6.05 ( bNF_re5653821019739307937at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ suc
% 5.68/6.05 @ suc ) ).
% 5.68/6.05
% 5.68/6.05 % Suc.rsp
% 5.68/6.05 thf(fact_10116_dup_Orsp,axiom,
% 5.68/6.05 ( bNF_re4712519889275205905nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 5.68/6.05 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 5.68/6.05
% 5.68/6.05 % dup.rsp
% 5.68/6.05 thf(fact_10117_plus__natural_Orsp,axiom,
% 5.68/6.05 ( bNF_re1345281282404953727at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re5653821019739307937at_nat
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.68/6.05 @ plus_plus_nat
% 5.68/6.05 @ plus_plus_nat ) ).
% 5.68/6.05
% 5.68/6.05 % plus_natural.rsp
% 5.68/6.05 thf(fact_10118_plus__integer_Orsp,axiom,
% 5.68/6.05 ( bNF_re711492959462206631nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re4712519889275205905nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/6.05 @ plus_plus_int
% 5.68/6.05 @ plus_plus_int ) ).
% 5.68/6.05
% 5.68/6.05 % plus_integer.rsp
% 5.68/6.05 thf(fact_10119_sub_Orsp,axiom,
% 5.68/6.05 ( bNF_re8402795839162346335um_int
% 5.68/6.05 @ ^ [Y5: num,Z5: num] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re1822329894187522285nt_int
% 5.68/6.05 @ ^ [Y5: num,Z5: num] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ^ [M6: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) )
% 5.68/6.05 @ ^ [M6: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % sub.rsp
% 5.68/6.05 thf(fact_10120_less__eq__integer_Orsp,axiom,
% 5.68/6.05 ( bNF_re3403563459893282935_int_o
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re5089333283451836215nt_o_o
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ord_less_eq_int
% 5.68/6.05 @ ord_less_eq_int ) ).
% 5.68/6.05
% 5.68/6.05 % less_eq_integer.rsp
% 5.68/6.05 thf(fact_10121_less__eq__natural_Orsp,axiom,
% 5.68/6.05 ( bNF_re578469030762574527_nat_o
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re4705727531993890431at_o_o
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ord_less_eq_nat
% 5.68/6.05 @ ord_less_eq_nat ) ).
% 5.68/6.05
% 5.68/6.05 % less_eq_natural.rsp
% 5.68/6.05 thf(fact_10122_inverse__real_Orsp,axiom,
% 5.68/6.05 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ( if_nat_rat @ ( vanishes @ X6 )
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) )
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ( if_nat_rat @ ( vanishes @ X6 )
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_real.rsp
% 5.68/6.05 thf(fact_10123_Real_Opositive_Otransfer,axiom,
% 5.68/6.05 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ? [R5: rat] :
% 5.68/6.05 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.68/6.05 & ? [K3: nat] :
% 5.68/6.05 ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.68/6.05 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.68/6.05 @ positive2 ) ).
% 5.68/6.05
% 5.68/6.05 % Real.positive.transfer
% 5.68/6.05 thf(fact_10124_real_Orel__eq__transfer,axiom,
% 5.68/6.05 ( bNF_re4521903465945308077real_o @ pcr_real
% 5.68/6.05 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ realrel
% 5.68/6.05 @ ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) ) ).
% 5.68/6.05
% 5.68/6.05 % real.rel_eq_transfer
% 5.68/6.05 thf(fact_10125_zero__real_Otransfer,axiom,
% 5.68/6.05 ( pcr_real
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ zero_zero_real ) ).
% 5.68/6.05
% 5.68/6.05 % zero_real.transfer
% 5.68/6.05 thf(fact_10126_real_Opcr__cr__eq,axiom,
% 5.68/6.05 pcr_real = cr_real ).
% 5.68/6.05
% 5.68/6.05 % real.pcr_cr_eq
% 5.68/6.05 thf(fact_10127_one__real_Otransfer,axiom,
% 5.68/6.05 ( pcr_real
% 5.68/6.05 @ ^ [N2: nat] : one_one_rat
% 5.68/6.05 @ one_one_real ) ).
% 5.68/6.05
% 5.68/6.05 % one_real.transfer
% 5.68/6.05 thf(fact_10128_cr__real__eq,axiom,
% 5.68/6.05 ( pcr_real
% 5.68/6.05 = ( ^ [X2: nat > rat,Y: real] :
% 5.68/6.05 ( ( cauchy @ X2 )
% 5.68/6.05 & ( ( real2 @ X2 )
% 5.68/6.05 = Y ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % cr_real_eq
% 5.68/6.05 thf(fact_10129_uminus__real_Otransfer,axiom,
% 5.68/6.05 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.68/6.05 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) )
% 5.68/6.05 @ uminus_uminus_real ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_real.transfer
% 5.68/6.05 thf(fact_10130_plus__real_Otransfer,axiom,
% 5.68/6.05 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) )
% 5.68/6.05 @ plus_plus_real ) ).
% 5.68/6.05
% 5.68/6.05 % plus_real.transfer
% 5.68/6.05 thf(fact_10131_times__real_Otransfer,axiom,
% 5.68/6.05 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.68/6.05 @ ^ [X6: nat > rat,Y7: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y7 @ N2 ) )
% 5.68/6.05 @ times_times_real ) ).
% 5.68/6.05
% 5.68/6.05 % times_real.transfer
% 5.68/6.05 thf(fact_10132_inverse__real_Otransfer,axiom,
% 5.68/6.05 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.68/6.05 @ ^ [X6: nat > rat] :
% 5.68/6.05 ( if_nat_rat @ ( vanishes @ X6 )
% 5.68/6.05 @ ^ [N2: nat] : zero_zero_rat
% 5.68/6.05 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) )
% 5.68/6.05 @ inverse_inverse_real ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_real.transfer
% 5.68/6.05 thf(fact_10133_plus__rat_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) )
% 5.68/6.05 @ plus_plus_rat ) ).
% 5.68/6.05
% 5.68/6.05 % plus_rat.transfer
% 5.68/6.05 thf(fact_10134_one__rat_Otransfer,axiom,
% 5.68/6.05 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 5.68/6.05
% 5.68/6.05 % one_rat.transfer
% 5.68/6.05 thf(fact_10135_zero__rat_Otransfer,axiom,
% 5.68/6.05 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 5.68/6.05
% 5.68/6.05 % zero_rat.transfer
% 5.68/6.05 thf(fact_10136_Fract_Otransfer,axiom,
% 5.68/6.05 ( bNF_re3461391660133120880nt_rat
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re2214769303045360666nt_rat
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ pcr_rat )
% 5.68/6.05 @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 5.68/6.05 @ fract ) ).
% 5.68/6.05
% 5.68/6.05 % Fract.transfer
% 5.68/6.05 thf(fact_10137_uminus__rat_Otransfer,axiom,
% 5.68/6.05 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.68/6.05 @ uminus_uminus_rat ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_rat.transfer
% 5.68/6.05 thf(fact_10138_times__rat_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) )
% 5.68/6.05 @ times_times_rat ) ).
% 5.68/6.05
% 5.68/6.05 % times_rat.transfer
% 5.68/6.05 thf(fact_10139_Rat_Opositive_Otransfer,axiom,
% 5.68/6.05 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.68/6.05 @ positive ) ).
% 5.68/6.05
% 5.68/6.05 % Rat.positive.transfer
% 5.68/6.05 thf(fact_10140_inverse__rat_Otransfer,axiom,
% 5.68/6.05 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.68/6.05 @ ^ [X2: product_prod_int_int] :
% 5.68/6.05 ( if_Pro3027730157355071871nt_int
% 5.68/6.05 @ ( ( product_fst_int_int @ X2 )
% 5.68/6.05 = zero_zero_int )
% 5.68/6.05 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.05 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.68/6.05 @ inverse_inverse_rat ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_rat.transfer
% 5.68/6.05 thf(fact_10141_times__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.68/6.05 @ times_times_int ) ).
% 5.68/6.05
% 5.68/6.05 % times_int.transfer
% 5.68/6.05 thf(fact_10142_zero__int_Otransfer,axiom,
% 5.68/6.05 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.68/6.05
% 5.68/6.05 % zero_int.transfer
% 5.68/6.05 thf(fact_10143_int__transfer,axiom,
% 5.68/6.05 ( bNF_re6830278522597306478at_int
% 5.68/6.05 @ ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.68/6.05 @ pcr_int
% 5.68/6.05 @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 5.68/6.05 @ semiri1314217659103216013at_int ) ).
% 5.68/6.05
% 5.68/6.05 % int_transfer
% 5.68/6.05 thf(fact_10144_uminus__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.68/6.05 @ ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) )
% 5.68/6.05 @ uminus_uminus_int ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_int.transfer
% 5.68/6.05 thf(fact_10145_one__int_Otransfer,axiom,
% 5.68/6.05 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.68/6.05
% 5.68/6.05 % one_int.transfer
% 5.68/6.05 thf(fact_10146_less__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.68/6.05 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.68/6.05 @ ord_less_int ) ).
% 5.68/6.05
% 5.68/6.05 % less_int.transfer
% 5.68/6.05 thf(fact_10147_less__eq__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.68/6.05 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.68/6.05 @ ord_less_eq_int ) ).
% 5.68/6.05
% 5.68/6.05 % less_eq_int.transfer
% 5.68/6.05 thf(fact_10148_plus__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.68/6.05 @ plus_plus_int ) ).
% 5.68/6.05
% 5.68/6.05 % plus_int.transfer
% 5.68/6.05 thf(fact_10149_minus__int_Otransfer,axiom,
% 5.68/6.05 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.68/6.05 @ minus_minus_int ) ).
% 5.68/6.05
% 5.68/6.05 % minus_int.transfer
% 5.68/6.05 thf(fact_10150_times__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_int.rsp
% 5.68/6.05 thf(fact_10151_intrel__iff,axiom,
% 5.68/6.05 ! [X: nat,Y2: nat,U: nat,V: nat] :
% 5.68/6.05 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y2 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.68/6.05 = ( ( plus_plus_nat @ X @ V )
% 5.68/6.05 = ( plus_plus_nat @ U @ Y2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % intrel_iff
% 5.68/6.05 thf(fact_10152_uminus__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.68/6.05 @ ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) )
% 5.68/6.05 @ ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_int.rsp
% 5.68/6.05 thf(fact_10153_less__RealD,axiom,
% 5.68/6.05 ! [Y6: nat > rat,X: real] :
% 5.68/6.05 ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ( ord_less_real @ X @ ( real2 @ Y6 ) )
% 5.68/6.05 => ? [N3: nat] : ( ord_less_real @ X @ ( field_7254667332652039916t_real @ ( Y6 @ N3 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % less_RealD
% 5.68/6.05 thf(fact_10154_of__rat__Real,axiom,
% 5.68/6.05 ( field_7254667332652039916t_real
% 5.68/6.05 = ( ^ [X2: rat] :
% 5.68/6.05 ( real2
% 5.68/6.05 @ ^ [N2: nat] : X2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % of_rat_Real
% 5.68/6.05 thf(fact_10155_zero__int_Orsp,axiom,
% 5.68/6.05 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.68/6.05
% 5.68/6.05 % zero_int.rsp
% 5.68/6.05 thf(fact_10156_of__rat__dense,axiom,
% 5.68/6.05 ! [X: real,Y2: real] :
% 5.68/6.05 ( ( ord_less_real @ X @ Y2 )
% 5.68/6.05 => ? [Q3: rat] :
% 5.68/6.05 ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q3 ) )
% 5.68/6.05 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % of_rat_dense
% 5.68/6.05 thf(fact_10157_Real__leI,axiom,
% 5.68/6.05 ! [X8: nat > rat,Y2: real] :
% 5.68/6.05 ( ( cauchy @ X8 )
% 5.68/6.05 => ( ! [N3: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X8 @ N3 ) ) @ Y2 )
% 5.68/6.05 => ( ord_less_eq_real @ ( real2 @ X8 ) @ Y2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Real_leI
% 5.68/6.05 thf(fact_10158_le__RealI,axiom,
% 5.68/6.05 ! [Y6: nat > rat,X: real] :
% 5.68/6.05 ( ( cauchy @ Y6 )
% 5.68/6.05 => ( ! [N3: nat] : ( ord_less_eq_real @ X @ ( field_7254667332652039916t_real @ ( Y6 @ N3 ) ) )
% 5.68/6.05 => ( ord_less_eq_real @ X @ ( real2 @ Y6 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % le_RealI
% 5.68/6.05 thf(fact_10159_one__int_Orsp,axiom,
% 5.68/6.05 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.68/6.05
% 5.68/6.05 % one_int.rsp
% 5.68/6.05 thf(fact_10160_intrel__def,axiom,
% 5.68/6.05 ( intrel
% 5.68/6.05 = ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] :
% 5.68/6.05 ( ( plus_plus_nat @ X2 @ V4 )
% 5.68/6.05 = ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % intrel_def
% 5.68/6.05 thf(fact_10161_less__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.68/6.05 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % less_int.rsp
% 5.68/6.05 thf(fact_10162_less__eq__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.68/6.05 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.68/6.05 @ ( produc8739625826339149834_nat_o
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc6081775807080527818_nat_o
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % less_eq_int.rsp
% 5.68/6.05 thf(fact_10163_plus__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_int.rsp
% 5.68/6.05 thf(fact_10164_minus__int_Orsp,axiom,
% 5.68/6.05 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.68/6.05 @ ( produc27273713700761075at_nat
% 5.68/6.05 @ ^ [X2: nat,Y: nat] :
% 5.68/6.05 ( produc2626176000494625587at_nat
% 5.68/6.05 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % minus_int.rsp
% 5.68/6.05 thf(fact_10165_DeMoivre2,axiom,
% 5.68/6.05 ! [R2: real,A: real,N: nat] :
% 5.68/6.05 ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 5.68/6.05 = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % DeMoivre2
% 5.68/6.05 thf(fact_10166_Re__rcis,axiom,
% 5.68/6.05 ! [R2: real,A: real] :
% 5.68/6.05 ( ( re @ ( rcis @ R2 @ A ) )
% 5.68/6.05 = ( times_times_real @ R2 @ ( cos_real @ A ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Re_rcis
% 5.68/6.05 thf(fact_10167_Im__rcis,axiom,
% 5.68/6.05 ! [R2: real,A: real] :
% 5.68/6.05 ( ( im @ ( rcis @ R2 @ A ) )
% 5.68/6.05 = ( times_times_real @ R2 @ ( sin_real @ A ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Im_rcis
% 5.68/6.05 thf(fact_10168_le__enumerate,axiom,
% 5.68/6.05 ! [S3: set_nat,N: nat] :
% 5.68/6.05 ( ~ ( finite_finite_nat @ S3 )
% 5.68/6.05 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % le_enumerate
% 5.68/6.05 thf(fact_10169_rcis__mult,axiom,
% 5.68/6.05 ! [R12: real,A: real,R23: real,B: real] :
% 5.68/6.05 ( ( times_times_complex @ ( rcis @ R12 @ A ) @ ( rcis @ R23 @ B ) )
% 5.68/6.05 = ( rcis @ ( times_times_real @ R12 @ R23 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % rcis_mult
% 5.68/6.05 thf(fact_10170_rcis__def,axiom,
% 5.68/6.05 ( rcis
% 5.68/6.05 = ( ^ [R5: real,A4: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R5 ) @ ( cis @ A4 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % rcis_def
% 5.68/6.05 thf(fact_10171_finite__le__enumerate,axiom,
% 5.68/6.05 ! [S3: set_nat,N: nat] :
% 5.68/6.05 ( ( finite_finite_nat @ S3 )
% 5.68/6.05 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.68/6.05 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % finite_le_enumerate
% 5.68/6.05 thf(fact_10172_Least__eq__0,axiom,
% 5.68/6.05 ! [P: nat > $o] :
% 5.68/6.05 ( ( P @ zero_zero_nat )
% 5.68/6.05 => ( ( ord_Least_nat @ P )
% 5.68/6.05 = zero_zero_nat ) ) ).
% 5.68/6.05
% 5.68/6.05 % Least_eq_0
% 5.68/6.05 thf(fact_10173_Least__Suc2,axiom,
% 5.68/6.05 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.68/6.05 ( ( P @ N )
% 5.68/6.05 => ( ( Q @ M )
% 5.68/6.05 => ( ~ ( P @ zero_zero_nat )
% 5.68/6.05 => ( ! [K2: nat] :
% 5.68/6.05 ( ( P @ ( suc @ K2 ) )
% 5.68/6.05 = ( Q @ K2 ) )
% 5.68/6.05 => ( ( ord_Least_nat @ P )
% 5.68/6.05 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Least_Suc2
% 5.68/6.05 thf(fact_10174_Least__Suc,axiom,
% 5.68/6.05 ! [P: nat > $o,N: nat] :
% 5.68/6.05 ( ( P @ N )
% 5.68/6.05 => ( ~ ( P @ zero_zero_nat )
% 5.68/6.05 => ( ( ord_Least_nat @ P )
% 5.68/6.05 = ( suc
% 5.68/6.05 @ ( ord_Least_nat
% 5.68/6.05 @ ^ [M6: nat] : ( P @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Least_Suc
% 5.68/6.05 thf(fact_10175_Sup__real__def,axiom,
% 5.68/6.05 ( comple1385675409528146559p_real
% 5.68/6.05 = ( ^ [X6: set_real] :
% 5.68/6.05 ( ord_Least_real
% 5.68/6.05 @ ^ [Z2: real] :
% 5.68/6.05 ! [X2: real] :
% 5.68/6.05 ( ( member_real @ X2 @ X6 )
% 5.68/6.05 => ( ord_less_eq_real @ X2 @ Z2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Sup_real_def
% 5.68/6.05 thf(fact_10176_divmod__nat__code,axiom,
% 5.68/6.05 ( divmod_nat
% 5.68/6.05 = ( ^ [M6: nat,N2: nat] :
% 5.68/6.05 ( produc8678311845419106900er_nat @ code_nat_of_integer @ code_nat_of_integer
% 5.68/6.05 @ ( if_Pro6119634080678213985nteger
% 5.68/6.05 @ ( ( code_integer_of_nat @ M6 )
% 5.68/6.05 = zero_z3403309356797280102nteger )
% 5.68/6.05 @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.68/6.05 @ ( if_Pro6119634080678213985nteger
% 5.68/6.05 @ ( ( code_integer_of_nat @ N2 )
% 5.68/6.05 = zero_z3403309356797280102nteger )
% 5.68/6.05 @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( code_integer_of_nat @ M6 ) )
% 5.68/6.05 @ ( code_divmod_abs @ ( code_integer_of_nat @ M6 ) @ ( code_integer_of_nat @ N2 ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % divmod_nat_code
% 5.68/6.05 thf(fact_10177_eventually__prod__sequentially,axiom,
% 5.68/6.05 ! [P: product_prod_nat_nat > $o] :
% 5.68/6.05 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.68/6.05 = ( ? [N6: nat] :
% 5.68/6.05 ! [M6: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ N6 @ M6 )
% 5.68/6.05 => ! [N2: nat] :
% 5.68/6.05 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.68/6.05 => ( P @ ( product_Pair_nat_nat @ N2 @ M6 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % eventually_prod_sequentially
% 5.68/6.05 thf(fact_10178_integer__of__nat__numeral,axiom,
% 5.68/6.05 ! [N: num] :
% 5.68/6.05 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 5.68/6.05 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.68/6.05
% 5.68/6.05 % integer_of_nat_numeral
% 5.68/6.05 thf(fact_10179_at__right__to__0,axiom,
% 5.68/6.05 ! [A: real] :
% 5.68/6.05 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.68/6.05 = ( filtermap_real_real
% 5.68/6.05 @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 5.68/6.05 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % at_right_to_0
% 5.68/6.05 thf(fact_10180_plus__rat_Orsp,axiom,
% 5.68/6.05 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_rat.rsp
% 5.68/6.05 thf(fact_10181_ratrel__iff,axiom,
% 5.68/6.05 ( ratrel
% 5.68/6.05 = ( ^ [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.68/6.05 ( ( ( product_snd_int_int @ X2 )
% 5.68/6.05 != zero_zero_int )
% 5.68/6.05 & ( ( product_snd_int_int @ Y )
% 5.68/6.05 != zero_zero_int )
% 5.68/6.05 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) )
% 5.68/6.05 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % ratrel_iff
% 5.68/6.05 thf(fact_10182_zero__rat_Orsp,axiom,
% 5.68/6.05 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 5.68/6.05
% 5.68/6.05 % zero_rat.rsp
% 5.68/6.05 thf(fact_10183_one__rat_Orsp,axiom,
% 5.68/6.05 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 5.68/6.05
% 5.68/6.05 % one_rat.rsp
% 5.68/6.05 thf(fact_10184_Fract_Orsp,axiom,
% 5.68/6.05 ( bNF_re157797125943740599nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ( bNF_re6250860962936578807nt_int
% 5.68/6.05 @ ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.68/6.05 @ ratrel )
% 5.68/6.05 @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) )
% 5.68/6.05 @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A4 @ B3 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Fract.rsp
% 5.68/6.05 thf(fact_10185_ratrel__def,axiom,
% 5.68/6.05 ( ratrel
% 5.68/6.05 = ( ^ [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.68/6.05 ( ( ( product_snd_int_int @ X2 )
% 5.68/6.05 != zero_zero_int )
% 5.68/6.05 & ( ( product_snd_int_int @ Y )
% 5.68/6.05 != zero_zero_int )
% 5.68/6.05 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) )
% 5.68/6.05 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % ratrel_def
% 5.68/6.05 thf(fact_10186_uminus__rat_Orsp,axiom,
% 5.68/6.05 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_rat.rsp
% 5.68/6.05 thf(fact_10187_times__rat_Orsp,axiom,
% 5.68/6.05 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_rat.rsp
% 5.68/6.05 thf(fact_10188_Rat_Opositive_Orsp,axiom,
% 5.68/6.05 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.68/6.05 @ ^ [Y5: $o,Z5: $o] : ( Y5 = Z5 )
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Rat.positive.rsp
% 5.68/6.05 thf(fact_10189_inverse__rat_Orsp,axiom,
% 5.68/6.05 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.68/6.05 @ ^ [X2: product_prod_int_int] :
% 5.68/6.05 ( if_Pro3027730157355071871nt_int
% 5.68/6.05 @ ( ( product_fst_int_int @ X2 )
% 5.68/6.05 = zero_zero_int )
% 5.68/6.05 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.05 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.68/6.05 @ ^ [X2: product_prod_int_int] :
% 5.68/6.05 ( if_Pro3027730157355071871nt_int
% 5.68/6.05 @ ( ( product_fst_int_int @ X2 )
% 5.68/6.05 = zero_zero_int )
% 5.68/6.05 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.05 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_rat.rsp
% 5.68/6.05 thf(fact_10190_plus__rat_Oabs__eq,axiom,
% 5.68/6.05 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.68/6.05 ( ( ratrel @ Xa2 @ Xa2 )
% 5.68/6.05 => ( ( ratrel @ X @ X )
% 5.68/6.05 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.68/6.05 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_rat.abs_eq
% 5.68/6.05 thf(fact_10191_one__rat__def,axiom,
% 5.68/6.05 ( one_one_rat
% 5.68/6.05 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % one_rat_def
% 5.68/6.05 thf(fact_10192_Fract_Oabs__eq,axiom,
% 5.68/6.05 ( fract
% 5.68/6.05 = ( ^ [Xa4: int,X2: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Fract.abs_eq
% 5.68/6.05 thf(fact_10193_zero__rat__def,axiom,
% 5.68/6.05 ( zero_zero_rat
% 5.68/6.05 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % zero_rat_def
% 5.68/6.05 thf(fact_10194_uminus__rat_Oabs__eq,axiom,
% 5.68/6.05 ! [X: product_prod_int_int] :
% 5.68/6.05 ( ( ratrel @ X @ X )
% 5.68/6.05 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 5.68/6.05 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_rat.abs_eq
% 5.68/6.05 thf(fact_10195_times__rat_Oabs__eq,axiom,
% 5.68/6.05 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 5.68/6.05 ( ( ratrel @ Xa2 @ Xa2 )
% 5.68/6.05 => ( ( ratrel @ X @ X )
% 5.68/6.05 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 5.68/6.05 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_rat.abs_eq
% 5.68/6.05 thf(fact_10196_Rat_Opositive_Oabs__eq,axiom,
% 5.68/6.05 ! [X: product_prod_int_int] :
% 5.68/6.05 ( ( ratrel @ X @ X )
% 5.68/6.05 => ( ( positive @ ( abs_Rat @ X ) )
% 5.68/6.05 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Rat.positive.abs_eq
% 5.68/6.05 thf(fact_10197_inverse__rat_Oabs__eq,axiom,
% 5.68/6.05 ! [X: product_prod_int_int] :
% 5.68/6.05 ( ( ratrel @ X @ X )
% 5.68/6.05 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 5.68/6.05 = ( abs_Rat
% 5.68/6.05 @ ( if_Pro3027730157355071871nt_int
% 5.68/6.05 @ ( ( product_fst_int_int @ X )
% 5.68/6.05 = zero_zero_int )
% 5.68/6.05 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.05 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_rat.abs_eq
% 5.68/6.05 thf(fact_10198_inverse__rat__def,axiom,
% 5.68/6.05 ( inverse_inverse_rat
% 5.68/6.05 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.68/6.05 @ ^ [X2: product_prod_int_int] :
% 5.68/6.05 ( if_Pro3027730157355071871nt_int
% 5.68/6.05 @ ( ( product_fst_int_int @ X2 )
% 5.68/6.05 = zero_zero_int )
% 5.68/6.05 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.68/6.05 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % inverse_rat_def
% 5.68/6.05 thf(fact_10199_uminus__rat__def,axiom,
% 5.68/6.05 ( uminus_uminus_rat
% 5.68/6.05 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % uminus_rat_def
% 5.68/6.05 thf(fact_10200_plus__rat__def,axiom,
% 5.68/6.05 ( plus_plus_rat
% 5.68/6.05 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % plus_rat_def
% 5.68/6.05 thf(fact_10201_times__rat__def,axiom,
% 5.68/6.05 ( times_times_rat
% 5.68/6.05 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.68/6.05 @ ^ [X2: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % times_rat_def
% 5.68/6.05 thf(fact_10202_of__nat__eq__id,axiom,
% 5.68/6.05 semiri1316708129612266289at_nat = id_nat ).
% 5.68/6.05
% 5.68/6.05 % of_nat_eq_id
% 5.68/6.05 thf(fact_10203_Rat_Opositive__def,axiom,
% 5.68/6.05 ( positive
% 5.68/6.05 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.68/6.05 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.68/6.05
% 5.68/6.05 % Rat.positive_def
% 5.68/6.05
% 5.68/6.05 % Helper facts (40)
% 5.68/6.05 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.68/6.05 ! [X: int,Y2: int] :
% 5.68/6.05 ( ( if_int @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.68/6.05 ! [X: int,Y2: int] :
% 5.68/6.05 ( ( if_int @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.68/6.05 ! [X: nat,Y2: nat] :
% 5.68/6.05 ( ( if_nat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.68/6.05 ! [X: nat,Y2: nat] :
% 5.68/6.05 ( ( if_nat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.68/6.05 ! [X: num,Y2: num] :
% 5.68/6.05 ( ( if_num @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.68/6.05 ! [X: num,Y2: num] :
% 5.68/6.05 ( ( if_num @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.68/6.05 ! [X: rat,Y2: rat] :
% 5.68/6.05 ( ( if_rat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.68/6.05 ! [X: rat,Y2: rat] :
% 5.68/6.05 ( ( if_rat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.68/6.05 ! [X: real,Y2: real] :
% 5.68/6.05 ( ( if_real @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.68/6.05 ! [X: real,Y2: real] :
% 5.68/6.05 ( ( if_real @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.68/6.05 ! [P: real > $o] :
% 5.68/6.05 ( ( P @ ( fChoice_real @ P ) )
% 5.68/6.05 = ( ? [X6: real] : ( P @ X6 ) ) ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.68/6.05 ! [X: complex,Y2: complex] :
% 5.68/6.05 ( ( if_complex @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.68/6.05 ! [X: complex,Y2: complex] :
% 5.68/6.05 ( ( if_complex @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.68/6.05 ! [X: extended_enat,Y2: extended_enat] :
% 5.68/6.05 ( ( if_Extended_enat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.68/6.05 ! [X: extended_enat,Y2: extended_enat] :
% 5.68/6.05 ( ( if_Extended_enat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.68/6.05 ! [X: code_integer,Y2: code_integer] :
% 5.68/6.05 ( ( if_Code_integer @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.68/6.05 ! [X: code_integer,Y2: code_integer] :
% 5.68/6.05 ( ( if_Code_integer @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: set_int,Y2: set_int] :
% 5.68/6.05 ( ( if_set_int @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: set_int,Y2: set_int] :
% 5.68/6.05 ( ( if_set_int @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.68/6.05 ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.68/6.05 ( ( if_VEBT_VEBT @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.68/6.05 ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 5.68/6.05 ( ( if_VEBT_VEBT @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: list_int,Y2: list_int] :
% 5.68/6.05 ( ( if_list_int @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: list_int,Y2: list_int] :
% 5.68/6.05 ( ( if_list_int @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: list_nat,Y2: list_nat] :
% 5.68/6.05 ( ( if_list_nat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: list_nat,Y2: list_nat] :
% 5.68/6.05 ( ( if_list_nat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.68/6.05 ! [X: nat > rat,Y2: nat > rat] :
% 5.68/6.05 ( ( if_nat_rat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.68/6.05 ! [X: nat > rat,Y2: nat > rat] :
% 5.68/6.05 ( ( if_nat_rat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: option_nat,Y2: option_nat] :
% 5.68/6.05 ( ( if_option_nat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: option_nat,Y2: option_nat] :
% 5.68/6.05 ( ( if_option_nat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.68/6.05 ! [X: option_num,Y2: option_num] :
% 5.68/6.05 ( ( if_option_num @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.68/6.05 ! [X: option_num,Y2: option_num] :
% 5.68/6.05 ( ( if_option_num @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 5.68/6.05 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.68/6.05 ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 5.68/6.05 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.68/6.05 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.68/6.05 ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.68/6.05 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.68/6.05 ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 5.68/6.05 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.68/6.05 ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 5.68/6.05 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.68/6.05 ! [P: $o] :
% 5.68/6.05 ( ( P = $true )
% 5.68/6.05 | ( P = $false ) ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.68/6.05 ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 5.68/6.05 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y2 )
% 5.68/6.05 = Y2 ) ).
% 5.68/6.05
% 5.68/6.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.68/6.05 ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 5.68/6.05 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y2 )
% 5.68/6.05 = X ) ).
% 5.68/6.05
% 5.68/6.05 % Conjectures (1)
% 6.89/7.32 thf(conj_0,conjecture,
% 6.89/7.32 ! [U3: nat] :
% 6.89/7.32 ( ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U3 )
% 6.89/7.32 | ~ ( ord_less_nat @ U3 @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.89/7.32
% 6.89/7.32 %------------------------------------------------------------------------------
% 6.89/7.32 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.6EY4mKj9TS/cvc5---1.0.5_14507.p...
% 6.89/7.32 (declare-sort $$unsorted 0)
% 6.89/7.32 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.89/7.32 (declare-sort tptp.set_Pr1281608226676607948nteger 0)
% 6.89/7.32 (declare-sort tptp.produc1908205239877642774nteger 0)
% 6.89/7.32 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.89/7.32 (declare-sort tptp.set_Pr9222295170931077689nt_int 0)
% 6.89/7.32 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 6.89/7.32 (declare-sort tptp.set_Pr8056137968301705908nteger 0)
% 6.89/7.32 (declare-sort tptp.produc8763457246119570046nteger 0)
% 6.89/7.32 (declare-sort tptp.set_Pr1872883991513573699nt_int 0)
% 6.89/7.32 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 6.89/7.32 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.89/7.32 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.89/7.32 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.89/7.32 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.89/7.32 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.89/7.32 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.89/7.32 (declare-sort tptp.produc6241069584506657477e_term 0)
% 6.89/7.32 (declare-sort tptp.set_Pr6308028481084910985omplex 0)
% 6.89/7.32 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.produc8551481072490612790e_term 0)
% 6.89/7.32 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 6.89/7.32 (declare-sort tptp.set_Pr2522554150109002629et_int 0)
% 6.89/7.32 (declare-sort tptp.produc8064648209034914857omplex 0)
% 6.89/7.32 (declare-sort tptp.option6357759511663192854e_term 0)
% 6.89/7.32 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.89/7.32 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.89/7.32 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.89/7.32 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.89/7.32 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.89/7.32 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 6.89/7.32 (declare-sort tptp.produc2115011035271226405et_int 0)
% 6.89/7.32 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.89/7.32 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.89/7.32 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.89/7.32 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.89/7.32 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.89/7.32 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.89/7.32 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.89/7.32 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.89/7.32 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.89/7.32 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.89/7.32 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.89/7.32 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.89/7.32 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.89/7.32 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.89/7.32 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.89/7.32 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.89/7.32 (declare-sort tptp.product_prod_num_num 0)
% 6.89/7.32 (declare-sort tptp.product_prod_nat_num 0)
% 6.89/7.32 (declare-sort tptp.product_prod_nat_nat 0)
% 6.89/7.32 (declare-sort tptp.product_prod_int_int 0)
% 6.89/7.32 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.89/7.32 (declare-sort tptp.set_list_complex 0)
% 6.89/7.32 (declare-sort tptp.set_set_complex 0)
% 6.89/7.32 (declare-sort tptp.list_list_nat 0)
% 6.89/7.32 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.89/7.32 (declare-sort tptp.set_list_nat 0)
% 6.89/7.32 (declare-sort tptp.set_list_int 0)
% 6.89/7.32 (declare-sort tptp.product_prod_nat_o 0)
% 6.89/7.32 (declare-sort tptp.product_prod_o_nat 0)
% 6.89/7.32 (declare-sort tptp.product_prod_o_int 0)
% 6.89/7.32 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.89/7.32 (declare-sort tptp.set_set_nat 0)
% 6.89/7.32 (declare-sort tptp.set_set_int 0)
% 6.89/7.32 (declare-sort tptp.set_Code_integer 0)
% 6.89/7.32 (declare-sort tptp.list_complex 0)
% 6.89/7.32 (declare-sort tptp.set_list_o 0)
% 6.89/7.32 (declare-sort tptp.product_prod_o_o 0)
% 6.89/7.32 (declare-sort tptp.set_complex 0)
% 6.89/7.32 (declare-sort tptp.filter_real 0)
% 6.89/7.32 (declare-sort tptp.option_num 0)
% 6.89/7.32 (declare-sort tptp.option_nat 0)
% 6.89/7.32 (declare-sort tptp.filter_nat 0)
% 6.89/7.32 (declare-sort tptp.set_char 0)
% 6.89/7.32 (declare-sort tptp.list_real 0)
% 6.89/7.32 (declare-sort tptp.set_real 0)
% 6.89/7.32 (declare-sort tptp.list_nat 0)
% 6.89/7.32 (declare-sort tptp.list_int 0)
% 6.89/7.32 (declare-sort tptp.vEBT_VEBT 0)
% 6.89/7.32 (declare-sort tptp.set_rat 0)
% 6.89/7.32 (declare-sort tptp.set_num 0)
% 6.89/7.32 (declare-sort tptp.set_nat 0)
% 6.89/7.32 (declare-sort tptp.set_int 0)
% 6.89/7.32 (declare-sort tptp.code_integer 0)
% 6.89/7.32 (declare-sort tptp.extended_enat 0)
% 6.89/7.32 (declare-sort tptp.list_o 0)
% 6.89/7.32 (declare-sort tptp.complex 0)
% 6.89/7.32 (declare-sort tptp.set_o 0)
% 6.89/7.32 (declare-sort tptp.char 0)
% 6.89/7.32 (declare-sort tptp.real 0)
% 6.89/7.32 (declare-sort tptp.rat 0)
% 6.89/7.32 (declare-sort tptp.num 0)
% 6.89/7.32 (declare-sort tptp.nat 0)
% 6.89/7.32 (declare-sort tptp.int 0)
% 6.89/7.32 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.89/7.32 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.89/7.32 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.89/7.32 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.89/7.32 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.89/7.32 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.89/7.32 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.89/7.32 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.89/7.32 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.89/7.32 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.89/7.32 (declare-fun tptp.code_positive (tptp.num) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.89/7.32 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.89/7.32 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.89/7.32 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.89/7.32 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.89/7.32 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.89/7.32 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.89/7.32 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.89/7.32 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.89/7.32 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.89/7.32 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.89/7.32 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.89/7.32 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.89/7.32 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.89/7.32 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.89/7.32 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.89/7.32 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.89/7.32 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.89/7.32 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.89/7.32 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.89/7.32 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.89/7.32 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.89/7.32 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.89/7.32 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.89/7.32 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.89/7.32 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.89/7.32 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.89/7.32 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 6.89/7.32 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.89/7.32 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.89/7.32 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.id_o (Bool) Bool)
% 6.89/7.32 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.89/7.32 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.one_one_int () tptp.int)
% 6.89/7.32 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.89/7.32 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.89/7.32 (declare-fun tptp.one_one_real () tptp.real)
% 6.89/7.32 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.89/7.32 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.89/7.32 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.89/7.32 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.89/7.32 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.89/7.32 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups6381953495645901045omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups8682486955453173170nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups8110221916422527690omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups6036352826371341000t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups6225526099057966256nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.89/7.32 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.89/7.32 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.89/7.32 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.89/7.32 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.89/7.32 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.89/7.32 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.89/7.32 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.89/7.32 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.89/7.32 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.89/7.32 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.89/7.32 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.89/7.32 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.89/7.32 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.89/7.32 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.89/7.32 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.89/7.32 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.nil_int () tptp.list_int)
% 6.89/7.32 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.89/7.32 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.89/7.32 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.32 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.89/7.32 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.89/7.32 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.89/7.32 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.89/7.32 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.nth_list_nat (tptp.list_list_nat tptp.nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.89/7.32 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.89/7.32 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.89/7.32 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.89/7.32 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.89/7.32 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.89/7.32 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.89/7.32 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.89/7.32 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.89/7.32 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.89/7.32 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.89/7.32 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.89/7.32 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.89/7.32 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.89/7.32 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.89/7.32 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.89/7.32 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.89/7.32 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.89/7.32 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.89/7.32 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.89/7.32 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.89/7.32 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.89/7.32 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.89/7.32 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.89/7.32 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.89/7.32 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.89/7.32 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.89/7.32 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.89/7.32 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.89/7.32 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.89/7.32 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.89/7.32 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.one () tptp.num)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.89/7.32 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.89/7.32 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.89/7.32 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.89/7.32 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.89/7.32 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.89/7.32 (declare-fun tptp.none_num () tptp.option_num)
% 6.89/7.32 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.89/7.32 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.89/7.32 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.89/7.32 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.89/7.32 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.89/7.32 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.89/7.32 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.89/7.32 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.89/7.32 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.bot_bo5358457235160185703eger_o ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bo1403522918969695512_int_o ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bo3000040243691356879eger_o ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bo8662317086119403298_int_o ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.89/7.32 (declare-fun tptp.bot_bo3145834390647256904nteger () tptp.set_Pr8056137968301705908nteger)
% 6.89/7.32 (declare-fun tptp.bot_bo4508923176915781079nt_int () tptp.set_Pr1872883991513573699nt_int)
% 6.89/7.32 (declare-fun tptp.bot_bo5443222936135328352nteger () tptp.set_Pr1281608226676607948nteger)
% 6.89/7.32 (declare-fun tptp.bot_bo572930865798478029nt_int () tptp.set_Pr9222295170931077689nt_int)
% 6.89/7.32 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 6.89/7.32 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.89/7.32 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 6.89/7.32 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.89/7.32 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 6.89/7.32 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le3636971675376928563eger_o ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2124322318746777828_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le4340812435750786203eger_o ((-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le5643404153117327598_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le6558929396352911974_nat_o ((-> tptp.list_nat tptp.list_nat Bool) (-> tptp.list_nat tptp.list_nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le1520216061033275535_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le1598226405681992910_int_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le5604493270027003598_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2556027599737686990_num_o ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2239182809043710856_num_o ((-> tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le3216752416896350996nteger (tptp.set_Pr8056137968301705908nteger tptp.set_Pr8056137968301705908nteger) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le135402666524580259nt_int (tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le653643898420964396nteger (tptp.set_Pr1281608226676607948nteger tptp.set_Pr1281608226676607948nteger) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le8725513860283290265nt_int (tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.89/7.32 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.89/7.32 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.89/7.32 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.89/7.32 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.89/7.32 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.89/7.32 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.89/7.32 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.89/7.32 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.89/7.32 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.89/7.32 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.89/7.32 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.89/7.32 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.89/7.32 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 6.89/7.32 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 6.89/7.32 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.89/7.32 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.89/7.32 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.89/7.32 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.89/7.32 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.89/7.32 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 6.89/7.32 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 6.89/7.32 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.89/7.32 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.89/7.32 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.89/7.32 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.89/7.32 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.89/7.32 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.89/7.32 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.89/7.32 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.89/7.32 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.89/7.32 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.89/7.32 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.89/7.32 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.89/7.32 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.89/7.32 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.89/7.32 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.89/7.32 (declare-fun tptp.produc3790773574474814305omplex (tptp.set_complex tptp.set_complex) tptp.produc8064648209034914857omplex)
% 6.89/7.32 (declare-fun tptp.produc6363374080413544029et_int (tptp.set_int tptp.set_int) tptp.produc2115011035271226405et_int)
% 6.89/7.32 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 6.89/7.32 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.89/7.32 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.89/7.32 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.89/7.32 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.89/7.32 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.produc8678311845419106900er_nat ((-> tptp.code_integer tptp.nat) (-> tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.produc127349428274296955eger_o ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc8763457246119570046nteger) Bool)
% 6.89/7.32 (declare-fun tptp.produc2592262431452330817omplex ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex) tptp.produc8763457246119570046nteger) tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.produc8604463032469472703et_int ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int) tptp.produc8763457246119570046nteger) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.produc3558942015123893603et_nat ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat) tptp.produc8763457246119570046nteger) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.produc815715089573277247t_real ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real) tptp.produc8763457246119570046nteger) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.produc2558449545302689196_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc7773217078559923341nt_int) Bool)
% 6.89/7.32 (declare-fun tptp.produc8289552606927098482et_nat ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat) tptp.produc7773217078559923341nt_int) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.produc6253627499356882019eger_o ((-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc1908205239877642774nteger) Bool)
% 6.89/7.32 (declare-fun tptp.produc1573362020775583542_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc2285326912895808259nt_int) Bool)
% 6.89/7.32 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.89/7.32 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.89/7.32 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.89/7.32 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.89/7.32 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.89/7.32 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.produc8580519160106071146omplex ((-> tptp.int tptp.int tptp.set_complex) tptp.product_prod_int_int) tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.produc73460835934605544et_int ((-> tptp.int tptp.int tptp.set_int) tptp.product_prod_int_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.produc4251311855443802252et_nat ((-> tptp.int tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.produc1656060378719767003at_nat ((-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_int_int) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.32 (declare-fun tptp.produc6452406959799940328t_real ((-> tptp.int tptp.int tptp.set_real) tptp.product_prod_int_int) tptp.set_real)
% 6.89/7.32 (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)
% 6.89/7.32 (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)
% 6.89/7.32 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.89/7.32 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.89/7.32 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.89/7.32 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.89/7.32 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.89/7.32 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.89/7.32 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.89/7.32 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.89/7.32 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.89/7.32 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.89/7.32 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.89/7.32 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.89/7.32 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.89/7.32 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.89/7.32 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.89/7.32 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.89/7.32 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.89/7.32 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.89/7.32 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.89/7.32 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.89/7.32 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.89/7.32 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.89/7.32 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.89/7.32 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.89/7.32 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.89/7.32 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.89/7.32 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.89/7.32 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.89/7.32 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.89/7.32 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.89/7.32 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.89/7.32 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.89/7.32 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.89/7.32 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.89/7.32 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.89/7.32 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.89/7.32 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.89/7.32 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.89/7.32 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.89/7.32 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.89/7.32 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.89/7.32 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.89/7.32 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.89/7.32 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.89/7.32 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.89/7.32 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.89/7.32 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.89/7.32 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.89/7.32 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.32 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.89/7.32 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 6.89/7.32 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.89/7.32 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.89/7.32 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 6.89/7.32 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.89/7.32 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.89/7.32 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.89/7.32 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.89/7.32 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.89/7.32 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.89/7.32 (declare-fun tptp.set_fo3699595496184130361el_nat (tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat) Bool)
% 6.89/7.32 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.89/7.32 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.89/7.32 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.89/7.32 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.89/7.32 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.89/7.32 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 6.89/7.32 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.89/7.32 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.89/7.32 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.89/7.32 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.89/7.32 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.89/7.32 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.89/7.32 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.89/7.32 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.89/7.32 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.89/7.33 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.89/7.33 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo3100542954746470799et_int ((-> tptp.nat tptp.set_int)) Bool)
% 6.89/7.33 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.89/7.33 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.89/7.33 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.89/7.33 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.89/7.33 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.89/7.33 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.89/7.33 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.89/7.33 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.89/7.33 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.89/7.33 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.89/7.33 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.pi () tptp.real)
% 6.89/7.33 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.89/7.33 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.89/7.33 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.89/7.33 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.89/7.33 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.89/7.33 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.33 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.89/7.33 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.33 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.89/7.33 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_V3895251965096974666el_nat (tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V452583751252753300el_num (tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_V7235779383477046023at_nat (tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.89/7.33 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P6019419558468335806at_nat ((-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool) tptp.produc4471711990508489141at_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P5496254298877145759on_nat ((-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool) tptp.produc8306885398267862888on_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P7605991808943153877on_num ((-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool) tptp.produc1193250871479095198on_num) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P3267385326087170368at_nat ((-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool) tptp.produc5542196010084753463at_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.89/7.33 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.89/7.33 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.finite8643634255014194347omplex () tptp.set_Pr6308028481084910985omplex)
% 6.89/7.33 (declare-fun tptp.finite_psubset_int () tptp.set_Pr2522554150109002629et_int)
% 6.89/7.33 (declare-fun tptp.finite_psubset_nat () tptp.set_Pr5488025237498180813et_nat)
% 6.89/7.33 (declare-fun tptp.measure_int ((-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 6.89/7.33 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.33 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.89/7.33 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.89/7.33 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.89/7.33 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.89/7.33 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.89/7.33 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.89/7.33 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.89/7.33 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.89/7.33 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.89/7.33 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.89/7.33 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.89/7.33 (declare-fun tptp.member3068662437193594005nteger (tptp.produc8763457246119570046nteger tptp.set_Pr8056137968301705908nteger) Bool)
% 6.89/7.33 (declare-fun tptp.member7034335876925520548nt_int (tptp.produc7773217078559923341nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 6.89/7.33 (declare-fun tptp.member4164122664394876845nteger (tptp.produc1908205239877642774nteger tptp.set_Pr1281608226676607948nteger) Bool)
% 6.89/7.33 (declare-fun tptp.member7618704894036264090nt_int (tptp.produc2285326912895808259nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 6.89/7.33 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.89/7.33 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.89/7.33 (declare-fun tptp.member351165363924911826omplex (tptp.produc8064648209034914857omplex tptp.set_Pr6308028481084910985omplex) Bool)
% 6.89/7.33 (declare-fun tptp.member2572552093476627150et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 6.89/7.33 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 6.89/7.33 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.89/7.33 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.89/7.33 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.89/7.33 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.89/7.33 (declare-fun tptp.deg () tptp.nat)
% 6.89/7.33 (declare-fun tptp.m () tptp.nat)
% 6.89/7.33 (declare-fun tptp.ma () tptp.nat)
% 6.89/7.33 (declare-fun tptp.mi () tptp.nat)
% 6.89/7.33 (declare-fun tptp.minilow () tptp.nat)
% 6.89/7.33 (declare-fun tptp.na () tptp.nat)
% 6.89/7.33 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.89/7.33 (declare-fun tptp.xa () tptp.nat)
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.minilow))
% 6.89/7.33 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X2)))))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.89/7.33 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y)))))))
% 6.89/7.33 (assert (not (= (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) tptp.none_nat)))
% 6.89/7.33 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.some_nat tptp.minilow)))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.89/7.33 (assert (not (forall ((Minilow tptp.nat)) (not (= (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.some_nat Minilow))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.89/7.33 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))
% 6.89/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))))) (or (= _let_2 tptp.none_nat) (not (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))) _let_2))))))
% 6.89/7.33 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)) (@ _let_1 tptp.na)))))
% 6.89/7.33 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) tptp.na))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))
% 6.89/7.33 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y tptp.nat)) (= X (@ tptp.some_nat Y))))))
% 6.89/7.33 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y))))))
% 6.89/7.33 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y tptp.num)) (= X (@ tptp.some_num Y))))))
% 6.89/7.33 (assert (forall ((X tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X (@ tptp.some_nat Y)))) (= X tptp.none_nat))))
% 6.89/7.33 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.89/7.33 (assert (forall ((X tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X (@ tptp.some_num Y)))) (= X tptp.none_num))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.89/7.33 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.89/7.33 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))))
% 6.89/7.33 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))))
% 6.89/7.33 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.89/7.33 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.89/7.33 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.89/7.33 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.89/7.33 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y2 tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y2 tptp.option_num)) (let ((_let_1 (@ (@ P X) Y2))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y2 tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y2 (@ tptp.some_num B2)) (@ (@ P X) Y2)))) _let_1))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X4 tptp.option_nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X4 tptp.option4927543243414619207at_nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X4 tptp.option_num)) (@ P2 X4))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X4 tptp.option_nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X4 tptp.option4927543243414619207at_nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.89/7.33 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X4 tptp.option_num)) (@ P2 X4))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.89/7.33 (assert (forall ((Y2 tptp.option_nat)) (=> (not (= Y2 tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y2 (@ tptp.some_nat X23))))))))
% 6.89/7.33 (assert (forall ((Y2 tptp.option4927543243414619207at_nat)) (=> (not (= Y2 tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.89/7.33 (assert (forall ((Y2 tptp.option_num)) (=> (not (= Y2 tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y2 (@ tptp.some_num X23))))))))
% 6.89/7.33 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.89/7.33 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.89/7.33 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.89/7.33 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.89/7.33 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.89/7.33 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y2) (or (@ (@ tptp.vEBT_vebt_member T) Y2) (= X Y2)))))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 6.89/7.33 (assert (and (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m)))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.89/7.33 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X5) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X5) (@ (@ tptp.ord_less_eq_nat X5) tptp.ma)))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 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 Y2) _let_1)) X)) N) X)))))
% 6.89/7.33 (assert (forall ((X tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 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 Y2) _let_1)) X)) N) Y2)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y2)) X))))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.89/7.33 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.89/7.33 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.89/7.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y2) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat Z2) X)) (@ (@ tptp.ord_less_eq_nat Z2) Y2)))))))
% 6.89/7.33 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N))) (let ((_let_2 (@ tptp.times_times_complex Y2))) (=> (= (@ (@ tptp.times_times_complex X) Y2) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N))) (let ((_let_2 (@ tptp.times_times_real Y2))) (=> (= (@ (@ tptp.times_times_real X) Y2) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y2))) (=> (= (@ (@ tptp.times_times_rat X) Y2) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y2))) (=> (= (@ (@ tptp.times_times_nat X) Y2) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y2))) (=> (= (@ (@ tptp.times_times_int X) Y2) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ _let_2 _let_1)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I2))))
% 6.89/7.33 (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)))
% 6.89/7.33 (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)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.89/7.33 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 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) Y2)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 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) Y2)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 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) Y2)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y2) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y2))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 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) Y2)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y2)))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) N2))) (@ (@ tptp.vEBT_VEBT_low X2) N2)))))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y2) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y2)) (@ tptp.some_nat Z)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 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)) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 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)) Y2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2)))))))
% 6.89/7.33 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) 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 TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N) (= Deg N))))
% 6.89/7.33 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S))))))
% 6.89/7.33 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.89/7.33 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.89/7.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.89/7.33 (assert (=> (= tptp.mi tptp.ma) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (K tptp.num) (L2 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 L2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L2)))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (K tptp.num) (L2 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 L2)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L2)))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y2)) (= X Y2))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.89/7.33 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.89/7.33 (assert (forall ((X tptp.list_VEBT_VEBT) (Y2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y2))) (not (= X Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.list_o) (Y2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y2))) (not (= X Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y2))) (not (= X Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.list_int) (Y2 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y2))) (not (= X Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y2))) (not (= X Y2)))))
% 6.89/7.33 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X2) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat Z2) Y))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N) M3))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (=> (= J (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X3 tptp.nat)) (@ (@ R X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (not (= M6 N2))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N2) (= M6 N2)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N3 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N3))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_real (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_num (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_int (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N4)) (@ F N))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F N))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F N))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N4))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 6.89/7.33 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.deg))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Px tptp.nat)) (= (= (@ (@ tptp.vEBT_vebt_pred tptp.summary) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt tptp.summary)) X) Px))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X5) tptp.na) (forall ((Xa tptp.nat) (Xb tptp.nat)) (= (= (@ (@ tptp.vEBT_vebt_pred X5) Xa) (@ tptp.some_nat Xb)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt X5)) Xa) Xb)))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (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))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 6.89/7.33 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Ma))))))
% 6.89/7.33 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))))
% 6.89/7.33 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))
% 6.89/7.33 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X5 tptp.real)) (@ (@ tptp.member_real X5) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))))
% 6.89/7.33 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.89/7.33 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.89/7.33 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.89/7.33 (assert (forall ((X5 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X5))))
% 6.89/7.33 (assert (forall ((X5 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X5))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A4))))
% 6.89/7.33 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A4))))
% 6.89/7.33 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A4))))
% 6.89/7.33 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A4))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))))
% 6.89/7.33 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A4))))
% 6.89/7.33 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A4))))
% 6.89/7.33 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A4))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (exists ((C3 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A4) C3))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y2) W)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y2) W)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y2) W)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.89/7.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_pred tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2)))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa))) (let ((_let_5 (= _let_3 tptp.none_nat))) (let ((_let_6 (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa))) (and (=> _let_5 (and (=> _let_6 (= _let_4 (@ tptp.some_nat tptp.mi))) (=> (not _let_6) (= _let_4 tptp.none_nat)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.vEBT_VEBT_add (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))) _let_3)) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat _let_3))))))))))))))
% 6.89/7.33 (assert (forall ((TreeList2 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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.89/7.33 (assert (forall ((TreeList2 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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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) TreeList2) Summary)) X))))))))
% 6.89/7.33 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ 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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.89/7.33 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 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) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.89/7.33 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ 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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M5) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.89/7.33 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.89/7.33 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.89/7.33 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.89/7.33 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.89/7.33 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.89/7.33 (assert (forall ((B tptp.real) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.rat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.int) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (assert (forall ((B tptp.real) (X tptp.nat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.rat) (X tptp.nat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (X tptp.nat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 6.89/7.33 (assert (forall ((B tptp.int) (X tptp.nat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 6.89/7.33 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.89/7.33 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.89/7.33 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.89/7.33 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.89/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.89/7.33 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.89/7.33 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.89/7.33 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.89/7.33 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 6.89/7.33 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 6.89/7.33 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y2)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y2) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y2)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y2) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y2)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y2) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.89/7.33 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.89/7.33 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.89/7.33 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y2) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y2) N)) tptp.one_one_complex))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y2) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y2) N)) tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y2) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y2) N)) tptp.one_one_rat))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y2) N)) tptp.one_one_nat))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y2) N)) tptp.one_one_int))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.89/7.33 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.89/7.33 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.89/7.33 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.89/7.33 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.89/7.33 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.89/7.33 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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 I2) J)) U)) M) N)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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) I2)) U)) N))))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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 I2) J)) U)) M)) N)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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) I2)) U)) N))))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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 I2) J)) U)) M)) N)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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) I2)) U)) N))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.89/7.33 (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.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.89/7.33 (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.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.89/7.33 (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.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.89/7.33 (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.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y2)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y2) X)) _let_1)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y2)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y2) X)) _let_1)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y2)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y2) X)) _let_1)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y2)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y2) X)) _let_1)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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) I2)) U)) N))))))
% 6.89/7.33 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) 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 I2) J)) U)) M)) N)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.89/7.33 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.89/7.33 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.89/7.33 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.89/7.33 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Y2 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) Y2)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y2) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 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) Y2)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 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) Y2)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y2) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 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) Y2)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y2) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y2)))))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))))
% 6.89/7.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred tptp.summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_2))) (let ((_let_11 (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_10)) _let_9)))) (and (=> _let_11 (= _let_7 (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_10)))) (=> (not _let_11) (= _let_7 (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa)) (@ tptp.some_nat tptp.mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))))))))))))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.89/7.33 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.89/7.33 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.89/7.33 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.89/7.33 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.89/7.33 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.89/7.33 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.89/7.33 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.89/7.33 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.89/7.33 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.89/7.33 (assert (forall ((Z tptp.extended_enat) (Y2 tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y2) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y2) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y2)) Z))))))
% 6.89/7.33 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.89/7.33 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.89/7.33 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.89/7.33 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.89/7.33 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.power_power_real X) N3))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_real X) Y2)) (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_rat X) Y2)) (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_int X) Y2)) (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.89/7.33 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 6.89/7.33 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 6.89/7.33 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((I2 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 I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 6.89/7.33 (assert (forall ((I2 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 I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 6.89/7.33 (assert (forall ((I2 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 I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 6.89/7.33 (assert (forall ((I2 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 I2) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.89/7.33 (assert (forall ((I2 tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N) K)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.89/7.33 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.minus_minus_real X) Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y2) Y2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y2)) (@ (@ tptp.minus_minus_rat X) Y2)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y2) Y2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y2)) (@ (@ tptp.minus_minus_int X) Y2)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 6.89/7.33 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (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.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.89/7.33 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.89/7.33 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.89/7.33 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.89/7.33 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb2 tptp.option4927543243414619207at_nat) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y2 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb2) Y2) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb2 tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (=> (= Xb2 (@ tptp.some_P7363390416028606310at_nat B2)) (not (= Y2 (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B2)))))))))))))))
% 6.89/7.33 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb2 tptp.option_num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb2) Y2) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb2 tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B2 tptp.num)) (=> (= Xb2 (@ tptp.some_num B2)) (not (= Y2 (@ tptp.some_num (@ (@ X A3) B2)))))))))))))))
% 6.89/7.33 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb2 tptp.option_nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb2) Y2) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb2 tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B2 tptp.nat)) (=> (= Xb2 (@ tptp.some_nat B2)) (not (= Y2 (@ tptp.some_nat (@ (@ X A3) B2)))))))))))))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.89/7.33 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.89/7.33 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_complex Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_real Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_list_nat Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu2 tptp.vEBT_VEBT)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_VEBT_VEBT Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu2 Bool)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_o Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_nat Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)))))))))
% 6.89/7.33 (assert (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_int Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)))))))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.89/7.33 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 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 TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.89/7.33 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.89/7.33 (assert (forall ((L2 tptp.num) (R2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 6.89/7.33 (assert (forall ((L2 tptp.num) (R2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 6.89/7.33 (assert (forall ((L2 tptp.num) (R2 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.89/7.33 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.89/7.33 (assert (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu3 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu3) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B2)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uu3) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B2)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu3 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu3) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B2)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu3 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu3) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu3) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu3 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu3) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_real) (B4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B4) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B4) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B4) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B4) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B4) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B4) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B4)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.89/7.33 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.89/7.33 (assert (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat C))))
% 6.89/7.33 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.89/7.33 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.89/7.33 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.89/7.33 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.89/7.33 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.89/7.33 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs2 Ys)))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.vEBT_VEBT)) (@ (@ P I3) X6)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 Bool)) (@ (@ P I3) X6)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs) I3)))))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.nat)) (@ (@ P I3) X6)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs) I3)))))))))
% 6.89/7.33 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.int)) (@ (@ P I3) X6)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs) I3)))))))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z5 tptp.list_VEBT_VEBT)) (= Y5 Z5)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) (@ (@ tptp.nth_VEBT_VEBT Ys3) I3))))))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.list_o) (Z5 tptp.list_o)) (= Y5 Z5)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) (@ (@ tptp.nth_o Ys3) I3))))))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.list_nat) (Z5 tptp.list_nat)) (= Y5 Z5)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys3) I3))))))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.list_int) (Z5 tptp.list_int)) (= Y5 Z5)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) (@ (@ tptp.nth_int Ys3) I3))))))))
% 6.89/7.33 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.89/7.33 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.89/7.33 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.89/7.33 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 6.89/7.33 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N)) (@ tptp.set_complex2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) X))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I4)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I4)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I3)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I3)))))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I3)))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.89/7.33 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.89/7.33 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (let ((_let_1 (not (= Y2 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y2) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (=> (exists ((Va3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va3)))) (not (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.89/7.33 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.89/7.33 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 6.89/7.33 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.89/7.33 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.89/7.33 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B3))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2)))))))
% 6.89/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat X5) A))))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.89/7.33 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.89/7.33 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.89/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y2) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y2)) (and (= X tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ tptp.size_size_list_nat Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J) (@ (@ tptp.nth_int Xs2) J)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I2) (@ (@ tptp.nth_int Xs2) I2)) Xs2)))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ (@ tptp.nth_nat Xs2) I2)) Xs2)))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) Xs2)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y2) Y2)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y2) Y2)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.89/7.33 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.89/7.33 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.89/7.33 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.89/7.33 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.89/7.33 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.89/7.33 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.89/7.33 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.89/7.33 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I2) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.89/7.33 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))))
% 6.89/7.33 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))))
% 6.89/7.33 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.89/7.33 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.89/7.33 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 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 Y2) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (= X Y2))))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 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 Y2) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (= X Y2))))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 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 Y2) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y2) _let_1)) (= X Y2))))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 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 Y2) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (= X Y2))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.89/7.33 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 6.89/7.33 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.89/7.33 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.89/7.33 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 6.89/7.33 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M6)))))))
% 6.89/7.33 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N5) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N5))))
% 6.89/7.33 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M6)))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 6.89/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.33 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Uu3 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu3) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S)) X3)))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y2)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y2)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y2) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y2) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y2) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y2) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y2)) (@ _let_1 Z))))))
% 6.89/7.33 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y2)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y2)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y2) Z)))))
% 6.89/7.33 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y2) Z)))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A5) B5)) C))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A5) B5)) C))))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A5) B5)) C))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A5) B5)) C))))))
% 6.89/7.33 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A5) B5)) C))))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) B5)) C))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A5) B5)) C))))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B5)) C))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((Y2 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y2 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.89/7.33 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu3 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu3) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.89/7.33 (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))))
% 6.89/7.33 (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))))
% 6.89/7.33 (assert (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.89/7.33 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) A2)))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N))))))))
% 6.89/7.33 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.89/7.33 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.89/7.33 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.89/7.33 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.33 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.89/7.33 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.89/7.33 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.89/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.complex) (Z5 tptp.complex)) (= Y5 Z5)) (lambda ((A4 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A4) B3) tptp.zero_zero_complex))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.real) (Z5 tptp.real)) (= Y5 Z5)) (lambda ((A4 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B3) tptp.zero_zero_real))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B3) tptp.zero_zero_rat))))
% 6.89/7.33 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B3) tptp.zero_zero_int))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.89/7.33 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.89/7.33 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.89/7.33 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((Y2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.suc Nat3))))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.89/7.33 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va3 tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va3))))))))))
% 6.89/7.33 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.89/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.89/7.33 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.89/7.33 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.89/7.33 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.89/7.33 (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))))))
% 6.89/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.89/7.33 (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 ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P J3))))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.89/7.33 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.89/7.33 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.89/7.33 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.89/7.33 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.89/7.33 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 6.89/7.33 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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))))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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)))))
% 6.89/7.33 (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 ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.89/7.33 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.89/7.33 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P4 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P4) (=> (@ (@ tptp.ord_less_nat M) P4) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P4) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P4))))) (@ P M)))))))
% 6.89/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N2)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y2) 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 Y2) (@ _let_1 Q22))))))))
% 6.89/7.34 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.89/7.34 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.89/7.34 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.89/7.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y2) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y2) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y2) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y2) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat)))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y2) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_real X) Y2) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_rat X) Y2) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_nat X) Y2) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y2 tptp.zero_zero_nat))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (= (@ (@ tptp.plus_plus_int X) Y2) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.89/7.34 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y2)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y2)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y2) tptp.zero_zero_int)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y2)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 6.89/7.34 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y2)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y2) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y2) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y2) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y2)))))))
% 6.89/7.34 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.89/7.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.89/7.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.89/7.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.89/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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 ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.89/7.34 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))))
% 6.89/7.34 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.34 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.34 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.89/7.34 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X3)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))
% 6.89/7.34 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu3) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B2 Bool) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) (@ tptp.suc (@ tptp.suc Va3)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu3 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu3) 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) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 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) Va2) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X3)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X3)))))))))))
% 6.89/7.34 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))
% 6.89/7.34 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.89/7.34 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y2) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.89/7.34 (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 ((S tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.89/7.34 (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 ((S tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu3) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.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))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.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))))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_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))))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_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))))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_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))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_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))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu3) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y2) E2)))) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y2) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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) Y2) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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) Y2) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y2)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) tptp.zero_zero_rat)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y2) W)))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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) Y2) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y2) W)))))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ 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 Y2) W))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y2) (=> (@ (@ 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 Y2) W))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ 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 Y2) W))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (=> (@ (@ 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 Y2) W))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y2) X)) X)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y2) X)) X)))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y2) X)) X)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y2)) X)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y2)) X)))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y2)) X)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2))) tptp.zero_zero_real))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y2) Y2))) tptp.zero_zero_rat))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y2) Y2))) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2))) (or (not (= X tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y2) Y2))) (or (not (= X tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y2) Y2))) (or (not (= X tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y2)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y2)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y2)) Z)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.89/7.34 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y2)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y2)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y2)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y2))) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y2) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y2 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y2))) (@ (@ tptp.times_times_complex Y2) Z)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_real Y2) Z)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_rat Y2) Z)))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M5)))))))))))
% 6.89/7.34 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.34 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.34 (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 ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.89/7.34 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.89/7.34 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs2)))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.89/7.34 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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 ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 6.89/7.34 (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 ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.89/7.34 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B2)))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X)) Y2)))) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X)) Y2)))) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (not Y2))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y2) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y2) (=> (=> (exists ((Uu3 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) true))) Y2) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y2))))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y2)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y2)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) Z)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) Z)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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)))))))))))
% 6.89/7.34 (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)))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (A tptp.real) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (A tptp.rat) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (A tptp.int) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (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))))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y2 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_real Y2) Z))) tptp.zero_zero_real))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y2 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y2)) (@ (@ 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) Y2))) (@ (@ tptp.times_times_rat Y2) Z))) tptp.zero_zero_rat))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Mi2)))))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.89/7.34 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.89/7.34 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.89/7.34 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.89/7.34 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat)))))))) (=> (=> (exists ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (not (= Y2 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y2 (@ tptp.some_nat Ma2)))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (not (= Y2 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (not (= Y2 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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 ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I3)) J3)) (@ P I3))))))))))
% 6.89/7.34 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.89/7.34 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.89/7.34 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va 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) Va) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.89/7.34 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve2)) Vf2) tptp.none_nat)))
% 6.89/7.34 (assert (forall ((X tptp.real) (A tptp.real) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (A tptp.rat) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (A tptp.int) (Y2 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 Y2) 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) Y2))) A)))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (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)))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_eq_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= X Y2))))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= X Y2))))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 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 Y2) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= X Y2))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= X Y2))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.89/7.34 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.34 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.34 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.34 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.34 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_real X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y2) (@ (@ tptp.ord_less_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y2) (@ (@ tptp.ord_less_nat X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_int X) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y2 tptp.zero_zero_real))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y2 tptp.zero_zero_rat))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y2 tptp.zero_zero_int))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y2 tptp.zero_zero_real)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y2 tptp.zero_zero_rat)))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y2 tptp.zero_zero_int)))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))) tptp.zero_zero_real)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 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 Y2) _let_1))) tptp.zero_zero_rat)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 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 Y2) _let_1))) tptp.zero_zero_int)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y2 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu3 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu3) tptp.zero_zero_nat) Uv2) Uw2))) Y2) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu3 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu3) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y2) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) Y2) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 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) Va2) Vb2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y2 (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu3) 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 ((Va2 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) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y2 (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (= Y2 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((U tptp.real) (X tptp.real) (Y2 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) Y2)) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.89/7.34 (assert (forall ((U tptp.rat) (X tptp.rat) (Y2 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) Y2)) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y2)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.89/7.34 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (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 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (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 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 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) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (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 ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 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) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (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 ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.89/7.34 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A4 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A4) B3))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 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) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 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 N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 6.89/7.34 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.89/7.34 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A2)))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B6 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B6) A2)))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A2)))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (exists ((Y tptp.real)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.real)) (=> (@ P Y) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.nat tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (exists ((Y tptp.real)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.real)) (=> (@ P Y) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.int tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (exists ((Y tptp.real)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.real)) (=> (@ P Y) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.complex tptp.real Bool))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (exists ((Y tptp.real)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.real)) (=> (@ P Y) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (exists ((Y tptp.nat)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.nat)) (=> (@ P Y) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (exists ((Y tptp.nat)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.nat)) (=> (@ P Y) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (exists ((Y tptp.nat)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.nat)) (=> (@ P Y) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (exists ((Y tptp.nat)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.nat)) (=> (@ P Y) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int P)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (exists ((Y tptp.int)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.int)) (=> (@ P Y) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int P)) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (exists ((Y tptp.int)) (and (@ P Y) (@ (@ Q X2) Y)))))) (forall ((Y tptp.int)) (=> (@ P Y) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ Q X2) Y))))))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.power_power_real Z2) N) tptp.one_one_real)))))))
% 6.89/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa2 _let_1) (=> (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y2 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y2 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.extended_enat) (Y2 tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y2)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y2) Z)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y2)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y2) Z)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y2)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y2) Z)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y2)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y2) Z)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y2)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y2) Z)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y2)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y2) Z)))))
% 6.89/7.34 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.89/7.34 (assert (forall ((I2 tptp.set_int) (L2 tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L2) U)) (and (@ (@ tptp.ord_less_eq_set_int L2) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))))
% 6.89/7.34 (assert (forall ((I2 tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))))
% 6.89/7.34 (assert (forall ((I2 tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I2) (@ (@ tptp.ord_less_eq_num I2) U)))))
% 6.89/7.34 (assert (forall ((I2 tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))))
% 6.89/7.34 (assert (forall ((I2 tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I2) (@ (@ tptp.ord_less_eq_int I2) U)))))
% 6.89/7.34 (assert (forall ((I2 tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I2) (@ (@ tptp.ord_less_eq_real I2) U)))))
% 6.89/7.34 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L2) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.89/7.34 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.89/7.34 (assert (forall ((L2 tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.89/7.34 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.89/7.34 (assert (forall ((L2 tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.89/7.34 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 6.89/7.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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 ((I3 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) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.89/7.34 (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 ((I3 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) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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 ((I3 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) I3)) J3))) (@ P I3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 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) I3)) J3))) (@ P I3))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K)) (@ (@ tptp.ord_less_eq_int K) I2))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B5 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B5)) (@ _let_1 B))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A5) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.89/7.34 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B5 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B5))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A5) B))))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L2)) L2)) tptp.one_one_int))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.89/7.34 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.89/7.34 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.89/7.34 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X5)) N3)))))))
% 6.89/7.34 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N3)))))))
% 6.89/7.34 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X5)) N3)))))))
% 6.89/7.34 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N3)))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.89/7.34 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.89/7.34 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.89/7.34 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.89/7.34 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.89/7.34 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N3)) Y2))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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 ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X3)))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((B5 tptp.real) (A5 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B5) A5)) (@ (@ tptp.ord_less_real A5) B5))))
% 6.89/7.34 (assert (forall ((B5 tptp.rat) (A5 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B5) A5)) (@ (@ tptp.ord_less_rat A5) B5))))
% 6.89/7.34 (assert (forall ((B5 tptp.num) (A5 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B5) A5)) (@ (@ tptp.ord_less_num A5) B5))))
% 6.89/7.34 (assert (forall ((B5 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B5) A5)) (@ (@ tptp.ord_less_nat A5) B5))))
% 6.89/7.34 (assert (forall ((B5 tptp.int) (A5 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B5) A5)) (@ (@ tptp.ord_less_int A5) B5))))
% 6.89/7.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.89/7.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.89/7.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real X3) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (@ (@ tptp.ord_less_eq_set_int X3) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real A) X3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (@ (@ tptp.ord_less_eq_set_int A) X3) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.89/7.34 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (@ tptp.finite_finite_nat A2)))))
% 6.89/7.34 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.89/7.34 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ tptp.finite_finite_int A2)))))
% 6.89/7.34 (assert (forall ((S3 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (not (@ tptp.finite_finite_nat S3)) (not (@ tptp.finite_finite_nat T3))))))
% 6.89/7.34 (assert (forall ((S3 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (not (@ tptp.finite3207457112153483333omplex S3)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 6.89/7.34 (assert (forall ((S3 tptp.set_int) (T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (not (@ tptp.finite_finite_int S3)) (not (@ tptp.finite_finite_int T3))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ tptp.finite_finite_nat B4) (@ tptp.finite_finite_nat A2)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ tptp.finite3207457112153483333omplex B4) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ tptp.finite_finite_int B4) (@ tptp.finite_finite_int A2)))))
% 6.89/7.34 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.89/7.34 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) B3))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) B3))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) B3))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) B3))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) B3))))
% 6.89/7.34 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) A4))))
% 6.89/7.34 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.num) (X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.int) (X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.89/7.34 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.89/7.34 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B3)))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B3)))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B3)))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B3)))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.89/7.34 (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) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.89/7.34 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.89/7.34 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.89/7.34 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.num) (X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.int) (X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y2)) (or (@ _let_1 X) (@ _let_1 Y2))))))
% 6.89/7.34 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.89/7.34 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.89/7.34 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B3)) (not (= A4 B3))))))
% 6.89/7.34 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.89/7.34 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.real)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.real)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((X2 tptp.real)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (F (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.real)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.nat)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.nat)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((X2 tptp.nat)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.nat)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.int)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.int)) (and (= Uu2 (@ F X2)) (@ P X2)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (F (-> tptp.real tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_real (@ tptp.collect_real Q)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.real) (Y tptp.real)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (F (-> tptp.real tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_real (@ tptp.collect_real Q)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.real) (Y tptp.real)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (F (-> tptp.real tptp.real tptp.int))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_real (@ tptp.collect_real Q)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((X2 tptp.real) (Y tptp.real)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (F (-> tptp.real tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_real (@ tptp.collect_real Q)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.real) (Y tptp.real)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.nat Bool)) (F (-> tptp.real tptp.nat tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat Q)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.real) (Y tptp.nat)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.nat Bool)) (F (-> tptp.real tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat Q)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.real) (Y tptp.nat)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.nat Bool)) (F (-> tptp.real tptp.nat tptp.int))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat Q)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((X2 tptp.real) (Y tptp.nat)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.nat Bool)) (F (-> tptp.real tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat Q)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((X2 tptp.real) (Y tptp.nat)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.int Bool)) (F (-> tptp.real tptp.int tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_int (@ tptp.collect_int Q)) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((X2 tptp.real) (Y tptp.int)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.int Bool)) (F (-> tptp.real tptp.int tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real P)) (=> (@ tptp.finite_finite_int (@ tptp.collect_int Q)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((X2 tptp.real) (Y tptp.int)) (and (= Uu2 (@ (@ F X2) Y)) (@ P X2) (@ Q Y))))))))))
% 6.89/7.34 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B3)) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B3)) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))
% 6.89/7.34 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y2 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y2 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y2 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu3 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu3) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y2 (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu3 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu3) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (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) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 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) Va2) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.89/7.34 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.89/7.34 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))))
% 6.89/7.34 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L2))) (=> (@ (@ 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) L2) _let_1))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B5) 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) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.89/7.34 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B5 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 B5) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B5) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((B5 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 B5) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ _let_1 Q5)))))))
% 6.89/7.34 (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 ((I3 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) I3)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 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) I3)) J3))) (@ P J3))))))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L2)) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L2)) L2))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 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) Va2) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (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 Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 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) Va2) Vb2))) (=> (= X _let_1) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y2 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X6 tptp.int)) (@ P X6)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B4) (@ P (@ (@ tptp.plus_plus_int Y) X2))))))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X6 tptp.int)) (@ P X6)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A2) (@ P (@ (@ tptp.minus_minus_int Y) X2))))))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X5) D4)) T))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.89/7.34 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.89/7.34 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_int I3) B)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (= X5 T)))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.89/7.34 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.89/7.34 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X) P) (and _let_2 P6))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X) P) (=> _let_2 P6))))))))
% 6.89/7.34 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.89/7.34 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.89/7.34 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.34 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.89/7.34 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.89/7.34 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.89/7.34 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.89/7.34 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.89/7.34 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I2))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) 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))))))))))
% 6.89/7.34 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) 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))))))))))
% 6.89/7.34 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X6 tptp.int)) (@ P X6)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X5) D4)) T))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.plus_plus_int X5) D4) T)))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.plus_plus_int X5) D4) T))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D4) T)))))))))
% 6.89/7.34 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D4) T))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B4) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (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))))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_nat A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_real A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C4) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (= (@ (@ tptp.minus_minus_set_int B4) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_set_nat C4) D4))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int D4) B4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_set_int C4) D4))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int B4) A2))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.89/7.34 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (@ _let_1 C4))))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.set_int) (Z5 tptp.set_int)) (= Y5 Z5)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X2 tptp.complex)) (=> (@ P X2) (@ Q X2))))))
% 6.89/7.34 (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 ((X2 tptp.real)) (=> (@ P X2) (@ Q X2))))))
% 6.89/7.34 (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 ((X2 tptp.list_nat)) (=> (@ P X2) (@ Q X2))))))
% 6.89/7.34 (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 ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))))
% 6.89/7.34 (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 ((X2 tptp.int)) (=> (@ P X2) (@ Q X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B6))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B6))))))
% 6.89/7.34 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B6))))))
% 6.89/7.34 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A6))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B6))))))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B6))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) A2)))
% 6.89/7.34 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_set_int B4) C4) (@ (@ tptp.ord_less_set_int A2) C4)))))
% 6.89/7.34 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))
% 6.89/7.34 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C4) (@ _let_1 C4))))))
% 6.89/7.34 (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))))
% 6.89/7.34 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (=> (@ (@ P B2) C2) (=> (@ (@ tptp.ord_less_eq_real A3) B2) (=> (@ (@ tptp.ord_less_eq_real B2) C2) (@ _let_1 C2))))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X3) (@ (@ tptp.ord_less_eq_real X3) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B2) A3)) D5)) (@ (@ P A3) B2)))))))) (@ (@ P A) B))))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_eq_real X) Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_eq_rat X) Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.int) (X tptp.int) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_eq_int X) Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_rat X) Y2))))))
% 6.89/7.34 (assert (forall ((Z tptp.int) (X tptp.int) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_int X) Y2))))))
% 6.89/7.34 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.89/7.34 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.89/7.34 (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)))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y2 I3)) tptp.one_one_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y2 I3)) tptp.one_one_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y2 I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y2 I3)) tptp.one_one_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y2 I3) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y2 I3)) tptp.one_one_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y2 I3)) tptp.one_one_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y2 I3)) tptp.one_one_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y2 I3) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y2 I3)) tptp.one_one_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y2 I3) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y2 I3)) tptp.one_one_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_rat (@ X I3)) (@ Y2 I3)) tptp.one_one_rat))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_rat (@ X I3)) (@ Y2 I3)) tptp.one_one_rat))))))))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.89/7.34 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.divide_divide_int K) L2) Q2))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.modulo_modulo_int K) L2) R2))))
% 6.89/7.34 (assert (forall ((L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L2)) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))) (= (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L2))) (=> (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)))))))))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_real X) Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_rat X) Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.int) (X tptp.int) (Y2 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 Y2) Z)) (@ (@ tptp.ord_less_int X) Y2)))))
% 6.89/7.34 (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)))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y2 I3)) tptp.zero_zero_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y2 I3)) tptp.zero_zero_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y2 I3)) tptp.zero_zero_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y2 I3)) tptp.zero_zero_complex))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y2 I3)) tptp.zero_zero_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y2 I3)) tptp.zero_zero_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y2 I3)) tptp.zero_zero_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y2 I3)) tptp.zero_zero_real))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I3)) (@ Y2 I3)) tptp.zero_zero_rat))))))))))
% 6.89/7.34 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y2 I3) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I3)) (@ Y2 I3)) tptp.zero_zero_rat))))))))))
% 6.89/7.34 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.89/7.34 (assert (forall ((X1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger X1) X22) (@ (@ tptp.produc6137756002093451184nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.89/7.34 (assert (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X22) (@ (@ tptp.produc8603105652947943368nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.89/7.34 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X22) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.89/7.34 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X22) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (and (= A A5) (= B B5)))))
% 6.89/7.34 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (and (= A A5) (= B B5)))))
% 6.89/7.34 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B5)) (and (= A A5) (= B B5)))))
% 6.89/7.34 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B5)) (and (= A A5) (= B B5)))))
% 6.89/7.34 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (and (= A A5) (= B B5)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y2 (@ (@ tptp.product_Pair_int_int A3) B2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y2 (@ (@ tptp.produc6137756002093451184nteger A3) B2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y2 (@ (@ tptp.produc8603105652947943368nteger A3) B2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y2 (@ (@ tptp.produc5700946648718959541nt_int A3) B2)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y2 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)))))))
% 6.89/7.34 (assert (forall ((P4 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 6.89/7.34 (assert (forall ((P4 tptp.produc8763457246119570046nteger)) (exists ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)))))
% 6.89/7.34 (assert (forall ((P4 tptp.produc1908205239877642774nteger)) (exists ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P4 (@ (@ tptp.produc8603105652947943368nteger X3) Y3)))))
% 6.89/7.34 (assert (forall ((P4 tptp.produc2285326912895808259nt_int)) (exists ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P4 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)))))
% 6.89/7.34 (assert (forall ((P4 tptp.produc7773217078559923341nt_int)) (exists ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P4 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P4 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B2))) (@ P P4))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (P4 tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) B2))) (@ P P4))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P4 tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) B2))) (@ P P4))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P4 tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) B2))) (@ P P4))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P4 tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) B2))) (@ P P4))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.89/7.34 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.89/7.34 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.89/7.34 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.89/7.34 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y2 (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C2))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y2 (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C2))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C2 tptp.int)) (not (= Y2 (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C2))))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C2 tptp.int)) (not (= Y2 (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C2))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (X tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C2 tptp.code_integer)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C2)))) (@ P X))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C2 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C2)))) (@ P X))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C2)))) (@ P X))))
% 6.89/7.34 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C2)))) (@ P X))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M5) N3)) (@ (@ P M5) N3)))) (@ (@ P M) N)))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ 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)) L2)))))))
% 6.89/7.34 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.89/7.34 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.89/7.34 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.89/7.34 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.89/7.34 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 6.89/7.34 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.89/7.34 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.89/7.34 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.89/7.34 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.89/7.34 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.89/7.34 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.89/7.34 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.89/7.34 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.89/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.89/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.89/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.89/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.89/7.34 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R2)))))
% 6.89/7.34 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.89/7.34 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.89/7.34 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.89/7.34 (assert (forall ((Y2 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y2) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y2) X) (= (@ (@ tptp.ord_less_eq_rat X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y2) X) (= (@ (@ tptp.ord_less_eq_num X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (= (@ (@ tptp.ord_less_eq_nat X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X) (= (@ (@ tptp.ord_less_eq_int X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y2)) (@ (@ tptp.ord_less_eq_rat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y2)) (@ (@ tptp.ord_less_eq_num Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.89/7.34 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y2) (@ (@ tptp.ord_less_eq_rat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y2) (@ (@ tptp.ord_less_eq_num Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y2) (@ (@ tptp.ord_less_eq_int Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_set_int X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_num X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_nat X) Y2))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (= X Y2) (@ (@ tptp.ord_less_eq_int X) Y2))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.set_int) (Z5 tptp.set_int)) (= Y5 Z5)) (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (@ (@ tptp.ord_less_eq_set_int B3) A4)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ tptp.ord_less_eq_rat B3) A4)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.num) (Z5 tptp.num)) (= Y5 Z5)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ tptp.ord_less_eq_num B3) A4)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ tptp.ord_less_eq_nat B3) A4)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ tptp.ord_less_eq_int B3) A4)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.set_int) (Z5 tptp.set_int)) (= Y5 Z5)) (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (@ (@ tptp.ord_less_eq_set_int A4) B3)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (@ (@ tptp.ord_less_eq_rat A4) B3)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.num) (Z5 tptp.num)) (= Y5 Z5)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (@ (@ tptp.ord_less_eq_num A4) B3)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (@ (@ tptp.ord_less_eq_nat A4) B3)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (@ (@ tptp.ord_less_eq_int A4) B3)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.89/7.34 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_int Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_num Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (=> (@ (@ tptp.ord_less_eq_set_int Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y2) (=> (@ (@ tptp.ord_less_eq_num Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) X) (= X Y2)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.set_int) (Z5 tptp.set_int)) (= Y5 Z5)) (lambda ((X2 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y) (@ (@ tptp.ord_less_eq_set_int Y) X2)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_rat Y) X2)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.num) (Z5 tptp.num)) (= Y5 Z5)) (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_eq_num Y) X2)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2)))))
% 6.89/7.34 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_int Y) X2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y2))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y2))) (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)))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y2))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y2))) (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)))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y2))) (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)))))))))))))))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y2))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y2))) (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)))))))))))))))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 6.89/7.34 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.89/7.34 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 6.89/7.34 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.89/7.34 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.89/7.34 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.89/7.34 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z3) (@ (@ tptp.ord_less_real Z3) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (exists ((Z3 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z3) (@ (@ tptp.ord_less_rat Z3) Y2))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X3) (@ P Y4))) (@ P X3))) (@ P A))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y2) X)) (= (not (@ (@ tptp.ord_less_real X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y2) X)) (= (not (@ (@ tptp.ord_less_rat X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y2) X)) (= (not (@ (@ tptp.ord_less_num X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y2) X)) (= (not (@ (@ tptp.ord_less_nat X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y2) X)) (= (not (@ (@ tptp.ord_less_int X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y2)) (=> (not (= X Y2)) (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y2)) (=> (not (= X Y2)) (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y2)) (=> (not (= X Y2)) (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (=> (not (= X Y2)) (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y2)) (=> (not (= X Y2)) (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.89/7.34 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.89/7.34 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.89/7.34 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.89/7.34 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.89/7.34 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.89/7.34 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X4 tptp.nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P3 N2) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (not (@ P3 M6)))))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.89/7.34 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y2)) (or (@ (@ tptp.ord_less_real Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y2)) (or (@ (@ tptp.ord_less_rat Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y2)) (or (@ (@ tptp.ord_less_num Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y2)) (or (@ (@ tptp.ord_less_nat Y2) X) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y2)) (or (@ (@ tptp.ord_less_int Y2) X) (= X Y2)))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (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))))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.89/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_real X) Y2)) (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_rat X) Y2)) (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_num X) Y2)) (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_int X) Y2)) (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (not (= X Y2)) (or (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (not (= X Y2)) (or (@ (@ tptp.ord_less_rat X) Y2) (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (not (= X Y2)) (or (@ (@ tptp.ord_less_num X) Y2) (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (not (= X Y2)) (or (@ (@ tptp.ord_less_nat X) Y2) (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (not (= X Y2)) (or (@ (@ tptp.ord_less_int X) Y2) (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.89/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_rat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_num Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ _let_1 Z))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.89/7.34 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.89/7.34 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.89/7.34 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.89/7.34 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.34 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) P))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y2) (=> (@ (@ tptp.ord_less_rat Y2) X) P))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y2) (=> (@ (@ tptp.ord_less_num Y2) X) P))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y2) (=> (@ (@ tptp.ord_less_nat Y2) X) P))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y2) (=> (@ (@ tptp.ord_less_int Y2) X) P))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y2) (= X Y2) (@ (@ tptp.ord_less_real Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y2) (= X Y2) (@ (@ tptp.ord_less_rat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y2) (= X Y2) (@ (@ tptp.ord_less_num Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y2) (= X Y2) (@ (@ tptp.ord_less_nat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y2) (= X Y2) (@ (@ tptp.ord_less_int Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (= Y2 X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (= Y2 X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (= Y2 X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (= Y2 X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (= Y2 X)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (not (@ (@ tptp.ord_less_real Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (not (@ (@ tptp.ord_less_rat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (not (@ (@ tptp.ord_less_num Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (not (@ (@ tptp.ord_less_nat Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (not (@ (@ tptp.ord_less_int Y2) X)))))
% 6.89/7.34 (assert (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I4))))))))
% 6.89/7.34 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I4))))))))
% 6.89/7.34 (assert (forall ((X tptp.product_prod_int_int)) (not (forall ((D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D3) I4)))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (not (@ (@ tptp.ord_less_real X) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y2) X) (not (@ (@ tptp.ord_less_set_int X) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y2) X) (not (@ (@ tptp.ord_less_rat X) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y2) X) (not (@ (@ tptp.ord_less_num X) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (not (@ (@ tptp.ord_less_nat X) Y2)))))
% 6.89/7.34 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X) (not (@ (@ tptp.ord_less_int X) Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y2)) (@ (@ tptp.ord_less_eq_rat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y2)) (@ (@ tptp.ord_less_eq_num Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (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)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y2)) (= (@ (@ tptp.ord_less_eq_real X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y2)) (= (@ (@ tptp.ord_less_eq_set_int X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y2)) (= (@ (@ tptp.ord_less_eq_rat X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y2)) (= (@ (@ tptp.ord_less_eq_num X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (= (@ (@ tptp.ord_less_eq_nat X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y2)) (= (@ (@ tptp.ord_less_eq_int X) Y2) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (= (not (@ (@ tptp.ord_less_real X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (= (not (@ (@ tptp.ord_less_set_int X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (= (not (@ (@ tptp.ord_less_rat X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y2) (= (not (@ (@ tptp.ord_less_num X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y2) (= (not (@ (@ tptp.ord_less_nat X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (= (not (@ (@ tptp.ord_less_int X) Y2)) (= X Y2)))))
% 6.89/7.34 (assert (forall ((Z tptp.real) (Y2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X3) (@ (@ tptp.ord_less_eq_real Y2) X3))) (@ (@ tptp.ord_less_eq_real Y2) Z))))
% 6.89/7.34 (assert (forall ((Z tptp.rat) (Y2 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (@ (@ tptp.ord_less_eq_rat Y2) X3))) (@ (@ tptp.ord_less_eq_rat Y2) Z))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (Z tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y2) (@ (@ tptp.ord_less_eq_real X3) Z))) (@ (@ tptp.ord_less_eq_real Y2) Z))))
% 6.89/7.34 (assert (forall ((Y2 tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat X3) Z))) (@ (@ tptp.ord_less_eq_rat Y2) Z))))
% 6.89/7.34 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y) (not (@ (@ tptp.ord_less_eq_real Y) X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y) (not (@ (@ tptp.ord_less_eq_set_int Y) X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (not (@ (@ tptp.ord_less_eq_rat Y) X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (not (@ (@ tptp.ord_less_eq_num Y) X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y) (not (@ (@ tptp.ord_less_eq_nat Y) X2))))))
% 6.89/7.34 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (not (@ (@ tptp.ord_less_eq_int Y) X2))))))
% 6.89/7.34 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y2) X)) (@ (@ tptp.ord_less_real X) Y2))))
% 6.89/7.35 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y2) X)) (@ (@ tptp.ord_less_rat X) Y2))))
% 6.89/7.35 (assert (forall ((Y2 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y2) X)) (@ (@ tptp.ord_less_num X) Y2))))
% 6.89/7.35 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y2) X)) (@ (@ tptp.ord_less_nat X) Y2))))
% 6.89/7.35 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y2) X)) (@ (@ tptp.ord_less_int X) Y2))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B3) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (= A4 B3))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (@ (@ tptp.ord_less_eq_real B3) A4))))))
% 6.89/7.35 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A4))))))
% 6.89/7.35 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (@ (@ tptp.ord_less_eq_rat B3) A4))))))
% 6.89/7.35 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (@ (@ tptp.ord_less_eq_num B3) A4))))))
% 6.89/7.35 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A4))))))
% 6.89/7.35 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (@ (@ tptp.ord_less_eq_int B3) A4))))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 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 Y2) W2)))) (@ (@ tptp.ord_less_eq_real Y2) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 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 Y2) W2)))) (@ (@ tptp.ord_less_eq_rat Y2) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y2) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y2) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y2) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y2) Z)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A4) (= A4 B3)))))
% 6.89/7.35 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (= A4 B3))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (@ (@ tptp.ord_less_eq_real A4) B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (not (@ (@ tptp.ord_less_eq_set_int A4) B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (@ (@ tptp.ord_less_eq_rat A4) B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (@ (@ tptp.ord_less_eq_num A4) B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B3))))))
% 6.89/7.35 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (@ (@ tptp.ord_less_eq_int A4) B3))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.89/7.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.89/7.35 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.89/7.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.89/7.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_set_int (lambda ((X2 tptp.set_int) (Y tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y)))))
% 6.89/7.35 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y) (not (= X2 Y))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y2)) (@ (@ tptp.ord_less_real Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y2)) (@ (@ tptp.ord_less_rat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y2)) (@ (@ tptp.ord_less_num Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y2)) (@ (@ tptp.ord_less_nat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y2)) (@ (@ tptp.ord_less_int Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y2)) (@ (@ tptp.ord_less_eq_real Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y2)) (@ (@ tptp.ord_less_eq_rat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y2)) (@ (@ tptp.ord_less_eq_num Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y2)) (@ (@ tptp.ord_less_eq_int Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y2) (@ (@ tptp.ord_less_eq_set_int X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y2) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y2) (@ (@ tptp.ord_less_eq_num X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y2) (@ (@ tptp.ord_less_eq_nat X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y2) (@ (@ tptp.ord_less_eq_int X) Y2))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_real Y2) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (=> (@ (@ tptp.ord_less_set_int Y2) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (=> (@ (@ tptp.ord_less_rat Y2) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y2) (=> (@ (@ tptp.ord_less_num Y2) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_set_int Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_rat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_num Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ _let_1 Z))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (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 ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_real Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y2) (@ (@ tptp.ord_less_rat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y2) (@ (@ tptp.ord_less_num Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y2) (@ (@ tptp.ord_less_nat Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y2) (@ (@ tptp.ord_less_int Y2) X))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (or (@ (@ tptp.ord_less_real X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (or (@ (@ tptp.ord_less_set_int X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (or (@ (@ tptp.ord_less_rat X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y2) (or (@ (@ tptp.ord_less_num X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y2) (or (@ (@ tptp.ord_less_nat X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (or (@ (@ tptp.ord_less_int X) Y2) (= X Y2)))))
% 6.89/7.35 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.89/7.35 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.89/7.35 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.89/7.35 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.89/7.35 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.89/7.35 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.89/7.35 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.89/7.35 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.89/7.35 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.89/7.35 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 6.89/7.35 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.89/7.35 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.89/7.35 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.89/7.35 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 6.89/7.35 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.89/7.35 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.89/7.35 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.89/7.35 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 6.89/7.35 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.89/7.35 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.89/7.35 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ P A3) B2) (@ (@ P B2) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B2))))) (@ (@ P A) B))))))
% 6.89/7.35 (assert (forall ((X tptp.extended_enat) (Y2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y2) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (= (@ (@ tptp.ord_max_set_int X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (= (@ (@ tptp.ord_max_rat X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.num) (Y2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y2) (= (@ (@ tptp.ord_max_num X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y2) (= (@ (@ tptp.ord_max_nat X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (= (@ (@ tptp.ord_max_int X) Y2) Y2))))
% 6.89/7.35 (assert (forall ((Y2 tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y2) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y2) X))))
% 6.89/7.35 (assert (forall ((Y2 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y2) X) (= (@ (@ tptp.ord_max_set_int X) Y2) X))))
% 6.89/7.35 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y2) X) (= (@ (@ tptp.ord_max_rat X) Y2) X))))
% 6.89/7.35 (assert (forall ((Y2 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y2) X) (= (@ (@ tptp.ord_max_num X) Y2) X))))
% 6.89/7.35 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (= (@ (@ tptp.ord_max_nat X) Y2) X))))
% 6.89/7.35 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y2) X) (= (@ (@ tptp.ord_max_int X) Y2) X))))
% 6.89/7.35 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B3)) B3) A4))))
% 6.89/7.35 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B3)) B3) A4))))
% 6.89/7.35 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B3)) B3) A4))))
% 6.89/7.35 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B3)) B3) A4))))
% 6.89/7.35 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))
% 6.89/7.35 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B3)) B3) A4))))
% 6.89/7.35 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.89/7.35 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 6.89/7.35 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.89/7.35 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.89/7.35 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.89/7.35 (assert (forall ((S3 tptp.set_real)) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) S3) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S3) (@ (@ tptp.ord_less_real Xa) X3))))))))))
% 6.89/7.35 (assert (forall ((S3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S3) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S3) (@ (@ tptp.ord_less_rat Xa) X3))))))))))
% 6.89/7.35 (assert (forall ((S3 tptp.set_num)) (=> (@ tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) S3) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S3) (@ (@ tptp.ord_less_num Xa) X3))))))))))
% 6.89/7.35 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S3) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S3) (@ (@ tptp.ord_less_nat Xa) X3))))))))))
% 6.89/7.35 (assert (forall ((S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S3) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S3) (@ (@ tptp.ord_less_int Xa) X3))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (assert (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.35 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.35 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.89/7.35 (assert (forall ((X tptp.set_real) (Y2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.set_nat) (Y2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y2))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (assert (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.89/7.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.89/7.35 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))
% 6.89/7.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.89/7.35 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.89/7.35 (assert (= tptp.dvd_dvd_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (=> (= A4 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B3 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B3) K3))))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K3))))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K3 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K3))))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K3))))))
% 6.89/7.35 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K3))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.89/7.35 (assert (forall ((P4 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P4) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P4 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.89/7.35 (assert (forall ((P4 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P4) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.89/7.35 (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) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.89/7.35 (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) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) N)))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y2) N)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y2) N)))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y2) N)))))
% 6.89/7.35 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y2) N)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.89/7.35 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 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 Z3) X5) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 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) Z3) (= _let_1 _let_1)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y2) M))))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y2) M))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y2) M))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y2) M))))))
% 6.89/7.35 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y2) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y2) M))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y2 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 Y2)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D))) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D3)))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 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 Y2) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y2)) (= X Y2)))))))
% 6.89/7.35 (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 ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.89/7.35 (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 ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.89/7.35 (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 ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X2 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X2))) (exists ((X2 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X2) tptp.zero_zero_complex)) (@ P X2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (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) D4))) T))))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (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) D4))) T))))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (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) D4))) T))))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4))) T))))))))
% 6.89/7.35 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (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) D4))) T)))))))))
% 6.89/7.35 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (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) D4))) T)))))))))
% 6.89/7.35 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (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) D4))) T)))))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4))) T)))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M5)))))))
% 6.89/7.35 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2))))))))
% 6.89/7.35 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.89/7.35 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B2)))))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B2)))))))))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2))))))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2))))))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2))))))))
% 6.89/7.35 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.89/7.35 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.89/7.35 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (= (lambda ((Y5 tptp.code_integer) (Z5 tptp.code_integer)) (= Y5 Z5)) (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B3) _let_1))))))))
% 6.89/7.35 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B3) _let_1))))))))
% 6.89/7.35 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A4 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B3) _let_1))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))))))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T))))))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 6.89/7.35 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (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) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y2)) Y2)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_Code_integer))))))))
% 6.89/7.35 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.89/7.35 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.89/7.35 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((W tptp.real) (Y2 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 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X) (= Y2 Z)))))))
% 6.89/7.35 (assert (forall ((W tptp.rat) (Y2 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 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X) (= Y2 Z)))))))
% 6.89/7.35 (assert (forall ((W tptp.nat) (Y2 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 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X) (= Y2 Z)))))))
% 6.89/7.35 (assert (forall ((W tptp.int) (Y2 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 Y2)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y2))) (or (= W X) (= Y2 Z)))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))))))))))
% 6.89/7.35 (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)))))))))))))
% 6.89/7.35 (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)))))))))))))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.89/7.35 (assert (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y2 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y2) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 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 N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 6.89/7.35 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N2 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 N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I2))))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I2))))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I2))))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y2)) (@ (@ tptp.ord_less_eq_set_int Y2) X))))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.89/7.35 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.89/7.35 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.89/7.35 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 6.89/7.35 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 6.89/7.35 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 6.89/7.35 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.89/7.35 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.89/7.35 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.89/7.35 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.89/7.35 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.89/7.35 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.89/7.35 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.89/7.35 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.89/7.35 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.89/7.35 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.89/7.35 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.89/7.35 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.89/7.35 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.89/7.35 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.89/7.35 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.89/7.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 6.89/7.35 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (N tptp.nat) (Y2 tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.product_prod_nat_nat) (N tptp.nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y2 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y2))) (and (= X Y2) (not (= N tptp.zero_zero_nat))))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I2) X))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I2) X))))
% 6.89/7.35 (assert (forall ((I2 tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I2) X))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.89/7.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.89/7.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.89/7.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.89/7.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.89/7.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y2))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y2)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num) (Y2 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))) Y2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y2))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.89/7.35 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.89/7.35 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))
% 6.89/7.35 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.89/7.35 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.89/7.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.89/7.35 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.89/7.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.89/7.35 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.89/7.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.89/7.35 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.89/7.35 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.89/7.35 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.89/7.35 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.89/7.35 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y2)) (@ tptp.uminus1532241313380277803et_int X)))))
% 6.89/7.35 (assert (forall ((Y2 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y2) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y2)))))
% 6.89/7.35 (assert (forall ((Y2 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y2)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y2))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.89/7.35 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A5) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A5)) B)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A5) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A5)) B)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.89/7.35 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.89/7.35 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.89/7.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.89/7.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.89/7.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.89/7.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.89/7.35 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.89/7.35 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.89/7.35 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.89/7.35 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_real N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_complex N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs2) N) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replic4235873036481779905at_nat N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_o N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_nat N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_int N) X))))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))))
% 6.89/7.35 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y2) (=> (@ (@ 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)) Y2))) V)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.89/7.35 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 6.89/7.35 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y)))))
% 6.89/7.35 (assert (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E2))) (= X tptp.zero_zero_rat))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y2)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y2) X))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y2)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y2) X))))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y2)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y2) X))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y2)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y2) X))))))
% 6.89/7.35 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y2) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y2))))))
% 6.89/7.35 (assert (forall ((Y2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y2) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y2) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y2))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.89/7.35 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.89/7.35 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.89/7.35 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.89/7.35 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 6.89/7.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.89/7.35 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.35 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.89/7.35 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) (@ tptp.uminus_uminus_real X)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y2))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.uminus_uminus_real X)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.89/7.35 (assert (forall ((Z tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y2) Z))) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y2 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y2) Z))) Z)))))
% 6.89/7.35 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y2 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y2) Z))) Z)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y2) _let_1)) (or (= X Y2) (= X (@ tptp.uminus_uminus_real Y2)))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y2) _let_1)) (or (= X Y2) (= X (@ tptp.uminus_uminus_int Y2)))))))
% 6.89/7.35 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y2) _let_1)) (or (= X Y2) (= X (@ tptp.uminus1482373934393186551omplex Y2)))))))
% 6.89/7.35 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (or (= X Y2) (= X (@ tptp.uminus1351360451143612070nteger Y2)))))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y2) _let_1)) (or (= X Y2) (= X (@ tptp.uminus_uminus_rat Y2)))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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)))))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B4) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.89/7.35 (assert (forall ((X tptp.code_integer) (Y2 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 Y2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))))))
% 6.89/7.35 (assert (forall ((X tptp.rat) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1))))))
% 6.89/7.35 (assert (forall ((X tptp.int) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.89/7.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.89/7.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.89/7.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 6.89/7.35 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 6.89/7.35 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L2) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L2))))))
% 6.89/7.35 (assert (forall ((Y2 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y2) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y2))))))
% 6.89/7.35 (assert (forall ((Y2 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) Y2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y2))))))
% 6.89/7.35 (assert (forall ((Y2 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) Y2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y2))))))
% 6.89/7.35 (assert (forall ((Y2 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) Y2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y2))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (@ (@ P X3) (@ (@ tptp.power_8256067586552552935nteger X3) (@ 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)))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ P X3) (@ (@ tptp.power_power_real X3) (@ 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)))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (@ (@ P X3) (@ (@ tptp.power_power_rat X3) (@ 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)))))))
% 6.89/7.35 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ P X3) (@ (@ tptp.power_power_int X3) (@ 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)))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.89/7.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.89/7.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.89/7.35 (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))))))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L2)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L2) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((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)))))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y2) Z)) (= Y2 (@ (@ tptp.plus_plus_real X) Z)))))
% 6.89/7.35 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (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.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))))))))))))))))
% 6.89/7.35 (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)))))))))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.89/7.35 (assert (forall ((X tptp.nat) (Y2 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 (= Y2 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y2) (=> (@ _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 ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (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 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _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)))))))))))))))))))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))))
% 6.89/7.35 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ 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)))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.89/7.35 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.89/7.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.89/7.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.89/7.35 (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)))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P4))) P4)))
% 6.89/7.35 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P4))) P4)))
% 6.89/7.35 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P4))) P4)))
% 6.89/7.35 (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)))
% 6.89/7.35 (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)))
% 6.89/7.35 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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))))))
% 6.89/7.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.89/7.35 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (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)))))
% 6.89/7.35 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.89/7.35 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.89/7.35 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y2)))))
% 6.89/7.35 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.89/7.35 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I3)) (@ G J3)))) B4))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B4 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B4)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I3)) (@ G J3)))) B4))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I3)) (@ G J3)))) B4))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ G J3)))) B4))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N2)))) A2))))
% 6.89/7.35 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N2)))) A2))))
% 6.89/7.35 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N2)))) A2))))
% 6.89/7.35 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N2)))) A2))))
% 6.89/7.35 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.89/7.35 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.89/7.35 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.89/7.35 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R2))) A2))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.89/7.35 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G) I5)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G) I5)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G) I5)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G) I5)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.real tptp.int)) (I5 tptp.set_real) (G (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I5) (@ (@ tptp.groups1932886352136224148al_int G) I5)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I5) (@ (@ tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((F (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I5) (@ (@ tptp.groups5690904116761175830ex_int G) I5)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I2) (@ G I2))))))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.89/7.35 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.89/7.35 (assert (forall ((Y2 tptp.num)) (=> (not (= Y2 tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y2 (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y2 (@ tptp.bit1 X33)))))))))
% 6.89/7.35 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))))
% 6.89/7.35 (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))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.89/7.35 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.89/7.35 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S3)) (@ (@ tptp.groups2073611262835488442omplex G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3049146728041665814omplex H2) S3)) (@ (@ tptp.groups3049146728041665814omplex G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S3)) (@ (@ tptp.groups8778361861064173332t_real G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S3)) (@ (@ tptp.groups5808333547571424918x_real G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S3)) (@ (@ tptp.groups2906978787729119204at_rat G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S3)) (@ (@ tptp.groups4541462559716669496nt_nat G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G) S3))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3539618377306564664at_int H2) S3)) (@ (@ tptp.groups3539618377306564664at_int G) S3))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (B4 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) B4) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (B4 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) B4) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B4 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) B4) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B4 tptp.rat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) B4) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B4 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B4) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B4 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B4) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B4 tptp.rat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) B4) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (B4 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) B4) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B4 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B4) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B4 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) B4) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B4)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.89/7.36 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.89/7.36 (assert (forall ((I2 tptp.int) (D tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I2))))))
% 6.89/7.36 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L2))) (@ tptp.abs_abs_int L2)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.89/7.36 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) T3) (@ (@ tptp.groups1300246762558778688al_rat H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) T3) (@ (@ tptp.groups5058264527183730370ex_rat H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1932886352136224148al_int G) T3) (@ (@ tptp.groups1932886352136224148al_int H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2073611262835488442omplex G) T3) (@ (@ tptp.groups2073611262835488442omplex H2) S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S3) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S3) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S3) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) S3) (@ (@ tptp.groups1300246762558778688al_rat H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) S3) (@ (@ tptp.groups5058264527183730370ex_rat H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S3) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S3) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1932886352136224148al_int G) S3) (@ (@ tptp.groups1932886352136224148al_int H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S3) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2073611262835488442omplex G) S3) (@ (@ tptp.groups2073611262835488442omplex H2) T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_nat) (A2 tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat C4) B4)) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((C4 tptp.set_nat) (A2 tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat C4) B4)) (= (@ H2 B2) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.89/7.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.89/7.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((K tptp.int) (L2 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)) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.89/7.36 (assert (forall ((K tptp.int) (L2 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 L2))) (@ _let_2 (@ _let_1 L2)))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B4) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B4) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B4))))))))))
% 6.89/7.36 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.nat) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.89/7.36 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.int) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.89/7.36 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I3 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I3 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I3 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I5) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I5) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I5) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) 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 ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K)))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y2)))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.89/7.36 (assert (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 6.89/7.36 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ 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 L2)) (@ (@ 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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.89/7.36 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.89/7.36 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.89/7.36 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.89/7.36 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.89/7.36 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.89/7.36 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.89/7.36 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.89/7.36 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.89/7.36 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.89/7.36 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.36 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.89/7.36 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 6.89/7.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) tptp.zero_zero_complex))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3)))) A2) tptp.zero_zero_rat))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) tptp.zero_zero_real))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) tptp.zero_zero_complex))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3))) (@ D I3)))) A2) tptp.zero_zero_rat))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) tptp.zero_zero_real))))))
% 6.89/7.36 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.89/7.36 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.89/7.36 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A2)) (@ (@ tptp.groups977919841031483927at_nat G) A2))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A2) (=> (not (= X2 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A2) (=> (not (= X2 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A2) (=> (not (= X2 Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.89/7.36 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) tptp.zero_zero_complex))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B4))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.36 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.89/7.36 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.89/7.36 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.89/7.36 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.36 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.89/7.36 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.89/7.36 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.89/7.36 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.89/7.36 (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.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ 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))))))
% 6.89/7.36 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) 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)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ 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))))))
% 6.89/7.36 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N2)))))))
% 6.89/7.36 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N2)))))))
% 6.89/7.36 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N2)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S3)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N7) (@ (@ tptp.member_nat N7) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.89/7.36 (assert (= tptp.ring_1_of_int_real (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_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.89/7.36 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.89/7.36 (assert (= tptp.ring_17405671764205052669omplex (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_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.89/7.36 (assert (= tptp.ring_18347121197199848620nteger (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.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ 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))))))))))
% 6.89/7.36 (assert (= tptp.ring_1_of_int_rat (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_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.89/7.36 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.89/7.36 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.89/7.36 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.89/7.36 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.89/7.36 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.89/7.36 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.89/7.36 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.89/7.36 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.89/7.36 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.89/7.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.89/7.36 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y2)) (= _let_1 Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y2)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y2))))
% 6.89/7.36 (assert (forall ((Y2 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y2) _let_1) (= Y2 _let_1)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.89/7.36 (assert (forall ((Y2 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 Y2) _let_1) (= Y2 _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y2)) (= _let_1 Y2)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (I2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N)) X))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 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 Y2)) (= _let_1 Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y2))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y2) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.89/7.36 (assert (forall ((Y2 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 Y2) _let_1) (= Y2 _let_1)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y2) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y2) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.int) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.int) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y2) (@ (@ tptp.times_times_int Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y2) (@ (@ tptp.times_times_real Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y2) (@ (@ tptp.times_times_nat Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y2) (@ (@ tptp.times_times_rat Y2) _let_1)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.89/7.36 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.89/7.36 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y)) __flatten_var_0))) F)))
% 6.89/7.36 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y)) __flatten_var_0))) F)))
% 6.89/7.36 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X2 tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y)))) F)))
% 6.89/7.36 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X2 tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y)))) F)))
% 6.89/7.36 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X2 tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y)))) F)))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.89/7.36 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.89/7.36 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.89/7.36 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.89/7.36 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.89/7.36 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 6.89/7.36 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N2 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y2)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y2)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y2)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y2)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X) Y2)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X)) (@ tptp.semiri681578069525770553at_rat Y2)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.89/7.36 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.89/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.89/7.36 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.89/7.36 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N2 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 6.89/7.36 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.89/7.36 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 6.89/7.36 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.89/7.36 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.89/7.36 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.89/7.36 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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 ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))
% 6.89/7.36 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.89/7.36 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y2 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y2))) (and (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y2)))) (=> (@ (@ tptp.ord_less_nat X) Y2) (@ P tptp.zero_zero_int))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ 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))))
% 6.89/7.36 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ 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))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.89/7.36 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.89/7.36 (assert (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 6.89/7.36 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.89/7.36 (assert (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.89/7.36 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ 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))))
% 6.89/7.36 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ 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))))
% 6.89/7.36 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ 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))))
% 6.89/7.36 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.89/7.36 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.89/7.36 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 6.89/7.36 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ 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))))))))
% 6.89/7.36 (assert (forall ((H2 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) H2))) (=> (not (= H2 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))) H2)) (@ _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 H2)))))))))))))
% 6.89/7.36 (assert (forall ((H2 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) H2))) (=> (not (= H2 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))) H2)) (@ (@ 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 H2))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X))))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc8763457246119570046nteger) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc127349428274296955eger_o C) P4))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc1908205239877642774nteger) (C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc8603105652947943368nteger A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc6253627499356882019eger_o C) P4))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc2285326912895808259nt_int) (C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc5700946648718959541nt_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc1573362020775583542_int_o C) P4))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc7773217078559923341nt_int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc2558449545302689196_int_o C) P4))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4947309494688390418_int_o C) P4))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ F A) B) (@ (@ tptp.produc127349428274296955eger_o F) (@ (@ tptp.produc6137756002093451184nteger A) B)))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ F A) B) (@ (@ tptp.produc6253627499356882019eger_o F) (@ (@ tptp.produc8603105652947943368nteger A) B)))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4251311855443802252et_nat C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc73460835934605544et_int C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc8580519160106071146omplex C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_int_int) (Z tptp.product_prod_nat_nat) (C (-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ tptp.produc1656060378719767003at_nat C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc8763457246119570046nteger) (Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc3558942015123893603et_nat C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc8763457246119570046nteger) (Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc815715089573277247t_real C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc8763457246119570046nteger) (Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc8604463032469472703et_int C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc8763457246119570046nteger) (Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex))) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger A3) B2)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2592262431452330817omplex C) P4)))))
% 6.89/7.36 (assert (forall ((P4 tptp.produc7773217078559923341nt_int) (Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat))) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc4305682042979456191nt_int A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc8289552606927098482et_nat C) P4)))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4251311855443802252et_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6452406959799940328t_real C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc73460835934605544et_int C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8580519160106071146omplex C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.product_prod_nat_nat) (C (-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1656060378719767003at_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3558942015123893603et_nat C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc815715089573277247t_real C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8604463032469472703et_int C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2592262431452330817omplex C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8289552606927098482et_nat C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.89/7.36 (assert (forall ((P4 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B2) P4) (@ (@ (@ C A3) B2) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P4) X))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4251311855443802252et_nat C) P4)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P4)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc73460835934605544et_int C) P4)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc8580519160106071146omplex C) P4)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.product_prod_nat_nat) (C (-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ tptp.produc1656060378719767003at_nat C) P4)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat)) (P4 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc3558942015123893603et_nat C) P4)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real)) (P4 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc815715089573277247t_real C) P4)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int)) (P4 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc8604463032469472703et_int C) P4)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex)) (P4 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2592262431452330817omplex C) P4)) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat)) (P4 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc8289552606927098482et_nat C) P4)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.89/7.36 (assert (forall ((C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P4 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.produc127349428274296955eger_o C) P4) (not (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc6137756002093451184nteger X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.89/7.36 (assert (forall ((C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P4 tptp.produc1908205239877642774nteger)) (=> (@ (@ tptp.produc6253627499356882019eger_o C) P4) (not (forall ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (=> (= P4 (@ (@ tptp.produc8603105652947943368nteger X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.89/7.36 (assert (forall ((C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P4 tptp.produc2285326912895808259nt_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o C) P4) (not (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.89/7.36 (assert (forall ((C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P4 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o C) P4) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P4 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.89/7.36 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P4) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.produc127349428274296955eger_o F) (@ (@ tptp.produc6137756002093451184nteger A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.produc6253627499356882019eger_o F) (@ (@ tptp.produc8603105652947943368nteger A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.89/7.36 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P4 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P4) Z) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C X3) Y3) Z))))))))
% 6.89/7.36 (assert (forall ((R (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R A) B) C))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.89/7.36 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.89/7.36 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X))))
% 6.89/7.36 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.89/7.36 (assert (forall ((A2 (-> tptp.int tptp.int Bool)) (B4 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A2) B4) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A2))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B4))))))
% 6.89/7.36 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S3))) (@ (@ tptp.groups8097168146408367636l_real G) S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S3))) (@ (@ tptp.groups8778361861064173332t_real G) S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.complex)) (G (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S3))) (@ (@ tptp.groups4567486121110086003t_real G) S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S3))) (@ (@ tptp.groups5808333547571424918x_real G) S3)))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.89/7.36 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I3)))) A2))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y2)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (R2 tptp.real) (Y2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y2 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y2))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y2))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (R2 tptp.real) (Y2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y2)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y2 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y2)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y2))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y2))) E))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y2))) E))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y2))) E))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y2))) E))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y2) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 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 Y2))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y2) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y2))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y2) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 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 Y2))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y2) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y2))) E))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y2))) E))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.89/7.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 6.89/7.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.89/7.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.89/7.36 (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 ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 6.89/7.36 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M6)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.89/7.36 (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))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2))) (=> (@ (@ 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) Y2)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (Y2 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 Y2))) (=> (@ (@ 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) Y2)))))))
% 6.89/7.36 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.89/7.36 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.89/7.36 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.89/7.36 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.89/7.36 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.89/7.36 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.89/7.36 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.89/7.36 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X)) (@ tptp.set_ord_lessThan_rat Y2)) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y2)) (@ (@ tptp.ord_less_eq_num X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y2)) (@ (@ tptp.ord_less_eq_int X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.89/7.36 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))))
% 6.89/7.36 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U2))))))
% 6.89/7.36 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))
% 6.89/7.36 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))
% 6.89/7.36 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))
% 6.89/7.36 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))
% 6.89/7.36 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 6.89/7.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.36 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 6.89/7.36 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 6.89/7.36 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S3) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.89/7.36 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y2)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.89/7.36 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N))) (=> (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.89/7.36 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.89/7.36 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) R2))) _let_1)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) R2))) _let_1)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) R2))) _let_1)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.89/7.36 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.89/7.36 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.89/7.36 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y2) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y2) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y2) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Y2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y2) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y2) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P5)) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y2) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P5)) (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y2) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P5)) (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P5)) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.89/7.36 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.times_times_rat (@ _let_1 X)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (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 ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ F I3)) (@ G I3)))) (@ 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 ((I3 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) tptp.one_one_nat)))) _let_1))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.89/7.36 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) R))) (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) S3))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) R))) (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) S3))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr8056137968301705908nteger) (S3 tptp.set_Pr8056137968301705908nteger)) (= (@ (@ tptp.ord_le3636971675376928563eger_o (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) R))) (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) S3))) (@ (@ tptp.ord_le3216752416896350996nteger R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1281608226676607948nteger) (S3 tptp.set_Pr1281608226676607948nteger)) (= (@ (@ tptp.ord_le4340812435750786203eger_o (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) R))) (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) S3))) (@ (@ tptp.ord_le653643898420964396nteger R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S3 tptp.set_Pr9222295170931077689nt_int)) (= (@ (@ tptp.ord_le5643404153117327598_int_o (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) R))) (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) S3))) (@ (@ tptp.ord_le8725513860283290265nt_int R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S3 tptp.set_Pr1872883991513573699nt_int)) (= (@ (@ tptp.ord_le2124322318746777828_int_o (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) R))) (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) S3))) (@ (@ tptp.ord_le135402666524580259nt_int R) S3))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ tptp.summable_real F))))
% 6.89/7.36 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 6.89/7.36 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.89/7.36 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.89/7.36 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.89/7.36 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ tptp.summable_int F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ tptp.summable_nat F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 6.89/7.36 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))))
% 6.89/7.36 (assert (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N7)))) E)))))))))))
% 6.89/7.36 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))))
% 6.89/7.36 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ (@ tptp.power_power_real Z) I3))))))))))
% 6.89/7.36 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R0) N3))) M7)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R2) N2)))))))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) R)) (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (= (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) R)) (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr8056137968301705908nteger) (S3 tptp.set_Pr8056137968301705908nteger)) (= (= (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) R)) (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1281608226676607948nteger) (S3 tptp.set_Pr1281608226676607948nteger)) (= (= (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) R)) (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S3 tptp.set_Pr9222295170931077689nt_int)) (= (= (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) R)) (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S3 tptp.set_Pr1872883991513573699nt_int)) (= (= (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) R)) (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) S3))) (= R S3))))
% 6.89/7.36 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) tptp.bot_bo2099793752762293965at_nat))))
% 6.89/7.36 (assert (= tptp.bot_bot_int_int_o (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) tptp.bot_bo1796632182523588997nt_int))))
% 6.89/7.36 (assert (= tptp.bot_bo5358457235160185703eger_o (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) tptp.bot_bo3145834390647256904nteger))))
% 6.89/7.36 (assert (= tptp.bot_bo3000040243691356879eger_o (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) tptp.bot_bo5443222936135328352nteger))))
% 6.89/7.36 (assert (= tptp.bot_bo8662317086119403298_int_o (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) tptp.bot_bo572930865798478029nt_int))))
% 6.89/7.36 (assert (= tptp.bot_bo1403522918969695512_int_o (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) tptp.bot_bo4508923176915781079nt_int))))
% 6.89/7.36 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 6.89/7.36 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 6.89/7.36 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.89/7.36 (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)))
% 6.89/7.36 (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)))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.36 (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))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.89/7.36 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr8056137968301705908nteger) (S2 tptp.set_Pr8056137968301705908nteger)) (=> (forall ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3216752416896350996nteger R2) S2))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr1281608226676607948nteger) (S2 tptp.set_Pr1281608226676607948nteger)) (=> (forall ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le653643898420964396nteger R2) S2))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr9222295170931077689nt_int) (S2 tptp.set_Pr9222295170931077689nt_int)) (=> (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8725513860283290265nt_int R2) S2))))
% 6.89/7.36 (assert (forall ((R2 tptp.set_Pr1872883991513573699nt_int) (S2 tptp.set_Pr1872883991513573699nt_int)) (=> (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le135402666524580259nt_int R2) S2))))
% 6.89/7.36 (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))
% 6.89/7.36 (assert (forall ((Y2 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 Y2))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y2))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.89/7.36 (assert (forall ((R tptp.set_nat) (S3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) R))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) S3))) (@ (@ tptp.ord_less_eq_set_nat R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_real) (S3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) R))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) S3))) (@ (@ tptp.ord_less_eq_set_real R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_complex) (S3 tptp.set_complex)) (= (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) R))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) S3))) (@ (@ tptp.ord_le211207098394363844omplex R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) R))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) S3))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S3))))
% 6.89/7.36 (assert (forall ((R tptp.set_int) (S3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) R))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) S3))) (@ (@ tptp.ord_less_eq_set_int R) S3))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (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))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((R1 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (R22 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2556027599737686990_num_o R1) R22) (@ (@ tptp.ord_le2239182809043710856_num_o (@ tptp.accp_P3113834385874906142um_num R22)) (@ tptp.accp_P3113834385874906142um_num R1)))))
% 6.89/7.36 (assert (forall ((R1 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (R22 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le5604493270027003598_nat_o R1) R22) (@ (@ tptp.ord_le704812498762024988_nat_o (@ tptp.accp_P4275260045618599050at_nat R22)) (@ tptp.accp_P4275260045618599050at_nat R1)))))
% 6.89/7.36 (assert (forall ((R1 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (R22 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le1598226405681992910_int_o R1) R22) (@ (@ tptp.ord_le8369615600986905444_int_o (@ tptp.accp_P1096762738010456898nt_int R22)) (@ tptp.accp_P1096762738010456898nt_int R1)))))
% 6.89/7.36 (assert (forall ((R1 (-> tptp.list_nat tptp.list_nat Bool)) (R22 (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6558929396352911974_nat_o R1) R22) (@ (@ tptp.ord_le1520216061033275535_nat_o (@ tptp.accp_list_nat R22)) (@ tptp.accp_list_nat R1)))))
% 6.89/7.36 (assert (forall ((R1 (-> tptp.nat tptp.nat Bool)) (R22 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_le2646555220125990790_nat_o R1) R22) (@ (@ tptp.ord_less_eq_nat_o (@ tptp.accp_nat R22)) (@ tptp.accp_nat R1)))))
% 6.89/7.36 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.36 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X6 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 M6))))))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 M5)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.89/7.36 (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)))
% 6.89/7.36 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.89/7.36 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.89/7.36 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.89/7.36 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.89/7.36 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.89/7.36 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))
% 6.89/7.36 (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)))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))
% 6.89/7.36 (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)))
% 6.89/7.36 (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))
% 6.89/7.36 (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)))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S2) T))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y2 (@ _let_1 (@ tptp.sin_real A3))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y2))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) A)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.89/7.36 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 6.89/7.36 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.89/7.36 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 6.89/7.36 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2))))) tptp.one_one_real)))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.89/7.36 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y2)) (= X Y2)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (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 Y2) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)) (@ _let_1 X))))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))))
% 6.89/7.36 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A tptp.zero_zero_nat))))
% 6.89/7.36 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)) (@ (@ tptp.ord_less_real Y2) X)))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S2))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X)))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) A2))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N2) A2)) (@ F N2)) (@ G N2)))) S5))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) tptp.pi))))))
% 6.89/7.36 (assert (forall ((Y2 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) Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.pi) (= X (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4)))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.89/7.36 (assert (exists ((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) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X3))))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y2) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y2)) (= Y4 X3)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T4)) (= Y2 (@ tptp.sin_real T4))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T4)) (not (= Y2 (@ tptp.sin_real T4))))))))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.89/7.36 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.89/7.36 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y2)) (= X Y2))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2)) (@ _let_1 Y2)))))))))))
% 6.89/7.36 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X))))
% 6.89/7.36 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y2 tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y2) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y2))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2)) (@ (@ tptp.ord_less_real X) Y2))))))))))
% 6.89/7.36 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y2)) (= Y4 X3)))))))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.89/7.36 (assert (forall ((D4 (-> tptp.product_prod_num_num Bool)) (R (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (X tptp.product_prod_num_num) (P (-> tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2239182809043710856_num_o D4) (@ tptp.accp_P3113834385874906142um_num R)) (=> (forall ((X3 tptp.product_prod_num_num) (Z3 tptp.product_prod_num_num)) (=> (@ D4 X3) (=> (@ (@ R Z3) X3) (@ D4 Z3)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (@ D4 X3) (=> (forall ((Z4 tptp.product_prod_num_num)) (=> (@ (@ R Z4) X3) (@ P Z4))) (@ P X3)))) (@ P X)))))))
% 6.89/7.36 (assert (forall ((D4 (-> tptp.product_prod_nat_nat Bool)) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le704812498762024988_nat_o D4) (@ tptp.accp_P4275260045618599050at_nat R)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (=> (@ D4 X3) (=> (@ (@ R Z3) X3) (@ D4 Z3)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ D4 X3) (=> (forall ((Z4 tptp.product_prod_nat_nat)) (=> (@ (@ R Z4) X3) (@ P Z4))) (@ P X3)))) (@ P X)))))))
% 6.89/7.36 (assert (forall ((D4 (-> tptp.product_prod_int_int Bool)) (R (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (X tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o D4) (@ tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X3 tptp.product_prod_int_int) (Z3 tptp.product_prod_int_int)) (=> (@ D4 X3) (=> (@ (@ R Z3) X3) (@ D4 Z3)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ D4 X3) (=> (forall ((Z4 tptp.product_prod_int_int)) (=> (@ (@ R Z4) X3) (@ P Z4))) (@ P X3)))) (@ P X)))))))
% 6.89/7.36 (assert (forall ((D4 (-> tptp.list_nat Bool)) (R (-> tptp.list_nat tptp.list_nat Bool)) (X tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le1520216061033275535_nat_o D4) (@ tptp.accp_list_nat R)) (=> (forall ((X3 tptp.list_nat) (Z3 tptp.list_nat)) (=> (@ D4 X3) (=> (@ (@ R Z3) X3) (@ D4 Z3)))) (=> (@ D4 X) (=> (forall ((X3 tptp.list_nat)) (=> (@ D4 X3) (=> (forall ((Z4 tptp.list_nat)) (=> (@ (@ R Z4) X3) (@ P Z4))) (@ P X3)))) (@ P X)))))))
% 6.89/7.36 (assert (forall ((D4 (-> tptp.nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o D4) (@ tptp.accp_nat R)) (=> (forall ((X3 tptp.nat) (Z3 tptp.nat)) (=> (@ D4 X3) (=> (@ (@ R Z3) X3) (@ D4 Z3)))) (=> (@ D4 X) (=> (forall ((X3 tptp.nat)) (=> (@ D4 X3) (=> (forall ((Z4 tptp.nat)) (=> (@ (@ R Z4) X3) (@ P Z4))) (@ P X3)))) (@ P X)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (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))))))) (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.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (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))))))) (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.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.89/7.36 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X6 (-> tptp.nat tptp.set_int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X6 (@ tptp.suc N2))) (@ X6 N2)))))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.89/7.36 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X8 M5)) (@ X8 N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.89/7.36 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y2 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y2) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (and (=> A3 (= Y2 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y2 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y2 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu3 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu3) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y2 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.89/7.36 (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 ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real X) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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))))))))))
% 6.89/7.36 (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 ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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))))))))))
% 6.89/7.36 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.89/7.36 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.89/7.36 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.89/7.36 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.89/7.36 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 6.89/7.36 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.89/7.36 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.89/7.36 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.89/7.36 (assert (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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))))))))
% 6.89/7.36 (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 ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ 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)))))))
% 6.89/7.36 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat F))) (let ((_let_2 (@ (@ (@ _let_1 A) B) Acc))) (let ((_let_3 (@ (@ tptp.ord_less_nat B) A))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F) (@ (@ tptp.produc487386426758144856at_nat A) (@ (@ tptp.product_Pair_nat_nat B) Acc)))) (and (=> _let_3 (= _let_2 Acc)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F A) Acc)))))))))))
% 6.89/7.36 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat X) (@ (@ tptp.produc487386426758144856at_nat Xa2) (@ (@ tptp.product_Pair_nat_nat Xb2) Xc)))))) (let ((_let_2 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_3 (@ (@ tptp.ord_less_nat Xb2) Xa2))) (=> (= (@ (@ (@ _let_2 Xa2) Xb2) Xc) Y2) (=> _let_1 (not (=> (and (=> _let_3 (= Y2 Xc)) (=> (not _let_3) (= Y2 (@ (@ (@ _let_2 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (@ (@ X Xa2) Xc))))) (not _let_1))))))))))
% 6.89/7.36 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb2 tptp.option4927543243414619207at_nat) (Y2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ tptp.produc2899441246263362727at_nat X))) (let ((_let_2 (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb2) Y2) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat Xa2) Xb2))) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) (=> (= Y2 tptp.none_P5556105721700978146at_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Xb2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_P5556105721700978146at_nat) (=> (= Y2 tptp.none_P5556105721700978146at_nat) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X) (@ (@ tptp.produc488173922507101015at_nat _let_1) tptp.none_P5556105721700978146at_nat))))))))) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat B2))) (=> (= Xb2 _let_1) (=> (= Y2 (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) _let_1)))))))))))))))))))
% 6.89/7.36 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb2 tptp.option_num) (Y2 tptp.option_num)) (let ((_let_1 (@ tptp.produc5778274026573060048on_num X))) (let ((_let_2 (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb2) Y2) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num Xa2) Xb2))) (=> (=> (= Xa2 tptp.none_num) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Xb2)))))) (=> (forall ((V2 tptp.num)) (let ((_let_1 (@ tptp.some_num V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_num) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X) (@ (@ tptp.produc8585076106096196333on_num _let_1) tptp.none_num))))))))) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B2 tptp.num)) (let ((_let_1 (@ tptp.some_num B2))) (=> (= Xb2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) _let_1)))))))))))))))))))
% 6.89/7.36 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb2 tptp.option_nat) (Y2 tptp.option_nat)) (let ((_let_1 (@ tptp.produc8929957630744042906on_nat X))) (let ((_let_2 (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb2) Y2) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat Xa2) Xb2))) (=> (=> (= Xa2 tptp.none_nat) (=> (= Y2 tptp.none_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Xb2)))))) (=> (forall ((V2 tptp.nat)) (let ((_let_1 (@ tptp.some_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb2 tptp.none_nat) (=> (= Y2 tptp.none_nat) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X) (@ (@ tptp.produc5098337634421038937on_nat _let_1) tptp.none_nat))))))))) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.some_nat B2))) (=> (= Xb2 _let_1) (=> (= Y2 (@ tptp.some_nat (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) _let_1)))))))))))))))))))
% 6.89/7.36 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X) N2))))))))
% 6.89/7.36 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X) N2))))))))
% 6.89/7.36 (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)))))))))))))
% 6.89/7.36 (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)))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.89/7.36 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.89/7.36 (assert (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))
% 6.89/7.36 (assert (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))
% 6.89/7.36 (assert (= tptp.diffs_rat (lambda ((C3 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C3 _let_1))))))
% 6.89/7.36 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((X3 tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X3) N2))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X) N2)))))))
% 6.89/7.36 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X3) N2))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X) N2)))))))
% 6.89/7.36 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb2) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb2) Xc) Y2) (and (=> _let_2 (= Y2 Xc)) (=> (not _let_2) (= Y2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (@ (@ X Xa2) Xc))))))))))
% 6.89/7.36 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B3 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A4)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B3) (@ (@ F3 A4) Acc2))))))
% 6.89/7.36 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y2) (@ tptp.tan_real X3)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y2) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y2)) (= Y4 X3)))))))))
% 6.89/7.36 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y2))) (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 Y2) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2)) (@ _let_1 Y2)))))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y2))))))
% 6.89/7.36 (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)))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y2)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y2)))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (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 Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (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 Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) K5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X3) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X) N2))))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) K5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X3) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X) N2))))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X3) Y2))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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) Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2))))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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) Y2) (= (@ tptp.arctan Y2) X)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arctan Y2))) (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) Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y2))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) 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))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y2))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) 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))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y2))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y2))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y2) 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))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y2))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y2))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y2) 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))))))))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y2))) (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 Y2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y2))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y2))) (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 Y2))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X)))))))
% 6.89/7.36 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.89/7.36 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.89/7.36 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.89/7.36 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.89/7.36 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.89/7.36 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.89/7.36 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) (@ tptp.measure_nat F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.int) (Y2 tptp.int) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) (@ tptp.measure_int F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y2)))))
% 6.89/7.36 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T4)) (@ tptp.sin_real T4)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (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 ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A2) B4)) tptp.finite_psubset_nat) (and (@ (@ tptp.ord_less_set_nat A2) B4) (@ tptp.finite_finite_nat B4)))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A2) B4)) tptp.finite_psubset_int) (and (@ (@ tptp.ord_less_set_int A2) B4) (@ tptp.finite_finite_int B4)))))
% 6.89/7.36 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.member351165363924911826omplex (@ (@ tptp.produc3790773574474814305omplex A2) B4)) tptp.finite8643634255014194347omplex) (and (@ (@ tptp.ord_less_set_complex A2) B4) (@ tptp.finite3207457112153483333omplex B4)))))
% 6.89/7.36 (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)))))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y2)) (= X Y2))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.89/7.36 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_real X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.89/7.36 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.89/7.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 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 Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.89/7.36 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y2) (@ (@ tptp.times_times_complex Y2) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y2) (@ (@ tptp.times_times_real Y2) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y2)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y2)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y2)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2))))))))
% 6.89/7.36 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2))))))
% 6.89/7.36 (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)))
% 6.89/7.36 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ 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))))))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.minus_minus_real Y2) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y2))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y2)) X)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y2)) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.89/7.36 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.89/7.36 (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))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.89/7.36 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ tptp.sqrt X) Y2)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y2)))))))
% 6.89/7.36 (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))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))) Y2) (= X tptp.zero_zero_real)))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1))) X) (= Y2 tptp.zero_zero_real)))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)))))))
% 6.89/7.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.89/7.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y2)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real X) Y2))))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.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)))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y2))))))
% 6.89/7.36 (assert (forall ((Y2 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 Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.89/7.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 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 Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)))))) tptp.one_one_real))))
% 6.89/7.36 (assert (forall ((X tptp.real) (U tptp.real) (Y2 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 Y2)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U))))))))
% 6.89/7.36 (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)))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.89/7.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.89/7.36 (assert (forall ((X tptp.real) (U tptp.real) (Y2 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 Y2) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U)))))))))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (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))))))))))
% 6.89/7.36 (assert (= tptp.arctan (lambda ((X2 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 X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.89/7.36 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.89/7.36 (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))))))))))
% 6.89/7.36 (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))))))))
% 6.89/7.36 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.89/7.36 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K3))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ 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 N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.89/7.36 (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))))))))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.89/7.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.89/7.36 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2)))))
% 6.89/7.36 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y2)) Y2)))))
% 6.89/7.36 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.36 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.36 (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))))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.89/7.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.89/7.36 (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)))))))))
% 6.89/7.36 (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)))))
% 6.89/7.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 6.89/7.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ tptp.arccos X)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_eq_real Y2) X))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y2)) (= X Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y2)) (= X Y2))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y2)) (@ tptp.arccos X)))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_real Y2) X))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) tptp.pi)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_real X) Y2))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2))))
% 6.89/7.37 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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) Y2)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) 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))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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 Y2))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (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)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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) Y2))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) 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) Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y2) (@ _let_1 (@ tptp.sin_real Y2)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (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)) Y2) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) X))))))))))
% 6.89/7.37 (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))))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_complex _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_rat _let_1) N))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.power_power_real _let_1) N))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))
% 6.89/7.37 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 6.89/7.37 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 6.89/7.37 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 6.89/7.37 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y2) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y2 (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) true))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> Y2 (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.89/7.37 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I2) K))))
% 6.89/7.37 (assert (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I2) K))))
% 6.89/7.37 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I2) K))))
% 6.89/7.37 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I2) K))))
% 6.89/7.37 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I2) K))))
% 6.89/7.37 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I2) K))))
% 6.89/7.37 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X)) (@ tptp.set_or58775011639299419et_int Y2)) (@ (@ tptp.ord_less_eq_set_int X) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X)) (@ tptp.set_ord_atMost_rat Y2)) (@ (@ tptp.ord_less_eq_rat X) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y2)) (@ (@ tptp.ord_less_eq_num X) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y2)) (@ (@ tptp.ord_less_eq_int X) Y2))))
% 6.89/7.37 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L2) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))))
% 6.89/7.37 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L2) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 6.89/7.37 (assert (forall ((L2 tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L2) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L2) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 6.89/7.37 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L2) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L2) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 6.89/7.37 (assert (forall ((L2 tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L2) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L2) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U2))))))
% 6.89/7.37 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) U2))))))
% 6.89/7.37 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U2))))))
% 6.89/7.37 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))))
% 6.89/7.37 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))))
% 6.89/7.37 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.89/7.37 (assert (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.89/7.37 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_atMost_nat K3))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.89/7.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X2) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) (@ D I3)))))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.int)) (B4 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N3))) B4)) (@ tptp.summable_int A)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.nat)) (B4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N3))) B4)) (@ tptp.summable_nat A)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N3))) B4)) (@ tptp.summable_real A)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_complex)))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real W2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ C K) tptp.zero_zero_real)))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_complex))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ C I3) tptp.zero_zero_real))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.37 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.37 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N))) (@ _let_2 (@ _let_1 (@ tptp.suc N))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (not (= (@ C I3) tptp.zero_zero_complex)))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (not (= (@ C I3) tptp.zero_zero_real)))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex) (not (forall ((B2 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat) (not (forall ((B2 (-> tptp.nat tptp.rat))) (not (forall ((Z4 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int) (not (forall ((B2 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real) (not (forall ((B2 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (A tptp.complex)) (exists ((B2 (-> tptp.nat tptp.complex))) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) _let_1))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.rat)) (N tptp.nat) (A tptp.rat)) (exists ((B2 (-> tptp.nat tptp.rat))) (forall ((Z4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I3)) (@ (@ tptp.power_power_rat Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) _let_1))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.int)) (N tptp.nat) (A tptp.int)) (exists ((B2 (-> tptp.nat tptp.int))) (forall ((Z4 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) _let_1))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (A tptp.real)) (exists ((B2 (-> tptp.nat tptp.real))) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) _let_1))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N) M))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J3)) N))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K3) I3)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N tptp.nat) (B (-> tptp.nat tptp.rat)) (X tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.complex)) (N tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_complex)))))))
% 6.89/7.37 (assert (forall ((C (-> tptp.nat tptp.real)) (N tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X2) I3)))) (@ tptp.set_ord_atMost_nat N)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)) (= (@ C X2) tptp.zero_zero_real)))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X) I3)))) (@ 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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ (@ tptp.sums_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ (@ tptp.sums_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ B (@ (@ tptp.minus_minus_nat K3) I3))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_int Z) N) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I3 N)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_complex Z) N) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I3 N)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I3 N)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_rat Z) N) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I3 N)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (= (@ (@ tptp.power_power_real Z) N) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I3 N)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I3)))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real)))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N)))) (@ _let_1 X)))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger I3))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int I3))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat I3))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real I3))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y2) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y2) K3))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y2) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y2) K3))) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y2) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y2) K3))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y2) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y2) K3))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) J3))))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.89/7.37 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.89/7.37 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.89/7.37 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.89/7.37 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N) I3)))) (@ 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))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_complex))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I3)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_rat))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) I3))))) (@ tptp.set_ord_atMost_nat N)) tptp.zero_zero_real))))
% 6.89/7.37 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.complex)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.89/7.37 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N)))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y2) I3)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X) I3)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y2) I3)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat Y2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) I3)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y2) I3)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int Y2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y2) I3)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I3) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (not (@ _let_2 N2)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (@ _let_2 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (@ _let_2 N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N2))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_complex Y2) (@ (@ tptp.minus_minus_nat P5) N2)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y2)))))
% 6.89/7.37 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.89/7.37 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.89/7.37 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.89/7.37 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 6.89/7.37 (assert (forall ((X tptp.real) (A tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y2)) (@ _let_2 (@ _let_1 Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (A tptp.real) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y2)) (@ _let_2 (@ _let_1 Y2)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X) Y2))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X)) Y2) (@ _let_1 (@ (@ tptp.times_times_complex X) Y2))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((B tptp.real) (U tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real U))) (= (= (@ (@ tptp.plus_plus_real B) (@ _let_1 A)) (@ (@ tptp.plus_plus_real A) (@ _let_1 B))) (or (= A B) (= U tptp.one_one_real))))))
% 6.89/7.37 (assert (forall ((B tptp.complex) (U tptp.real) (A tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex U))) (= (= (@ (@ tptp.plus_plus_complex B) (@ _let_1 A)) (@ (@ tptp.plus_plus_complex A) (@ _let_1 B))) (or (= A B) (= U tptp.one_one_real))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X) Y2)) N) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y2) N)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X) Y2)) N) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_complex Y2) N)))))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.89/7.37 (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)))
% 6.89/7.37 (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)))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.89/7.37 (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)))
% 6.89/7.37 (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)))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y2))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_complex (@ _let_1 X)) (@ _let_1 Y2))))))
% 6.89/7.37 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A2)) (@ (@ tptp.groups708209901874060359at_nat H2) A2)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A2)) (@ (@ tptp.groups705719431365010083at_int H2) A2)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A2)) (@ (@ tptp.groups1705073143266064639nt_int H2) A2)))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N))) A2))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 6.89/7.37 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.89/7.37 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) X)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real A) B)) X) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.real_V2046097035970521341omplex B) X)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X) Y2)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y2) Xa2)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real X) Y2)) Xa2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex X) Xa2)) (@ (@ tptp.real_V2046097035970521341omplex Y2) Xa2)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.37 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A4)))) A2))))
% 6.89/7.37 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A4)))) A2))))
% 6.89/7.37 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A4)))) A2))))
% 6.89/7.37 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.89/7.37 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A4 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) tptp.one_one_real))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) tptp.one_one_rat))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) tptp.one_one_rat))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) tptp.one_one_nat))))
% 6.89/7.37 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups6464643781859351333omplex H2) S3)) (@ (@ tptp.groups6464643781859351333omplex G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups7440179247065528705omplex H2) S3)) (@ (@ tptp.groups7440179247065528705omplex G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3708469109370488835omplex H2) S3)) (@ (@ tptp.groups3708469109370488835omplex G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S3)) (@ (@ tptp.groups129246275422532515t_real G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S3)) (@ (@ tptp.groups2316167850115554303t_real G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H2) S3)) (@ (@ tptp.groups766887009212190081x_real G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H2) S3)) (@ (@ tptp.groups73079841787564623at_rat G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H2) S3)) (@ (@ tptp.groups1072433553688619179nt_rat G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X15) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups225925009352817453ex_rat H2) S3)) (@ (@ tptp.groups225925009352817453ex_rat G) S3))))))))
% 6.89/7.37 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X15) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_nat X15) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H2) S3)) (@ (@ tptp.groups1707563613775114915nt_nat G) S3))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.code_integer)) (G (-> tptp.real tptp.code_integer))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups6225526099057966256nteger F) A2)) (@ (@ tptp.groups6225526099057966256nteger G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3455450783089532116nteger F) A2)) (@ (@ tptp.groups3455450783089532116nteger G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer)) (G (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups8682486955453173170nteger F) A2)) (@ (@ tptp.groups8682486955453173170nteger G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3827104343326376752nteger F) A2)) (@ (@ tptp.groups3827104343326376752nteger G) B4)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) B4)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.89/7.37 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I3)))) _let_1)))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.89/7.37 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (@ _let_1 B4))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat H2))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B4)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat H2))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat H2))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B4 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B4) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C4) B4)) (= (@ H2 B2) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B4 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C4) B4)) (= (@ H2 B2) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B4))))))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S3) (@ (@ tptp.groups1681761925125756287l_real H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups766887009212190081x_real G) S3) (@ (@ tptp.groups766887009212190081x_real H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) S3) (@ (@ tptp.groups4061424788464935467al_rat H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups225925009352817453ex_rat G) S3) (@ (@ tptp.groups225925009352817453ex_rat H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S3) (@ (@ tptp.groups4696554848551431203al_nat H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S3) (@ (@ tptp.groups861055069439313189ex_nat H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.one_one_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4694064378042380927al_int G) S3) (@ (@ tptp.groups4694064378042380927al_int H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.one_one_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups858564598930262913ex_int G) S3) (@ (@ tptp.groups858564598930262913ex_int H2) T3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups713298508707869441omplex G) T3) (@ (@ tptp.groups713298508707869441omplex H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T3) (@ (@ tptp.groups3708469109370488835omplex H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T3) (@ (@ tptp.groups1681761925125756287l_real H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups766887009212190081x_real G) T3) (@ (@ tptp.groups766887009212190081x_real H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) T3) (@ (@ tptp.groups4061424788464935467al_rat H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups225925009352817453ex_rat G) T3) (@ (@ tptp.groups225925009352817453ex_rat H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) T3) (@ (@ tptp.groups4696554848551431203al_nat H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) T3) (@ (@ tptp.groups861055069439313189ex_nat H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4694064378042380927al_int G) T3) (@ (@ tptp.groups4694064378042380927al_int H2) S3))))))))
% 6.89/7.37 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups858564598930262913ex_int G) T3) (@ (@ tptp.groups858564598930262913ex_int H2) S3))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y2 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) Y2) (=> (@ _let_1 B) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) Y2)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_complex X) X))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3455450783089532116nteger F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3827104343326376752nteger F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups8682486955453173170nteger F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.sin_real X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X) N2)))) (@ tptp.sin_complex X))))
% 6.89/7.37 (assert (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.89/7.37 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.cos_real X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X) N2)))) (@ tptp.cos_complex X))))
% 6.89/7.37 (assert (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.89/7.37 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X) N2)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X) N2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X) N2)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X) N2)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (Z (-> tptp.real tptp.real)) (W (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups1681761925125756287l_real Z) I5)) (@ (@ tptp.groups1681761925125756287l_real W) I5)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (Z (-> tptp.int tptp.real)) (W (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2316167850115554303t_real Z) I5)) (@ (@ tptp.groups2316167850115554303t_real W) I5)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (Z (-> tptp.complex tptp.real)) (W (-> tptp.complex tptp.real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups766887009212190081x_real Z) I5)) (@ (@ tptp.groups766887009212190081x_real W) I5)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (Z (-> tptp.product_prod_nat_nat tptp.real)) (W (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6036352826371341000t_real Z) I5)) (@ (@ tptp.groups6036352826371341000t_real W) I5)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_real) (Z (-> tptp.real tptp.complex)) (W (-> tptp.real tptp.complex))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups713298508707869441omplex Z) I5)) (@ (@ tptp.groups713298508707869441omplex W) I5)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_int) (Z (-> tptp.int tptp.complex)) (W (-> tptp.int tptp.complex))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7440179247065528705omplex Z) I5)) (@ (@ tptp.groups7440179247065528705omplex W) I5)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_complex) (Z (-> tptp.complex tptp.complex)) (W (-> tptp.complex tptp.complex))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups3708469109370488835omplex Z) I5)) (@ (@ tptp.groups3708469109370488835omplex W) I5)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (Z (-> tptp.product_prod_nat_nat tptp.complex)) (W (-> tptp.product_prod_nat_nat tptp.complex))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups8110221916422527690omplex Z) I5)) (@ (@ tptp.groups8110221916422527690omplex W) I5)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I3 tptp.product_prod_nat_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (Z (-> tptp.nat tptp.real)) (W (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups129246275422532515t_real Z) I5)) (@ (@ tptp.groups129246275422532515t_real W) I5)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((I5 tptp.set_nat) (Z (-> tptp.nat tptp.complex)) (W (-> tptp.nat tptp.complex))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z) I5)) (@ (@ tptp.groups6464643781859351333omplex W) I5)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I3)) (@ W I3))))) I5))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.89/7.37 (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 ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((B4 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B4)))))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) N))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) N))))
% 6.89/7.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) N))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) N2))))) (@ tptp.sin_real X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) N2))))) (@ tptp.sin_complex X))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) N2)))) (@ tptp.cos_real X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) N2)))) (@ tptp.cos_complex X))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.89/7.37 (assert (= tptp.gbinomial_complex (lambda ((A4 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)) A4)) tptp.one_one_complex)) K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_real (lambda ((A4 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)) A4)) tptp.one_one_real)) K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_rat (lambda ((A4 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)) A4)) tptp.one_one_rat)) K3)))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.89/7.37 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.89/7.37 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.89/7.37 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.89/7.37 (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 ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (assert (= tptp.gbinomial_complex (lambda ((A4 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 A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_rat (lambda ((A4 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 A4)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_real (lambda ((A4 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 A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.89/7.37 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.89/7.37 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M)))))
% 6.89/7.37 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M)))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.89/7.37 (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ 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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.89/7.37 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.37 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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 Y2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.37 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.89/7.37 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))))
% 6.89/7.37 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y)))))
% 6.89/7.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.89/7.37 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.89/7.37 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 6.89/7.37 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.89/7.37 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.89/7.37 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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 Y2) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y2)))))))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.89/7.37 (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)))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.37 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.89/7.37 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.89/7.37 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 6.89/7.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 6.89/7.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y)))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.89/7.37 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.89/7.37 (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)))))))))))
% 6.89/7.37 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.89/7.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.89/7.37 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 6.89/7.37 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.89/7.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y2))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (=> (@ (@ 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 Y2)) (@ _let_1 X)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) B))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y2)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y2)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y2)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y2) A))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y2)) (@ (@ tptp.times_times_real Y2) (@ tptp.ln_ln_real X))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (B tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y2)) (@ (@ tptp.times_times_real Y2) (@ _let_1 X)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real X) Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real Y2) X))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.89/7.37 (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)))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 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 Y2)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y2)))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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 Y2) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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)) Y2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y2)))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y2))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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) Y2)) X) (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y2)))))))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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 Y2) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y2)) X))))))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y2))))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 6.89/7.37 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.89/7.37 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))))))
% 6.89/7.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.89/7.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 6.89/7.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (exists ((A3 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A3))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y2)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y2) R2)))))
% 6.89/7.37 (assert (forall ((R2 tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y2)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y2)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R2)) Y2))))
% 6.89/7.37 (assert (forall ((R2 tptp.real) (X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X)) Y2))))
% 6.89/7.37 (assert (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 6.89/7.37 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.89/7.37 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.89/7.37 (assert (= tptp.complex2 (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A3))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A3)))))))))
% 6.89/7.37 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 6.89/7.37 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R2))))
% 6.89/7.37 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.89/7.37 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z2) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.89/7.37 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.89/7.37 (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 ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A1)))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y))))))))
% 6.89/7.37 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((L2 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 L2))) (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)))))))))))))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L2) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.89/7.37 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L2)) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L2) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L2)) (@ tptp.sgn_sgn_int L2))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.89/7.37 (assert (forall ((V tptp.int) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (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))))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))))))
% 6.89/7.37 (assert (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y)))))))
% 6.89/7.37 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))))))
% 6.89/7.37 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A32) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q3) A22)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) 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 Q3) A22)) R3)))))))))))))
% 6.89/7.37 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L) (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L) (= A33 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))))
% 6.89/7.37 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.89/7.37 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real))))))
% 6.89/7.37 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))
% 6.89/7.37 (assert (forall ((L2 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 L2))) (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)))))))))))))))))))
% 6.89/7.37 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (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 L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L 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 L) K3))))) _let_2)))))))))))
% 6.89/7.37 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L))) (@ 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 L) K3))))))))))))
% 6.89/7.37 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.89/7.37 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.89/7.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.89/7.37 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.89/7.37 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y2))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.89/7.37 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.89/7.37 (assert (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2)))))
% 6.89/7.37 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X4 tptp.nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.89/7.37 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X4 tptp.nat)) (@ P2 X4))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 6.89/7.37 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 6.89/7.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.89/7.37 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.89/7.37 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.divide_divide_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 6.89/7.37 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.89/7.37 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.89/7.37 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.89/7.37 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.89/7.37 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))))
% 6.89/7.37 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L2)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (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))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.89/7.37 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.89/7.37 (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)))))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I2)))))))))))))
% 6.89/7.37 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L 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) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))
% 6.89/7.37 (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)))
% 6.89/7.37 (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)))
% 6.89/7.37 (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)))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int) (L2 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) L2) (@ (@ _let_2 R2) S2)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S2)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Z)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) X))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y2))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Z)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.89/7.37 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ 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 L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.89/7.37 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (not (@ _let_2 L)))))) (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 L) _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 L) _let_1))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 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 Xa2)))))) (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 Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y2) (and (=> _let_5 (= Y2 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y2 (@ (@ 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 Xa2) _let_1)))))))))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 6.89/7.37 (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)))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 6.89/7.37 (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)))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.89/7.37 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y2)) (@ tptp.inc (@ _let_1 Y2))))))
% 6.89/7.37 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.89/7.37 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.89/7.37 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.89/7.37 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.89/7.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y2)) (@ (@ tptp.plus_plus_num (@ _let_1 Y2)) X)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I3)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I3) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))))))
% 6.89/7.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.89/7.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 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 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (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 Xa2)))))) (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 Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_6 (= Y2 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y2 (@ (@ 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 Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L2))) (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 L2) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (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 L2) _let_1))))))))))))))))
% 6.89/7.37 (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) (L4 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) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A1)))))
% 6.89/7.37 (assert (= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= Z2 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ 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) N2))))))))
% 6.89/7.37 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L 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) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)) (@ (@ tptp.plus_plus_int X) Y2))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) 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 L2) (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 6.89/7.37 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N2 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) N2))))))))
% 6.89/7.37 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 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 Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)) _let_1)))))))
% 6.89/7.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 6.89/7.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 6.89/7.37 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.89/7.37 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.89/7.37 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 6.89/7.37 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.89/7.37 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y2 tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y2) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (not (= Y2 _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit0 N3))) (=> _let_1 (not (= Y2 (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))))
% 6.89/7.37 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 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 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.89/7.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.89/7.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 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 M6)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.89/7.37 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 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) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit1 M5)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.89/7.37 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (= (@ _let_1 K) (@ _let_1 L2))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.89/7.37 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 6.89/7.37 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y2)))))))
% 6.89/7.37 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.89/7.37 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.89/7.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.89/7.37 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.89/7.37 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.89/7.37 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.89/7.37 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 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 Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y2)) _let_1)))))))
% 6.89/7.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 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))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.89/7.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L 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 L)) (@ (@ (@ tptp.if_int (= L _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L 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 L) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ 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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.89/7.37 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.89/7.37 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.89/7.37 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.89/7.37 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.89/7.37 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.89/7.37 (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)))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 6.89/7.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 6.89/7.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 6.89/7.37 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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 ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J2))))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.89/7.37 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.89/7.37 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.89/7.37 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.89/7.37 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.89/7.37 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.89/7.37 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ 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))))
% 6.89/7.37 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.89/7.37 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.37 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.89/7.37 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.89/7.37 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.89/7.37 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.89/7.37 (assert (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I4 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I4))))))))
% 6.89/7.37 (assert (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I4 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I4))))))))
% 6.89/7.37 (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))))))))))
% 6.89/7.37 (assert (= tptp.code_positive tptp.numera6620942414471956472nteger))
% 6.89/7.37 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X)))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X)))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_eq_int Xa2) X))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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 ((L 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 L)))) (@ (@ (@ 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)))))))))
% 6.89/7.37 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.89/7.37 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.89/7.37 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.89/7.37 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))))
% 6.89/7.37 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L)))))
% 6.89/7.37 (assert (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))
% 6.89/7.37 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.89/7.37 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))))
% 6.89/7.37 (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 ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L))) (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))))))))
% 6.89/7.37 (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 ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L))) (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.89/7.37 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.89/7.37 (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) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N)))) N)))
% 6.89/7.37 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N)))) (@ tptp.suc N))))
% 6.89/7.37 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L2))))
% 6.89/7.37 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y2)))))
% 6.89/7.37 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.89/7.37 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.89/7.37 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.89/7.37 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))))
% 6.89/7.37 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) N)))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) N))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.89/7.37 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (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 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 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 L) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L 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) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 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 L)) S6)))))) _let_1))))))))))))
% 6.89/7.37 (assert (= tptp.csqrt (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z2))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_4 (@ tptp.im Z2))) (@ (@ 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)))))))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y2)))))
% 6.89/7.37 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 6.89/7.37 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y2))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y2))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y2))))))
% 6.89/7.37 (assert (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y))))))
% 6.89/7.37 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 6.89/7.37 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.re Y))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ 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))))))))))
% 6.89/7.37 (assert (= tptp.exp_complex (lambda ((Z2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z2)))) (@ tptp.cis (@ tptp.im Z2))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z2 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 Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ 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)))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ 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)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (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)))))))))
% 6.89/7.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (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 X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ 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)))))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y2) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y2) X) (and (= X tptp.zero_zero_complex) (= Y2 tptp.zero_zero_complex)))))))
% 6.89/7.37 (assert (forall ((Y2 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y2) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y2)) (and (= X tptp.zero_zero_complex) (= Y2 tptp.zero_zero_complex)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A4) (@ tptp.cnj B3))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y2)))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X)) N))))
% 6.89/7.37 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X)) (@ tptp.cnj Y2)))))
% 6.89/7.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.89/7.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.89/7.37 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z2 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu2 tptp.nat)) true)) Nat))))
% 6.89/7.37 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu2 tptp.nat)) false)) Nat))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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 ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M3)))) M)))))
% 6.89/7.37 (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 ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N)))) M)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.89/7.37 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.89/7.37 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.89/7.37 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y)))))
% 6.89/7.37 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S) (forall ((T4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T4) (not (= R2 (@ (@ tptp.plus_plus_rat S) T4)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y2) (and (=> _let_2 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A4)) B3)) (@ tptp.abs_abs_int A4))))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((Q2 tptp.int) (P4 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P4)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.89/7.37 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 6.89/7.37 (assert (forall ((P4 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.89/7.37 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.89/7.37 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C3) B3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) B3)) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((R2 tptp.rat) (N tptp.int) (D tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int N) D)) (= R2 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D))))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int B3) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int B3) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((R2 tptp.rat) (P4 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 6.89/7.37 (assert (forall ((R2 tptp.product_prod_int_int) (P4 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.89/7.37 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P4 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P4) S2) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.89/7.37 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B3 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C3) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.89/7.37 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B3 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C3) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.89/7.37 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.89/7.37 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L2))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L2)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.89/7.37 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P4)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P4)))) tptp.one_one_int))))
% 6.89/7.37 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.89/7.37 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.89/7.37 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 6.89/7.37 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y2) (= (@ (@ tptp.bezw X) Y2) (@ (@ 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) Y2)))))))))))
% 6.89/7.37 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X2) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y 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 X2) Y)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y2) (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y2 (@ (@ 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) Xa2))))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_4 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y2 (@ (@ 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) Xa2)))))))) (not _let_1)))))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.89/7.37 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N7)) S3))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y2))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X)) (@ (@ tptp.times_times_int V2) Y2)) (@ (@ tptp.gcd_gcd_int X) Y2)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.int) (Y2 tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y2)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y2))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y2) 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 Y2))) (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 Y2)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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 ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.89/7.37 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.89/7.37 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X3))) (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)))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y2))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y2)) (@ (@ 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 Y2)))))))
% 6.89/7.37 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_2 (= Y2 X)) (=> (not _let_2) (= Y2 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.89/7.37 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.89/7.37 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y2)) (= X Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 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 Y2)) (@ (@ tptp.ord_less_real X) Y2))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 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 Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 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) Y2)) (@ _let_1 Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 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) Y2)) (@ _let_1 Y2))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 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) Y2)) (@ _let_1 Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 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) Y2)) (@ _let_1 Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y2))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y2))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y2) N))) (@ tptp.abs_abs_real Y2)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.power_power_real Y2) N) X) (= (@ (@ tptp.root N) X) Y2))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y2) N) X) (= (@ (@ tptp.root N) X) Y2)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N))) Y2))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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 ((Y tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)) X) (@ P Y))))))))
% 6.89/7.37 (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 ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L2)))))
% 6.89/7.37 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.89/7.37 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X2))) (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X2))))
% 6.89/7.37 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 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 L)) S6)))))) _let_1))))))))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 6.89/7.37 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.89/7.37 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.89/7.37 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 6.89/7.37 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2))) X)))))
% 6.89/7.37 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.89/7.37 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.89/7.37 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.89/7.37 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 6.89/7.37 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.89/7.37 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.89/7.37 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.89/7.37 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2))))))
% 6.89/7.37 (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 ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.89/7.37 (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 ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))))))
% 6.89/7.37 (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 ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))
% 6.89/7.37 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.89/7.37 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y2)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y2))) X)))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.89/7.37 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.89/7.37 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y2)) (@ tptp.sqr (@ _let_1 Y2))))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.89/7.37 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y2) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (= Y2 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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) TreeList3) Summary2)) (= Y2 (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu3 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (=> (= Y2 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) 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) (=> (= Y2 (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu3 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu3) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6))))))) (@ 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 ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 6.89/7.37 (assert (= tptp.complete_Sup_Sup_int (lambda ((X6 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X6) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) X6) (@ (@ tptp.ord_less_eq_int Y) X2)))))))))
% 6.89/7.37 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.89/7.37 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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 ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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 ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))))
% 6.89/7.37 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.89/7.37 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.89/7.37 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.89/7.37 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.89/7.37 (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 ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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 ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.89/7.37 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X2 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X2))) A4))) (@ (@ tptp.product_Pair_nat_num N2) M6)))))
% 6.89/7.37 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I3 tptp.int) (N2 tptp.nat)) (and (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X3) (@ (@ tptp.ord_less_real X3) Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X3)))))
% 6.89/7.37 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I3 tptp.int) (J3 tptp.int)) (and (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y2) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y2 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))))))))))))))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y2) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y2 tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))))))))))))))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 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) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ 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 ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ 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 ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 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) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y2 tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y2) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))))))))))))))))))))
% 6.89/7.37 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.89/7.37 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.89/7.37 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.89/7.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.89/7.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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 ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.89/7.37 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 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) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.89/7.37 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.89/7.37 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int) (P4 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A) B))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P4) Q2)) (= (@ (@ tptp.fract P4) Q2) _let_1)))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int) (P4 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ tptp.product_Pair_int_int P4) Q2)) (= (@ (@ tptp.fract P4) Q2) (@ (@ tptp.fract A) B)))))
% 6.89/7.37 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.89/7.37 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.89/7.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A) B)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((C tptp.nat) (Y2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y2))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y2))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y2))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y2) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((M7 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N5))))
% 6.89/7.37 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.89/7.37 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.89/7.37 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.89/7.37 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y2) (@ tptp.positive (@ (@ tptp.plus_plus_rat X) Y2))))))
% 6.89/7.37 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y2) (@ tptp.positive (@ (@ tptp.times_times_rat X) Y2))))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (assert (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ 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)))))))
% 6.89/7.37 (assert (= tptp.comple4887499456419720421f_real (lambda ((X6 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X6))))))
% 6.89/7.37 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))
% 6.89/7.37 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.89/7.37 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I4))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I3)))) tptp.top_top_set_nat)))))))
% 6.89/7.37 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.89/7.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.89/7.37 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (= tptp.root (lambda ((N2 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2)))) X2)))))
% 6.89/7.37 (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)))))))))))
% 6.89/7.37 (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)))))))))))))
% 6.89/7.37 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.89/7.37 (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))))))))))))
% 6.89/7.37 (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))))))))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= 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) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H4))) (@ F X)))))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H4))))))))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z3)))))))))
% 6.89/7.37 (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 ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X3) 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)))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L2 tptp.zero_zero_real))))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L2 tptp.zero_zero_real))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (X tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) 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))))
% 6.89/7.37 (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 ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) 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)))))
% 6.89/7.37 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z2 tptp.real)) (@ (@ tptp.powr_real Z2) 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)))))
% 6.89/7.37 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N3))) (@ (@ F4 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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 ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) 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)))))))
% 6.89/7.37 (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 ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ 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)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X3) N2)))))) (=> (@ (@ 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 ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.89/7.37 (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)))))))
% 6.89/7.37 (assert (forall ((H2 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) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.89/7.37 (assert (forall ((H2 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) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.89/7.37 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real H2) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) 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 ((T4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T4))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T4) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T4) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real C) T4) (@ (@ tptp.ord_less_real T4) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.89/7.37 (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 ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real A) T4) (@ (@ tptp.ord_less_real T4) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.89/7.37 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T5 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) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T5)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T5) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T5) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real))))))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 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 X9) _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)))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (exists ((L6 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 L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M8)) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) Y4)))))))))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.89/7.37 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.89/7.37 (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 ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.89/7.37 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.89/7.37 (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 ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.89/7.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C2))))))))))))
% 6.89/7.37 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) (@ 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)))
% 6.89/7.37 (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 ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.89/7.37 (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 ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.89/7.37 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.89/7.37 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.89/7.37 (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))))
% 6.89/7.37 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I4))) B4)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.89/7.37 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.89/7.37 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.89/7.37 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.89/7.37 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.89/7.37 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.89/7.37 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.89/7.37 (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))))
% 6.89/7.37 (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)))))
% 6.89/7.37 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.89/7.38 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.89/7.38 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.89/7.38 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 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 N2)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 6.89/7.38 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((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)))))))
% 6.89/7.38 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((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)))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.89/7.38 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ 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))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))))))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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)))))))))
% 6.89/7.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.89/7.38 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ tptp.suc I3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.89/7.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.89/7.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I3) K)))) tptp.at_top_nat))))
% 6.89/7.38 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F5)))))
% 6.89/7.38 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.89/7.38 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N2)))))))
% 6.89/7.38 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C3)))))))
% 6.89/7.38 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.89/7.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) K)) (@ tptp.exp_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.89/7.38 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y))) Y))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.89/7.38 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.89/7.38 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X3) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.89/7.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.89/7.38 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.89/7.38 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_top_real) F5))))))
% 6.89/7.38 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.89/7.38 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_bot_real) F5))))))
% 6.89/7.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.89/7.38 (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))))
% 6.89/7.38 (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)))))
% 6.89/7.38 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.89/7.38 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.89/7.38 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X2) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B4) (@ X8 I4))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.89/7.38 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B4) (@ X8 I4))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I)))))))))))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.89/7.38 (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 ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) G))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) 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) C2) (@ (@ tptp.ord_less_real C2) 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))))))))))))
% 6.89/7.38 (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.89/7.38 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arcosh_real (@ F X2)))))))))
% 6.89/7.38 (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 ((C2 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D3)) (@ (@ tptp.ord_less_eq_real C2) D3)))))))
% 6.89/7.38 (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))))
% 6.89/7.38 (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))))
% 6.89/7.38 (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 ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.89/7.38 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y2) (=> _let_1 (not (=> (and (=> _let_2 (= Y2 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y2 tptp.nil_int))) (not _let_1)))))))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))))
% 6.89/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.89/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.89/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.89/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.89/7.38 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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))))))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 6.89/7.38 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J3)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.89/7.38 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y2) (and (=> _let_1 (= Y2 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y2 tptp.nil_int)))))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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))))))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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)))))))
% 6.89/7.38 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.89/7.38 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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)))))))))
% 6.89/7.38 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.89/7.38 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.89/7.38 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.89/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B4)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B4)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I)) L6))))))))))
% 6.89/7.38 (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 ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 6.89/7.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X2 tptp.nat)) (@ F (@ G X2)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.89/7.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.89/7.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)))) tptp.top_top_set_real))))
% 6.89/7.38 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N5) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N5))))
% 6.89/7.38 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 6.89/7.38 (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 ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.89/7.38 (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 ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.89/7.38 (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))))))))))))
% 6.89/7.38 (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 ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (forall ((X3 tptp.nat)) (=> (not (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X3) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.89/7.38 (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))))))
% 6.89/7.38 (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)))))
% 6.89/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.89/7.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.89/7.38 (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)))))
% 6.89/7.38 (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))))))
% 6.89/7.38 (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))))))
% 6.89/7.38 (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)))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I2))))
% 6.89/7.38 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R2)))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))))
% 6.89/7.38 (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 ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M3)))) M))))
% 6.89/7.38 (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 ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N)))) M))))
% 6.89/7.38 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.89/7.38 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.89/7.38 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 6.89/7.38 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.89/7.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) 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))))))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.89/7.38 (assert (= tptp.upt (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I3) J3)) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J3))) tptp.nil_nat))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.89/7.38 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))
% 6.89/7.38 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))
% 6.89/7.38 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))))
% 6.89/7.38 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))
% 6.89/7.38 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X) Xs2)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs2)))))
% 6.89/7.38 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.89/7.38 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.89/7.38 (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 ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N5))))))))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M)) tptp.one_one_nat)) N5))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.89/7.38 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 6.89/7.38 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 6.89/7.38 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.89/7.38 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 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) N2)) M6))))))))
% 6.89/7.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.89/7.38 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.89/7.38 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.89/7.38 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.89/7.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 6.89/7.38 (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))))
% 6.89/7.38 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X2) Y)))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))))
% 6.89/7.38 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.89/7.38 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.89/7.38 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.89/7.38 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.89/7.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.89/7.38 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))
% 6.89/7.38 (assert (forall ((X tptp.list_nat) (Y2 tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y2) (=> (=> (= X tptp.nil_nat) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.89/7.38 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs2)))))))
% 6.89/7.38 (assert (forall ((X tptp.list_nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y2) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y2 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs3))) (=> (= X _let_1) (=> (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.89/7.38 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.89/7.38 (assert (forall ((Xs2 tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs2)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs2) tptp.zero_zero_nat))))
% 6.89/7.38 (assert (forall ((Xs2 tptp.list_int)) (= (@ tptp.gcd_Gcd_int (@ tptp.set_int2 Xs2)) (@ (@ (@ tptp.fold_int_int tptp.gcd_gcd_int) Xs2) tptp.zero_zero_int))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (exists ((A7 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A7) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) A7)))) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N2 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2)))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N7))) R2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) R3)))))) (@ tptp.vanishes X8))))
% 6.89/7.38 (assert (= tptp.vanishes (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N2))) R5)))))))))
% 6.89/7.38 (assert (= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 N2)))) R5)))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2)))))))
% 6.89/7.38 (assert (forall ((X tptp.rat)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) X))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N7))) B2)))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (=> (@ tptp.cauchy Y6) (=> (not (@ tptp.vanishes Y6)) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2)))) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X8 N2))) (@ tptp.inverse_inverse_rat (@ Y6 N2))))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K2 tptp.nat)) (or (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N7) (@ (@ tptp.ord_less_rat B2) (@ tptp.uminus_uminus_rat (@ X8 N7))))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N7) (@ (@ tptp.ord_less_rat B2) (@ X8 N7))))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B2 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (exists ((K2 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N7) (@ (@ tptp.ord_less_rat B2) (@ tptp.abs_abs_rat (@ X8 N7))))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ 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 ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M2)) (@ X8 N7)))) R2))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M5)) (@ X8 N3)))) R3)))))))) (@ tptp.cauchy X8))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) (@ (@ tptp.plus_plus_rat (@ Y6 N2)) R5))))))))))))
% 6.89/7.38 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((X10 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X10) (@ P (@ tptp.real2 X10)))) (@ P X))))
% 6.89/7.38 (assert (= tptp.ring_1_of_int_real (lambda ((X2 tptp.int)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.ring_1_of_int_rat X2))))))
% 6.89/7.38 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X2 tptp.nat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X2))))))
% 6.89/7.38 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.zero_zero_rat))))
% 6.89/7.38 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.one_one_rat))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X8)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y6 N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.times_times_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y6 N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X8)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (= (= (@ tptp.real2 X8) (@ tptp.real2 Y6)) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X8)))) (let ((_let_2 (@ tptp.vanishes X8))) (=> (@ tptp.cauchy X8) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N2))))))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (not (@ tptp.positive2 (@ tptp.real2 X8))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) R5))))))))))
% 6.89/7.38 (assert (forall ((X tptp.real)) (=> (not (@ tptp.positive2 X)) (=> (not (= X tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X))))))
% 6.89/7.38 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X) Y2))))))
% 6.89/7.38 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y2) (@ tptp.positive2 (@ (@ tptp.times_times_real X) Y2))))))
% 6.89/7.38 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.89/7.38 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X2)))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.positive2 (@ tptp.real2 X8)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2)))))))))))
% 6.89/7.38 (assert (= tptp.positive2 (lambda ((X2 tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X2) N2))))))))))
% 6.89/7.38 (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 ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ (@ tptp.realrel X8) X8))))
% 6.89/7.38 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)))
% 6.89/7.38 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.one_one_rat)) (lambda ((N2 tptp.nat)) tptp.one_one_rat)))
% 6.89/7.38 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((Y3 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y3) Y3) (@ P (@ tptp.real2 Y3)))) (@ P X))))
% 6.89/7.38 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X N2))))))))
% 6.89/7.38 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa2)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa2 N2)) (@ X N2)))))))))
% 6.89/7.38 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa2)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa2 N2)) (@ X N2)))))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y6) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y6 N2)))) (@ (@ tptp.realrel X8) Y6))))))
% 6.89/7.38 (assert (= tptp.realrel (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X6) (@ tptp.cauchy Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X6 N2)) (@ Y7 N2))))))))
% 6.89/7.38 (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 ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X N2)))))))))))
% 6.89/7.38 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0)))))
% 6.89/7.38 (assert (= tptp.cr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X2) X2) (= (@ tptp.real2 X2) Y)))))
% 6.89/7.38 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2))))))
% 6.89/7.38 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2))))))
% 6.89/7.38 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y7 N2))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5))) (lambda ((X6 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X6 N2))))))))) (lambda ((X6 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X6 N2))))))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y7 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y7 N2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)))) tptp.times_times_int) tptp.times_times_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) tptp.suc) tptp.suc))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)))) tptp.plus_plus_int) tptp.plus_plus_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y5 tptp.num) (Z5 tptp.num)) (= Y5 Z5))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y5 tptp.num) (Z5 tptp.num)) (= Y5 Z5))) (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)))) (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M6)) (@ tptp.numeral_numeral_int N2)))) (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M6)) (@ tptp.numeral_numeral_int N2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5))) (lambda ((X6 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X6 N2))))))))) tptp.positive2))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) tptp.realrel) (lambda ((Y5 tptp.real) (Z5 tptp.real)) (= Y5 Z5))))
% 6.89/7.38 (assert (@ (@ tptp.pcr_real (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 6.89/7.38 (assert (= tptp.pcr_real tptp.cr_real))
% 6.89/7.38 (assert (@ (@ tptp.pcr_real (lambda ((N2 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.89/7.38 (assert (= tptp.pcr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ tptp.cauchy X2) (= (@ tptp.real2 X2) Y)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))) tptp.uminus_uminus_real))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y7 N2)))) tptp.plus_plus_real))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2)))) tptp.times_times_real))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat))
% 6.89/7.38 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.89/7.38 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) tptp.pcr_rat)) (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A4) B3)))) tptp.fract))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) tptp.uminus_uminus_rat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y))))) tptp.times_times_rat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) tptp.positive))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) tptp.inverse_inverse_rat))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.89/7.38 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))) tptp.uminus_uminus_int))
% 6.89/7.38 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 6.89/7.38 (assert (forall ((X tptp.nat) (Y2 tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y2)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))))
% 6.89/7.38 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y6) (=> (@ (@ tptp.ord_less_real X) (@ tptp.real2 Y6)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.field_7254667332652039916t_real (@ Y6 N3))))))))
% 6.89/7.38 (assert (= tptp.field_7254667332652039916t_real (lambda ((X2 tptp.rat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) X2)))))
% 6.89/7.38 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.89/7.38 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (exists ((Q3 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q3))) (and (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real _let_1) Y2)))))))
% 6.89/7.38 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y2 tptp.real)) (=> (@ tptp.cauchy X8) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X8 N3))) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) Y2)))))
% 6.89/7.38 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y6) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.field_7254667332652039916t_real (@ Y6 N3)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.real2 Y6))))))
% 6.89/7.38 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.89/7.38 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X2) V4) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))))
% 6.89/7.38 (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)))))
% 6.89/7.38 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.cos_real A)))))
% 6.89/7.38 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.sin_real A)))))
% 6.89/7.38 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N)))))
% 6.89/7.38 (assert (forall ((R12 tptp.real) (A tptp.real) (R23 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R12) A)) (@ (@ tptp.rcis R23) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R12) R23)) (@ (@ tptp.plus_plus_real A) B)))))
% 6.89/7.38 (assert (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))
% 6.89/7.38 (assert (forall ((S3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S3)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S3) N))))))
% 6.89/7.38 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.89/7.38 (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)))))))))
% 6.89/7.38 (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 ((M6 tptp.nat)) (@ P (@ tptp.suc M6))))))))))
% 6.89/7.38 (assert (= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) X6) (@ (@ tptp.ord_less_eq_real X2) Z2))))))))
% 6.89/7.38 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.code_integer_of_nat N2))) (let ((_let_2 (@ tptp.code_integer_of_nat M6))) (let ((_let_3 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.produc8678311845419106900er_nat tptp.code_nat_of_integer) tptp.code_nat_of_integer) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ _let_3 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= _let_1 tptp.zero_z3403309356797280102nteger)) (@ _let_3 _let_2)) (@ (@ tptp.code_divmod_abs _let_2) _let_1))))))))))
% 6.89/7.38 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M6))))))))))
% 6.89/7.38 (assert (forall ((N tptp.num)) (= (@ tptp.code_integer_of_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6620942414471956472nteger N))))
% 6.89/7.38 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 6.89/7.38 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))
% 6.89/7.38 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.89/7.38 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5))) tptp.ratrel)) (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A4) B3)))) (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A4) B3)))))
% 6.89/7.38 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y))))) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y5 Bool) (Z5 Bool)) (= Y5 Z5))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))))
% 6.89/7.38 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1))))))
% 6.89/7.38 (assert (forall ((Xa2 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 Xa2))) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa2)) (@ 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 Xa2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 6.89/7.38 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 6.89/7.38 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))
% 6.89/7.38 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.89/7.38 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.uminus_uminus_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X))) (@ tptp.product_snd_int_int X)))))))
% 6.89/7.38 (assert (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa2)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa2)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa2)) (@ tptp.product_snd_int_int X)))))))))
% 6.89/7.38 (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)))))))
% 6.89/7.38 (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))))))))
% 6.89/7.38 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1)))))))
% 6.89/7.38 (assert (= tptp.uminus_uminus_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2))))))
% 6.89/7.38 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 6.89/7.38 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y)))))))
% 6.89/7.38 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.89/7.38 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 6.89/7.38 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X6 tptp.real)) (@ P X6)))))
% 6.89/7.38 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.extended_enat) (Y2 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y2) Y2)))
% 6.89/7.38 (assert (forall ((X tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y2) X)))
% 6.89/7.38 (assert (forall ((X tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y2 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.option_nat) (Y2 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y2 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y2 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y2) X)))
% 283.60/283.91 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 283.60/283.91 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y2 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y2) Y2)))
% 283.60/283.91 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y2 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y2) X)))
% 283.60/283.91 (assert (not (forall ((U3 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (or (not (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) U3)) (not (@ (@ tptp.ord_less_nat U3) (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))))))))
% 283.60/283.91 (set-info :filename cvc5---1.0.5_14507)
% 283.60/283.91 (check-sat-assuming ( true ))
% 283.60/283.91 ------- get file name : TPTP file name is ITP240^3
% 283.60/283.91 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14507.smt2...
% 283.60/283.91 --- Run --ho-elim --full-saturate-quant at 10...
% 283.60/283.91 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 283.60/283.91 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 283.60/283.91 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 283.60/283.91 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 283.60/283.91 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 283.60/283.91 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 283.60/283.91 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 283.60/283.91 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 283.60/283.91 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 283.60/283.91 % SZS status Theorem for ITP240^3
% 283.60/283.91 % SZS output start Proof for ITP240^3
% 283.60/283.91 (
% 283.60/283.91 (let ((_let_1 (not (forall ((U3 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (or (not (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))) U3)) (not (@ (@ tptp.ord_less_nat U3) (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))))))))) (let ((_let_2 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_3 (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat))) (let ((_let_4 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) _let_3))) (let ((_let_5 (= tptp.times_times_rat (@ _let_4 (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y)))))))) (let ((_let_6 (= tptp.plus_plus_rat (@ _let_4 (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))) (let ((_let_7 (= tptp.uminus_uminus_rat (@ _let_3 (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2))))))) (let ((_let_8 (= tptp.inverse_inverse_rat (@ _let_3 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 X2)) _let_1)))))))) (let ((_let_9 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_10 (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))) (let ((_let_11 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_12 (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel))) (let ((_let_13 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) _let_12))) (let ((_let_14 (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))) (let ((_let_15 (= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) X6) (@ (@ tptp.ord_less_eq_real X2) Z2))))))))) (let ((_let_16 (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))) (let ((_let_17 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_18 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_17))) (let ((_let_19 (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel))) (let ((_let_20 (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel))) (let ((_let_21 (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X2) V4) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))) (let ((_let_22 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_23 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_24 (= tptp.field_7254667332652039916t_real (lambda ((X2 tptp.rat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) X2)))))) (let ((_let_25 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_26 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_25))) (let ((_let_27 (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int))) (let ((_let_28 (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int))) (let ((_let_29 (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat))) (let ((_let_30 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) _let_29))) (let ((_let_31 (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real))) (let ((_let_32 (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) _let_31))) (let ((_let_33 (= tptp.pcr_real tptp.cr_real))) (let ((_let_34 (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real))) (let ((_let_35 (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel))) (let ((_let_36 (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) _let_35))) (let ((_let_37 (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2))) (let ((_let_38 (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) _let_37))) (let ((_let_39 (= tptp.plus_plus_real (@ _let_38 (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y7 N2))))))) (let ((_let_40 (= tptp.times_times_real (@ _let_38 (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y7 N2))))))) (let ((_let_41 (= tptp.uminus_uminus_real (@ _let_37 (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2))))))) (let ((_let_42 (= tptp.cr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X2) X2) (= (@ tptp.real2 X2) Y)))))) (let ((_let_43 (= tptp.inverse_inverse_real (@ _let_37 (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0)))))) (let ((_let_44 (= tptp.realrel (lambda ((X6 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X6) (@ tptp.cauchy Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X6 N2)) (@ Y7 N2))))))))) (let ((_let_45 (= tptp.positive2 (lambda ((X2 tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X2) N2))))))))))) (let ((_let_46 (= tptp.ring_1_of_int_real (lambda ((X2 tptp.int)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.ring_1_of_int_rat X2))))))) (let ((_let_47 (= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 N2)))) R5)))))))))))) (let ((_let_48 (= tptp.vanishes (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N2))) R5)))))))))) (let ((_let_49 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))) (let ((_let_50 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_51 (= tptp.bNF_Ca8459412986667044542atLess _let_50))) (let ((_let_52 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_53 (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))) (let ((_let_54 (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))) (let ((_let_55 (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))))) (let ((_let_56 (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))) (let ((_let_57 (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))) (let ((_let_58 (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))) (let ((_let_59 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_60 (@ tptp.bit0 tptp.one))) (let ((_let_61 (@ tptp.bit0 _let_60))) (let ((_let_62 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_61))))))))) (let ((_let_63 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_62))) (let ((_let_64 (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_65 (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)))))) (let ((_let_66 (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_67 (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))) (let ((_let_68 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_69 (@ tptp.numeral_numeral_real _let_60))) (let ((_let_70 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_71 (@ _let_70 _let_69))) (let ((_let_72 (@ tptp.uminus_uminus_real _let_71))) (let ((_let_73 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_74 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_75 (@ tptp.topolo2177554685111907308n_real _let_71))) (let ((_let_76 (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C3)))))))) (let ((_let_77 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_78 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_63)))) (let ((_let_79 (= tptp.root (lambda ((N2 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2)))) X2)))))) (let ((_let_80 (@ tptp.numeral_numeral_nat _let_60))) (let ((_let_81 (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))) (let ((_let_82 (= tptp.comple4887499456419720421f_real (lambda ((X6 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X6))))))) (let ((_let_83 (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ 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)))))))) (let ((_let_84 (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))) (let ((_let_85 (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))) (let ((_let_86 (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))) (let ((_let_87 (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))) (let ((_let_88 (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))) (let ((_let_89 (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I3 tptp.int) (N2 tptp.nat)) (and (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))) (let ((_let_90 (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_91 (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))) (let ((_let_92 (= tptp.complete_Sup_Sup_int (lambda ((X6 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X6) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) X6) (@ (@ tptp.ord_less_eq_int Y) X2)))))))))) (let ((_let_93 (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))) (let ((_let_94 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))) (let ((_let_95 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_96 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_95))) (let ((_let_97 (@ _let_95 (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))))) (let ((_let_98 (= tptp.uminus_uminus_int _let_97))) (let ((_let_99 (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))) (let ((_let_100 (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))) (let ((_let_101 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_102 (= tptp.sqrt (@ tptp.root _let_80)))) (let ((_let_103 (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))) (let ((_let_104 (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_105 (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_106 (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))) (let ((_let_107 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_108 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_109 (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))) (let ((_let_110 (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))) (let ((_let_111 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))) (let ((_let_112 (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (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)))))))))) (let ((_let_113 (= tptp.real_V1022390504157884413omplex (lambda ((Z2 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 Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))) (let ((_let_114 (= tptp.exp_complex (lambda ((Z2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z2)))) (@ tptp.cis (@ tptp.im Z2))))))) (let ((_let_115 (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))) (let ((_let_116 (= tptp.csqrt (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z2))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_4 (@ tptp.im Z2))) (@ (@ 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)))))))))))) (let ((_let_117 (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_118 (= 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)))))))) (let ((_let_119 (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))))) (let ((_let_120 (@ tptp.numera6620942414471956472nteger _let_60))) (let ((_let_121 (@ tptp.code_integer_of_num tptp.one))) (let ((_let_122 (= _let_121 tptp.one_one_Code_integer))) (let ((_let_123 (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))) (let ((_let_124 (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))))) (let ((_let_125 (= tptp.code_positive tptp.numera6620942414471956472nteger))) (let ((_let_126 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_127 (= tptp.code_Target_positive tptp.numeral_numeral_int))) (let ((_let_128 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_129 (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))) (let ((_let_130 (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))) (let ((_let_131 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_132 (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))) (let ((_let_133 (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))) (let ((_let_134 (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_135 (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_136 (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))) (let ((_let_137 (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_138 (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))) (let ((_let_139 (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))) (let ((_let_140 (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))) (let ((_let_141 (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))))) (let ((_let_142 (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_143 (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))) (let ((_let_144 (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))) (let ((_let_145 (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N2 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) N2))))))))) (let ((_let_146 (= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= Z2 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))) (let ((_let_147 (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_148 (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))) (let ((_let_149 (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_150 (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_151 (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))) (let ((_let_152 (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (let ((_let_153 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_154 (@ tptp.suc _let_153))) (let ((_let_155 (@ tptp.numeral_numeral_int _let_60))) (let ((_let_156 (@ tptp.nat2 _let_155))) (let ((_let_157 (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (let ((_let_158 (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))) (let ((_let_159 (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))) (let ((_let_160 (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_161 (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))) (let ((_let_162 (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L))) (@ 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 L) K3))))))))))))) (let ((_let_163 (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (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 L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L 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 L) K3))))) _let_2)))))))))))) (let ((_let_164 (@ tptp.times_times_real _let_69))) (let ((_let_165 (= tptp.pi (@ _let_164 (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))) (let ((_let_166 (@ tptp.power_power_nat _let_80))) (let ((_let_167 (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_166)))) (let ((_let_168 (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L) (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L) (= A33 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))))) (let ((_let_169 (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y)))))))) (let ((_let_170 (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y))))))))) (let ((_let_171 (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y))))))))) (let ((_let_172 (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z2))))))))) (let ((_let_173 (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z2) (@ (@ tptp.ord_less_int Z6) Z2))))))))) (let ((_let_174 (@ tptp.sqrt _let_69))) (let ((_let_175 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_176 (= tptp.complex2 (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))) (let ((_let_177 (@ tptp.numera6690914467698888265omplex _let_60))) (let ((_let_178 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_179 (@ tptp.times_times_complex _let_178))) (let ((_let_180 (@ tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_181 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_182 (@ _let_164 tptp.pi))) (let ((_let_183 (@ tptp.cis _let_71))) (let ((_let_184 (= _let_183 tptp.imaginary_unit))) (let ((_let_185 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_186 (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y)))))) (let ((_let_187 (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y)))))) (let ((_let_188 (= tptp.gbinomial_real (lambda ((A4 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 A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))) (let ((_let_189 (= tptp.gbinomial_rat (lambda ((A4 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 A4)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))) (let ((_let_190 (= tptp.gbinomial_complex (lambda ((A4 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 A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))) (let ((_let_191 (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))) (let ((_let_192 (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))) (let ((_let_193 (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_complex X2) N2)))))))) (let ((_let_194 (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N2)) (@ (@ tptp.power_power_real X2) N2)))))))) (let ((_let_195 (= tptp.real_V1485227260804924795R_real tptp.times_times_real))) (let ((_let_196 (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))))) (let ((_let_197 (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))))) (let ((_let_198 (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))))) (let ((_let_199 (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))))) (let ((_let_200 (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))))) (let ((_let_201 (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))))) (let ((_let_202 (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))))) (let ((_let_203 (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))))) (let ((_let_204 (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U2))))))) (let ((_let_205 (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) U2))))))) (let ((_let_206 (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U2))))))) (let ((_let_207 (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))) (let ((_let_208 (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))) (let ((_let_209 (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N2) tptp.zero_zero_real))))) (let ((_let_210 (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N2) tptp.zero_zero_int))))) (let ((_let_211 (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))) (let ((_let_212 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_213 (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))) (let ((_let_214 (@ tptp.bit1 tptp.one))) (let ((_let_215 (@ tptp.numeral_numeral_real _let_214))) (let ((_let_216 (@ tptp.sqrt _let_215))) (let ((_let_217 (@ (@ tptp.divide_divide_real _let_216) _let_69))) (let ((_let_218 (@ _let_70 _let_215))) (let ((_let_219 (@ _let_70 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_214))))) (let ((_let_220 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_221 (@ (@ tptp.divide_divide_real _let_174) _let_69))) (let ((_let_222 (@ tptp.numeral_numeral_real _let_61))) (let ((_let_223 (@ _let_70 _let_222))) (let ((_let_224 (@ _let_220 _let_69))) (let ((_let_225 (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))) (let ((_let_226 (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))) (let ((_let_227 (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))) (let ((_let_228 (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))) (let ((_let_229 (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))) (let ((_let_230 (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))) (let ((_let_231 (= tptp.diffs_rat (lambda ((C3 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C3 _let_1))))))) (let ((_let_232 (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))) (let ((_let_233 (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))) (let ((_let_234 (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))) (let ((_let_235 (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))) (let ((_let_236 (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))) (let ((_let_237 (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))) (let ((_let_238 (@ tptp.numeral_numeral_rat _let_60))) (let ((_let_239 (@ tptp.cos_real _let_69))) (let ((_let_240 (@ tptp.divide_divide_real _let_215))) (let ((_let_241 (@ (@ tptp.times_times_real (@ _let_240 _let_69)) tptp.pi))) (let ((_let_242 (= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_243 (= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_244 (= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_245 (= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_246 (= tptp.topolo3100542954746470799et_int (lambda ((X6 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_set_int (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_247 (= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 M6))))))))) (let ((_let_248 (@ tptp.bit1 _let_214))) (let ((_let_249 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_60)))) (let ((_let_250 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_251 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_252 (= tptp.bot_bo1403522918969695512_int_o (lambda ((X2 (-> tptp.int tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X2) Y)) tptp.bot_bo4508923176915781079nt_int))))) (let ((_let_253 (= tptp.bot_bo8662317086119403298_int_o (lambda ((X2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X2) Y)) tptp.bot_bo572930865798478029nt_int))))) (let ((_let_254 (= tptp.bot_bo3000040243691356879eger_o (lambda ((X2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member4164122664394876845nteger (@ (@ tptp.produc8603105652947943368nteger X2) Y)) tptp.bot_bo5443222936135328352nteger))))) (let ((_let_255 (= tptp.bot_bo5358457235160185703eger_o (lambda ((X2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y tptp.produc8923325533196201883nteger)) (@ (@ tptp.member3068662437193594005nteger (@ (@ tptp.produc6137756002093451184nteger X2) Y)) tptp.bot_bo3145834390647256904nteger))))) (let ((_let_256 (= tptp.bot_bot_int_int_o (lambda ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y)) tptp.bot_bo1796632182523588997nt_int))))) (let ((_let_257 (= tptp.bot_bot_nat_nat_o (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y)) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_258 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_259 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_260 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_261 (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))) (let ((_let_262 (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))) (let ((_let_263 (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))) (let ((_let_264 (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))) (let ((_let_265 (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))) (let ((_let_266 (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U2))))))) (let ((_let_267 (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))) (let ((_let_268 (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ 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))))) (let ((_let_269 (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ 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))))) (let ((_let_270 (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ 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))))) (let ((_let_271 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))) (let ((_let_272 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))) (let ((_let_273 (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))) (let ((_let_274 (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))) (let ((_let_275 (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_276 (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_277 (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_278 (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))) (let ((_let_279 (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))) (let ((_let_280 (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))) (let ((_let_281 (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))) (let ((_let_282 (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))) (let ((_let_283 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_284 (@ tptp.numeral_numeral_int _let_214))) (let ((_let_285 (@ tptp.numeral_numeral_rat _let_214))) (let ((_let_286 (@ tptp.numera6690914467698888265omplex _let_214))) (let ((_let_287 (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N2))))))))))) (let ((_let_288 (@ tptp.numeral_numeral_rat tptp.one))) (let ((_let_289 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_290 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_291 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_292 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_293 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_294 (@ tptp.ord_less_rat _let_108))) (let ((_let_295 (@ tptp.ord_le6747313008572928689nteger _let_283))) (let ((_let_296 (@ tptp.ord_less_int _let_107))) (let ((_let_297 (@ tptp.ord_less_real _let_212))) (let ((_let_298 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_299 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_300 (@ tptp.ord_less_eq_int _let_107))) (let ((_let_301 (@ tptp.ord_less_eq_rat _let_108))) (let ((_let_302 (@ tptp.ord_le3102999989581377725nteger _let_283))) (let ((_let_303 (@ tptp.ord_less_eq_real _let_212))) (let ((_let_304 (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))) (let ((_let_305 (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))) (let ((_let_306 (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))) (let ((_let_307 (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))) (let ((_let_308 (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))) (let ((_let_309 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_310 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_311 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_312 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_313 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_314 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_315 (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))) (let ((_let_316 (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))) (let ((_let_317 (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))) (let ((_let_318 (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))) (let ((_let_319 (@ tptp.uminus_uminus_rat _let_238))) (let ((_let_320 (@ tptp.uminus1351360451143612070nteger _let_120))) (let ((_let_321 (@ tptp.uminus1482373934393186551omplex _let_177))) (let ((_let_322 (@ tptp.uminus_uminus_int _let_155))) (let ((_let_323 (@ tptp.uminus_uminus_real _let_69))) (let ((_let_324 (= (@ (@ tptp.modulo364778990260209775nteger _let_283) _let_120) tptp.one_one_Code_integer))) (let ((_let_325 (= (@ (@ tptp.modulo_modulo_int _let_107) _let_155) tptp.one_one_int))) (let ((_let_326 (@ tptp.minus_minus_rat _let_108))) (let ((_let_327 (@ tptp.minus_8373710615458151222nteger _let_283))) (let ((_let_328 (@ tptp.minus_minus_complex _let_181))) (let ((_let_329 (@ tptp.minus_minus_int _let_107))) (let ((_let_330 (@ tptp.minus_minus_real _let_212))) (let ((_let_331 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_332 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_333 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_334 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_335 (@ tptp.plus_plus_rat _let_108))) (let ((_let_336 (@ tptp.plus_p5714425477246183910nteger _let_283))) (let ((_let_337 (@ tptp.plus_plus_complex _let_181))) (let ((_let_338 (@ tptp.plus_plus_int _let_107))) (let ((_let_339 (@ tptp.plus_plus_real _let_212))) (let ((_let_340 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_341 (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_283) tptp.zero_z3403309356797280102nteger))) (let ((_let_342 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_343 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_344 (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (let ((_let_345 (@ tptp.dvd_dvd_int _let_155))) (let ((_let_346 (@ tptp.dvd_dvd_nat _let_80))) (let ((_let_347 (@ tptp.dvd_dvd_Code_integer _let_120))) (let ((_let_348 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_349 (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K3))))))) (let ((_let_350 (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K3))))))) (let ((_let_351 (= tptp.dvd_dvd_Code_integer (lambda ((B3 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B3) K3))))))) (let ((_let_352 (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))) (let ((_let_353 (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))) (let ((_let_354 (= tptp.dvd_dvd_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (=> (= A4 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))) (let ((_let_355 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_356 (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_357 (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))))))) (let ((_let_358 (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))))))) (let ((_let_359 (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))) (let ((_let_360 (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))) (let ((_let_361 (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))) (let ((_let_362 (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))) (let ((_let_363 (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_364 (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_365 (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_366 (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_367 (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_368 (@ _let_298 tptp.zero_zero_int))) (let ((_let_369 (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B3)) B3) A4))))) (let ((_let_370 (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B3)) B3) A4))))) (let ((_let_371 (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B3)) (not (= A4 B3))))))) (let ((_let_372 (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B3)) (not (= A4 B3))))))) (let ((_let_373 (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B3)) (not (= A4 B3))))))) (let ((_let_374 (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3)) (not (= A4 B3))))))) (let ((_let_375 (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B3) B3))))) (let ((_let_376 (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B3) B3))))) (let ((_let_377 (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B3) B3))))) (let ((_let_378 (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B3) B3))))) (let ((_let_379 (forall ((B5 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B5) A5)) (@ (@ tptp.ord_less_nat A5) B5))))) (let ((_let_380 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_381 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_382 (@ _let_342 tptp.one_one_int))) (let ((_let_383 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_384 (@ _let_383 tptp.one_one_nat))) (let ((_let_385 (@ _let_340 tptp.one_one_rat))) (let ((_let_386 (@ _let_343 tptp.one_one_real))) (let ((_let_387 (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))) (let ((_let_388 (@ _let_293 tptp.one_one_int))) (let ((_let_389 (@ _let_380 tptp.one_one_nat))) (let ((_let_390 (@ _let_292 tptp.one_one_rat))) (let ((_let_391 (@ _let_251 tptp.one_one_real))) (let ((_let_392 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_393 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_394 (@ _let_298 tptp.one_one_int))) (let ((_let_395 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_396 (@ _let_395 tptp.one_one_nat))) (let ((_let_397 (@ _let_299 tptp.one_one_rat))) (let ((_let_398 (@ _let_250 tptp.one_one_real))) (let ((_let_399 (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))) (let ((_let_400 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_401 (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M6)))))))) (let ((_let_402 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_155) tptp.zero_zero_int))) (let ((_let_403 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_80))) (let ((_let_404 (= _let_403 tptp.zero_zero_nat))) (let ((_let_405 (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) _let_120) tptp.one_one_Code_integer))) (let ((_let_406 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_155) tptp.one_one_int))) (let ((_let_407 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_80) tptp.one_one_nat))) (let ((_let_408 (@ _let_333 tptp.one_one_int))) (let ((_let_409 (= _let_408 tptp.zero_zero_int))) (let ((_let_410 (@ _let_331 tptp.one_one_rat))) (let ((_let_411 (= _let_410 tptp.zero_zero_rat))) (let ((_let_412 (@ _let_334 tptp.one_one_real))) (let ((_let_413 (= _let_412 tptp.zero_zero_real))) (let ((_let_414 (@ _let_332 tptp.one_one_complex))) (let ((_let_415 (= _let_414 tptp.zero_zero_complex))) (let ((_let_416 (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_417 (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))) (let ((_let_418 (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))) (let ((_let_419 (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_int Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)))))))))) (let ((_let_420 (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_nat Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)))))))))) (let ((_let_421 (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu2 Bool)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_o Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)))))))))) (let ((_let_422 (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu2 tptp.vEBT_VEBT)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_VEBT_VEBT Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))) (let ((_let_423 (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_list_nat Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))) (let ((_let_424 (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_real Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)))))))))) (let ((_let_425 (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (exists ((I3 tptp.nat)) (and (= Uu2 (@ (@ tptp.nth_complex Xs) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)))))))))) (let ((_let_426 (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))) (let ((_let_427 (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))) (let ((_let_428 (@ tptp.divide_divide_nat tptp.deg))) (let ((_let_429 (@ _let_428 _let_80))) (let ((_let_430 (@ tptp.vEBT_VEBT_high tptp.xa))) (let ((_let_431 (@ _let_430 _let_429))) (let ((_let_432 (@ (@ tptp.vEBT_vebt_pred tptp.summary) _let_431))) (let ((_let_433 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_434 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ _let_166 _let_429))))) (let ((_let_435 (@ (@ tptp.vEBT_VEBT_add (@ _let_434 _let_432)) (@ tptp.vEBT_vebt_maxt (@ _let_433 (@ tptp.the_nat _let_432)))))) (let ((_let_436 (@ tptp.some_nat tptp.mi))) (let ((_let_437 (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa))) (let ((_let_438 (= _let_432 tptp.none_nat))) (let ((_let_439 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary))) (let ((_let_440 (@ (@ tptp.vEBT_vebt_pred _let_439) tptp.xa))) (let ((_let_441 (@ _let_433 _let_431))) (let ((_let_442 (@ tptp.vEBT_vebt_mint _let_441))) (let ((_let_443 (@ tptp.vEBT_VEBT_low tptp.xa))) (let ((_let_444 (@ _let_443 _let_429))) (let ((_let_445 (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_444)) _let_442))) (let ((_let_446 (= _let_442 tptp.none_nat))) (let ((_let_447 (not _let_446))) (let ((_let_448 (and _let_447 _let_445))) (let ((_let_449 (= _let_384 _let_80))) (let ((_let_450 (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (let ((_let_451 (= _let_381 tptp.one_one_nat))) (let ((_let_452 (= _let_290 tptp.one_one_int))) (let ((_let_453 (= _let_288 tptp.one_one_rat))) (let ((_let_454 (= _let_291 tptp.one_one_real))) (let ((_let_455 (= _let_289 tptp.one_one_complex))) (let ((_let_456 (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))) (let ((_let_457 (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X2) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat Z2) Y))))))))) (let ((_let_458 (= tptp.mi tptp.ma))) (let ((_let_459 (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))) (let ((_let_460 (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) N2))) (@ (@ tptp.vEBT_VEBT_low X2) N2)))))) (let ((_let_461 (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))) (let ((_let_462 (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))))) (let ((_let_463 (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))) (let ((_let_464 (@ _let_166 tptp.m))) (let ((_let_465 (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_466 (= _let_465 _let_464))) (let ((_let_467 (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))) (let ((_let_468 (= tptp.m (@ tptp.suc tptp.na)))) (let ((_let_469 (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))) (let ((_let_470 (@ (@ tptp.vEBT_invar_vebt _let_441) tptp.na))) (let ((_let_471 (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))) (let ((_let_472 (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y)))))) (let ((_let_473 (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_474 (@ tptp.some_nat tptp.minilow))) (let ((_let_475 (= _let_442 _let_474))) (let ((_let_476 (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y)))))))) (let ((_let_477 (= _let_429 tptp.na))) (let ((_let_478 (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X2)))))))) (let ((_let_479 (@ (@ tptp.ord_less_eq_nat _let_444) tptp.minilow))) (let ((_let_480 (ho_4196 k_4195 tptp.one))) (let ((_let_481 (ho_4209 (ho_4211 k_4210 _let_480) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_480)))) (let ((_let_482 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_483 (ho_4216 (ho_4215 k_4221 tptp.deg) _let_482))) (let ((_let_484 (ho_4216 (ho_4215 k_4214 _let_482) _let_483))) (let ((_let_485 (ho_4219 k_4218 k_4217))) (let ((_let_486 (ho_4216 (ho_4215 k_4221 tptp.xa) _let_484))) (let ((_let_487 (ho_4216 (ho_4215 k_4223 tptp.xa) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_485 _let_486) _let_481)) (ho_4209 (ho_4220 _let_485 _let_484) _let_481)))))) (let ((_let_488 (ho_4290 k_4289 _let_487))) (let ((_let_489 (ho_4290 k_4289 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10445))) (let ((_let_490 (ho_4292 k_4291 _let_489))) (let ((_let_491 (ho_4293 _let_490 _let_488))) (let ((_let_492 (ho_4290 k_4289 tptp.minilow))) (let ((_let_493 (ho_4293 _let_490 _let_492))) (let ((_let_494 (= tptp.minilow _let_487))) (let ((_let_495 (not _let_491))) (let ((_let_496 (ho_4537 (ho_4536 k_4535 tptp.treeList) _let_486))) (let ((_let_497 (ho_4288 (ho_5602 k_9441 _let_496) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10445))) (let ((_let_498 (not _let_497))) (let ((_let_499 (or _let_498 _let_495))) (let ((_let_500 (forall ((U3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) (ho_4216 (ho_4215 k_4221 tptp.deg) _let_3)))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4216 (ho_4215 k_4221 tptp.xa) _let_4))) (or (not (ho_4288 (ho_5602 k_9441 (ho_4537 (ho_4536 k_4535 tptp.treeList) _let_6)) U3)) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 U3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 tptp.xa) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 _let_6) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2))))))))))))))))) (let ((_let_501 (not _let_499))) (let ((_let_502 (not _let_500))) (let ((_let_503 (not (forall ((U3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_2 (@ (@ tptp.plus_plus_int _let_1) (@ (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat ll_2)) _let_1)))) (let ((_let_3 (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat tptp.deg) _let_3)))) (let ((_let_5 (@ tptp.semiri8420488043553186161ux_int ll_3))) (let ((_let_6 (@ (@ tptp.divide_divide_nat tptp.xa) _let_4))) (or (not (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_6)) U3)) (not (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat U3)) (@ tptp.some_nat (@ (@ tptp.minus_minus_nat tptp.xa) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ (@ _let_5 _let_6) _let_2)) (@ (@ _let_5 _let_4) _let_2)))))))))))))))))) (let ((_let_504 (EQ_RESOLVE (ASSUME :args (_let_478)) (MACRO_SR_EQ_INTRO :args (_let_478 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_505 (SYMM (ASSUME :args (_let_477))))) (let ((_let_506 (EQ_RESOLVE (ASSUME :args (_let_476)) (MACRO_SR_EQ_INTRO :args (_let_476 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_507 (ASSUME :args (_let_473)))) (let ((_let_508 (ASSUME :args (_let_472)))) (let ((_let_509 (ASSUME :args (_let_471)))) (let ((_let_510 (AND_INTRO _let_509 _let_508 _let_507 _let_506 _let_505 _let_504))) (let ((_let_511 (EQ_RESOLVE (ASSUME :args (_let_468)) (MACRO_SR_EQ_INTRO _let_510 :args (_let_468 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_512 (ASSUME :args (_let_467)))) (let ((_let_513 (ASSUME :args (_let_462)))) (let ((_let_514 (ASSUME :args (_let_461)))) (let ((_let_515 (EQ_RESOLVE (ASSUME :args (_let_460)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_460 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_516 (ASSUME :args (_let_459)))) (let ((_let_517 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_457)) (MACRO_SR_EQ_INTRO :args (_let_457 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X2) (forall ((Z2 tptp.nat)) (or (not (@ (@ tptp.member_nat Z2) Xs)) (not (@ (@ tptp.ord_less_nat Z2) X2)) (@ (@ tptp.ord_less_eq_nat Z2) Y)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_518 (ASSUME :args (_let_456)))) (let ((_let_519 (SYMM (ASSUME :args (_let_455))))) (let ((_let_520 (SYMM (ASSUME :args (_let_454))))) (let ((_let_521 (SYMM (ASSUME :args (_let_453))))) (let ((_let_522 (SYMM (ASSUME :args (_let_451))))) (let ((_let_523 (SYMM (ASSUME :args (_let_452))))) (let ((_let_524 (EQ_RESOLVE (ASSUME :args (_let_450)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_450 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_525 (ASSUME :args (_let_427)))) (let ((_let_526 (ASSUME :args (_let_426)))) (let ((_let_527 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_425)) (MACRO_SR_EQ_INTRO :args (_let_425 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu2 tptp.complex)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_complex Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_528 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_424)) (MACRO_SR_EQ_INTRO :args (_let_424 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_real Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_529 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_423)) (MACRO_SR_EQ_INTRO :args (_let_423 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu2 tptp.list_nat)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_list_nat Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_530 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_422)) (MACRO_SR_EQ_INTRO :args (_let_422 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu2 tptp.vEBT_VEBT)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_VEBT_VEBT Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_531 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_421)) (MACRO_SR_EQ_INTRO :args (_let_421 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu2 Bool)) (not (forall ((I3 tptp.nat)) (or (= (@ (@ tptp.nth_o Xs) I3) (not Uu2)) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_532 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_420)) (MACRO_SR_EQ_INTRO :args (_let_420 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu2 tptp.nat)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_nat Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_533 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_419)) (MACRO_SR_EQ_INTRO :args (_let_419 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu2 tptp.int)) (not (forall ((I3 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.nth_int Xs) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_534 (ASSUME :args (_let_418)))) (let ((_let_535 (EQ_RESOLVE (ASSUME :args (_let_417)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_417 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_536 (ASSUME :args (_let_416)))) (let ((_let_537 (EQ_RESOLVE (SYMM (ASSUME :args (_let_415))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_complex _let_414) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_538 (EQ_RESOLVE (SYMM (ASSUME :args (_let_413))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_real _let_412) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_539 (EQ_RESOLVE (SYMM (ASSUME :args (_let_411))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_rat _let_410) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_540 (EQ_RESOLVE (SYMM (ASSUME :args (_let_409))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_int _let_408) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_541 (EQ_RESOLVE (SYMM (ASSUME :args (_let_404))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_nat _let_403) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_542 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_401)) (MACRO_SR_EQ_INTRO :args (_let_401 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (not (forall ((M6 tptp.nat)) (not (forall ((X2 tptp.nat)) (or (not (@ (@ tptp.member_nat X2) N6)) (@ (@ tptp.ord_less_nat X2) M6)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_543 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_399)) (MACRO_SR_EQ_INTRO :args (_let_399 SB_DEFAULT SBA_FIXPOINT))) :args (2)))) (let ((_let_544 (ASSUME :args (_let_387)))) (let ((_let_545 (EQ_RESOLVE (ASSUME :args (_let_378)) (MACRO_SR_EQ_INTRO :args (_let_378 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_546 (EQ_RESOLVE (ASSUME :args (_let_377)) (MACRO_SR_EQ_INTRO :args (_let_377 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_547 (EQ_RESOLVE (ASSUME :args (_let_376)) (MACRO_SR_EQ_INTRO :args (_let_376 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_548 (EQ_RESOLVE (ASSUME :args (_let_375)) (MACRO_SR_EQ_INTRO :args (_let_375 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_549 (EQ_RESOLVE (ASSUME :args (_let_374)) (MACRO_SR_EQ_INTRO :args (_let_374 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_550 (EQ_RESOLVE (ASSUME :args (_let_373)) (MACRO_SR_EQ_INTRO :args (_let_373 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_551 (EQ_RESOLVE (ASSUME :args (_let_372)) (MACRO_SR_EQ_INTRO :args (_let_372 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_552 (EQ_RESOLVE (ASSUME :args (_let_371)) (MACRO_SR_EQ_INTRO :args (_let_371 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_553 (ASSUME :args (_let_370)))) (let ((_let_554 (EQ_RESOLVE (ASSUME :args (_let_369)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_369 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_555 (EQ_RESOLVE (ASSUME :args (_let_367)) (MACRO_SR_EQ_INTRO :args (_let_367 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_556 (EQ_RESOLVE (ASSUME :args (_let_366)) (MACRO_SR_EQ_INTRO :args (_let_366 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_557 (EQ_RESOLVE (ASSUME :args (_let_365)) (MACRO_SR_EQ_INTRO :args (_let_365 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_558 (EQ_RESOLVE (ASSUME :args (_let_364)) (MACRO_SR_EQ_INTRO :args (_let_364 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_559 (EQ_RESOLVE (ASSUME :args (_let_363)) (MACRO_SR_EQ_INTRO :args (_let_363 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_560 (EQ_RESOLVE (ASSUME :args (_let_362)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_362 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_561 (ASSUME :args (_let_361)))) (let ((_let_562 (ASSUME :args (_let_360)))) (let ((_let_563 (ASSUME :args (_let_359)))) (let ((_let_564 (AND_INTRO _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504))) (let ((_let_565 (EQ_RESOLVE (ASSUME :args (_let_356)) (MACRO_SR_EQ_INTRO _let_564 :args (_let_356 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_566 (EQ_RESOLVE (SYMM (ASSUME :args (_let_355))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.zero_zero_nat tptp.bot_bot_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_567 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_354)) (MACRO_SR_EQ_INTRO :args (_let_354 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.dvd_dvd_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (=> (= tptp.zero_zero_complex A4) (= tptp.zero_zero_complex B3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_568 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_353)) (MACRO_SR_EQ_INTRO :args (_let_353 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= tptp.zero_zero_real A4) (= tptp.zero_zero_real B3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_569 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_352)) (MACRO_SR_EQ_INTRO :args (_let_352 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= tptp.zero_zero_rat A4) (= tptp.zero_zero_rat B3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_570 (EQ_RESOLVE (ASSUME :args (_let_351)) (MACRO_SR_EQ_INTRO :args (_let_351 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_571 (EQ_RESOLVE (ASSUME :args (_let_350)) (MACRO_SR_EQ_INTRO :args (_let_350 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_572 (EQ_RESOLVE (ASSUME :args (_let_349)) (MACRO_SR_EQ_INTRO :args (_let_349 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_573 (SYMM (ASSUME :args (_let_348))))) (let ((_let_574 (EQ_RESOLVE (ASSUME :args (_let_344)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_344 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_575 (SYMM (ASSUME :args (_let_341))))) (let ((_let_576 (EQ_RESOLVE (ASSUME :args (_let_318)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_318 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_577 (EQ_RESOLVE (ASSUME :args (_let_317)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_317 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_578 (EQ_RESOLVE (ASSUME :args (_let_316)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_316 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_579 (EQ_RESOLVE (ASSUME :args (_let_315)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_315 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_580 (ASSUME :args (_let_308)))) (let ((_let_581 (ASSUME :args (_let_307)))) (let ((_let_582 (ASSUME :args (_let_306)))) (let ((_let_583 (ASSUME :args (_let_305)))) (let ((_let_584 (ASSUME :args (_let_304)))) (let ((_let_585 (EQ_RESOLVE (ASSUME :args (_let_287)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_287 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_586 (EQ_RESOLVE (ASSUME :args (_let_282)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_282 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_587 (EQ_RESOLVE (ASSUME :args (_let_281)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_281 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_588 (EQ_RESOLVE (ASSUME :args (_let_280)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_280 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_589 (EQ_RESOLVE (ASSUME :args (_let_279)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_279 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_590 (EQ_RESOLVE (ASSUME :args (_let_278)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_278 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_591 (ASSUME :args (_let_277)))) (let ((_let_592 (EQ_RESOLVE (ASSUME :args (_let_276)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_276 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_593 (ASSUME :args (_let_275)))) (let ((_let_594 (EQ_RESOLVE (ASSUME :args (_let_274)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_274 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_595 (EQ_RESOLVE (ASSUME :args (_let_273)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_273 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_596 (EQ_RESOLVE (ASSUME :args (_let_272)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_272 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_597 (EQ_RESOLVE (ASSUME :args (_let_271)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_271 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_598 (EQ_RESOLVE (ASSUME :args (_let_270)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_270 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_599 (EQ_RESOLVE (ASSUME :args (_let_269)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_269 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_600 (EQ_RESOLVE (ASSUME :args (_let_268)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_268 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_601 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_267)) (MACRO_SR_EQ_INTRO :args (_let_267 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= tptp.zero_zero_int R5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_602 (EQ_RESOLVE (ASSUME :args (_let_266)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_266 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_603 (EQ_RESOLVE (ASSUME :args (_let_265)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_265 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_604 (EQ_RESOLVE (ASSUME :args (_let_264)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_264 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_605 (EQ_RESOLVE (ASSUME :args (_let_263)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_263 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_606 (EQ_RESOLVE (ASSUME :args (_let_262)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_262 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_607 (EQ_RESOLVE (ASSUME :args (_let_261)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_261 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_608 (ASSUME :args (_let_257)))) (let ((_let_609 (ASSUME :args (_let_256)))) (let ((_let_610 (ASSUME :args (_let_255)))) (let ((_let_611 (ASSUME :args (_let_254)))) (let ((_let_612 (ASSUME :args (_let_253)))) (let ((_let_613 (ASSUME :args (_let_252)))) (let ((_let_614 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_247)) (MACRO_SR_EQ_INTRO :args (_let_247 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo6980174941875973593q_real (lambda ((X6 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_real (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_real (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_615 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_246)) (MACRO_SR_EQ_INTRO :args (_let_246 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo3100542954746470799et_int (lambda ((X6 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_set_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_set_int (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_616 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_245)) (MACRO_SR_EQ_INTRO :args (_let_245 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo4267028734544971653eq_rat (lambda ((X6 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_rat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_rat (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_617 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_244)) (MACRO_SR_EQ_INTRO :args (_let_244 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo1459490580787246023eq_num (lambda ((X6 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_num (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_num (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_618 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_243)) (MACRO_SR_EQ_INTRO :args (_let_243 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo4902158794631467389eq_nat (lambda ((X6 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_nat (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_nat (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_619 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_242)) (MACRO_SR_EQ_INTRO :args (_let_242 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo4899668324122417113eq_int (lambda ((X6 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_int (@ X6 M6)) (@ X6 N2)))) (forall ((M6 tptp.nat) (N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N2)) (@ (@ tptp.ord_less_eq_int (@ X6 N2)) (@ X6 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_620 (EQ_RESOLVE (ASSUME :args (_let_237)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_237 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_621 (EQ_RESOLVE (ASSUME :args (_let_236)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_236 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_622 (ASSUME :args (_let_235)))) (let ((_let_623 (ASSUME :args (_let_234)))) (let ((_let_624 (EQ_RESOLVE (ASSUME :args (_let_233)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_233 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_625 (EQ_RESOLVE (ASSUME :args (_let_232)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_232 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_626 (EQ_RESOLVE (ASSUME :args (_let_231)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_231 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_627 (EQ_RESOLVE (ASSUME :args (_let_230)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_230 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_628 (EQ_RESOLVE (ASSUME :args (_let_229)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_229 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_629 (EQ_RESOLVE (ASSUME :args (_let_228)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_228 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_630 (EQ_RESOLVE (ASSUME :args (_let_227)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_227 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_631 (EQ_RESOLVE (ASSUME :args (_let_226)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_226 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_632 (EQ_RESOLVE (ASSUME :args (_let_225)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_225 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_633 (EQ_RESOLVE (ASSUME :args (_let_213)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_213 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_634 (EQ_RESOLVE (ASSUME :args (_let_211)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_211 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_635 (EQ_RESOLVE (ASSUME :args (_let_210)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_210 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_636 (EQ_RESOLVE (ASSUME :args (_let_209)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_209 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_637 (EQ_RESOLVE (ASSUME :args (_let_208)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_208 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_638 (EQ_RESOLVE (ASSUME :args (_let_207)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_207 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_639 (EQ_RESOLVE (ASSUME :args (_let_206)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_206 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_640 (EQ_RESOLVE (ASSUME :args (_let_205)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_205 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_641 (EQ_RESOLVE (ASSUME :args (_let_204)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_204 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_642 (EQ_RESOLVE (ASSUME :args (_let_203)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_203 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_643 (EQ_RESOLVE (ASSUME :args (_let_202)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_202 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_644 (EQ_RESOLVE (ASSUME :args (_let_201)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_201 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_645 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_200)) (MACRO_SR_EQ_INTRO :args (_let_200 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat N2)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_646 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_199)) (MACRO_SR_EQ_INTRO :args (_let_199 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_nat N2)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_647 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_198)) (MACRO_SR_EQ_INTRO :args (_let_198 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N2)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_648 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_197)) (MACRO_SR_EQ_INTRO :args (_let_197 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_nat N2)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_649 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_196)) (MACRO_SR_EQ_INTRO :args (_let_196 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N2)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_650 (SYMM (ASSUME :args (_let_195))))) (let ((_let_651 (EQ_RESOLVE (ASSUME :args (_let_194)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_194 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_652 (EQ_RESOLVE (ASSUME :args (_let_193)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_193 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_653 (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_192 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_654 (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_191 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_655 (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_190 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_656 (EQ_RESOLVE (ASSUME :args (_let_189)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_189 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_657 (EQ_RESOLVE (ASSUME :args (_let_188)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_188 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_658 (EQ_RESOLVE (ASSUME :args (_let_187)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_187 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_659 (ASSUME :args (_let_186)))) (let ((_let_660 (EQ_RESOLVE (SYMM (ASSUME :args (_let_184))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.imaginary_unit _let_183) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_661 (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_176 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_662 (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_173 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_663 (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_172 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_664 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO :args (_let_171 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= Y (@ tptp.tan_real X2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_665 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_170)) (MACRO_SR_EQ_INTRO :args (_let_170 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= Y (@ tptp.sin_real X2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_666 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_169)) (MACRO_SR_EQ_INTRO :args (_let_169 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= Y (@ tptp.cos_real X2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_667 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_168)) (MACRO_SR_EQ_INTRO :args (_let_168 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (let ((_let_1 (= tptp.zero_zero_int A23))) (or (not (or (not _let_1) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12))))) (not (or _let_1 (forall ((Q4 tptp.int)) (or (not (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int))) (not (= A12 (@ (@ tptp.times_times_int Q4) A23))))))) (not (forall ((R5 tptp.int) (Q4 tptp.int)) (or (not (= A33 (@ (@ tptp.product_Pair_int_int Q4) R5))) (not (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int A23))) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int A23))) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) A23)) R5)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_668 (ASSUME :args (_let_167)))) (let ((_let_669 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_165)) (MACRO_SR_EQ_INTRO :args (_let_165 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.pi (@ _let_164 (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= tptp.zero_zero_real (@ tptp.cos_real X2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_670 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO :args (_let_163 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (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 L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int L)) K3) (@ (@ (@ tptp.if_int (= _let_3 (@ tptp.sgn_sgn_int K3))) (@ _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 L) K3))))) _let_2)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_671 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_162)) (MACRO_SR_EQ_INTRO :args (_let_162 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int L)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L))) (@ 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 L) K3))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_672 (ASSUME :args (_let_161)))) (let ((_let_673 (EQ_RESOLVE (ASSUME :args (_let_160)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_160 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_674 (EQ_RESOLVE (ASSUME :args (_let_159)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_159 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_675 (EQ_RESOLVE (ASSUME :args (_let_158)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_158 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_676 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_157)) (MACRO_SR_EQ_INTRO :args (_let_157 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_real A4)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_677 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_678 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_679 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_680 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_681 (EQ_RESOLVE (ASSUME :args (_let_148)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_148 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_682 (EQ_RESOLVE (ASSUME :args (_let_147)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_147 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_683 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_complex Z2)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_684 (EQ_RESOLVE (ASSUME :args (_let_145)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_145 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_685 (EQ_RESOLVE (ASSUME :args (_let_144)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_144 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_686 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_687 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_688 (EQ_RESOLVE (ASSUME :args (_let_141)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_141 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_689 (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_140 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_690 (EQ_RESOLVE (ASSUME :args (_let_139)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_139 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_691 (EQ_RESOLVE (ASSUME :args (_let_138)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_138 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_692 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_693 (EQ_RESOLVE (ASSUME :args (_let_136)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_136 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_694 (ASSUME :args (_let_135)))) (let ((_let_695 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_696 (ASSUME :args (_let_133)))) (let ((_let_697 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_698 (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_130 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_699 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (not (forall ((M9 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_228126 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M9))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_228126)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 BOUND_VARIABLE_228126)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_700 (ASSUME :args (_let_128)))) (let ((_let_701 (ASSUME :args (_let_127)))) (let ((_let_702 (ASSUME :args (_let_125)))) (let ((_let_703 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_704 (ASSUME :args (_let_123)))) (let ((_let_705 (EQ_RESOLVE (SYMM (ASSUME :args (_let_122))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.one_one_Code_integer _let_121) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_706 (ASSUME :args (_let_119)))) (let ((_let_707 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_708 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_709 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO :args (_let_116 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.csqrt (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z2))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_4 (@ tptp.im Z2))) (@ (@ 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 (= tptp.zero_zero_real _let_4)) 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)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_710 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_711 (ASSUME :args (_let_114)))) (let ((_let_712 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_713 (EQ_RESOLVE (ASSUME :args (_let_112)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_112 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_714 (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_111 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_715 (EQ_RESOLVE (ASSUME :args (_let_110)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_110 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_716 (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_109 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_717 (ASSUME :args (_let_106)))) (let ((_let_718 (EQ_RESOLVE (ASSUME :args (_let_105)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_105 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_719 (EQ_RESOLVE (ASSUME :args (_let_104)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_104 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_720 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO :args (_let_103 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int _let_1)) (@ (@ 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)))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_721 (EQ_RESOLVE (ASSUME :args (_let_102)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_102 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_722 (ASSUME :args (_let_100)))) (let ((_let_723 (ASSUME :args (_let_99)))) (let ((_let_724 (ASSUME :args (_let_98)))) (let ((_let_725 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_726 (ASSUME :args (_let_93)))) (let ((_let_727 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO :args (_let_92 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.complete_Sup_Sup_int (lambda ((X6 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X6) (forall ((Y tptp.int)) (or (not (@ (@ tptp.member_int Y) X6)) (@ (@ tptp.ord_less_eq_int Y) X2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_728 (SYMM (ASSUME :args (_let_91))))) (let ((_let_729 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO :args (_let_90 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= tptp.zero_zero_nat _let_1)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_730 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO :args (_let_89 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu2 tptp.real)) (not (forall ((I3 tptp.int) (N2 tptp.nat)) (or (not (= Uu2 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N2)))) (= tptp.zero_zero_nat N2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_731 (SYMM (ASSUME :args (_let_88))))) (let ((_let_732 (SYMM (ASSUME :args (_let_87))))) (let ((_let_733 (SYMM (ASSUME :args (_let_86))))) (let ((_let_734 (SYMM (ASSUME :args (_let_85))))) (let ((_let_735 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_736 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_737 (ASSUME :args (_let_82)))) (let ((_let_738 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO :args (_let_81 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (not (forall ((K3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_739 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_79)) (MACRO_SR_EQ_INTRO :args (_let_79 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.root (lambda ((N2 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N2)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2)))) X2)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_740 (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_78 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_741 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (not (forall ((C3 tptp.real)) (not (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C3)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_742 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_743 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_744 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_745 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_746 (ASSUME :args (_let_59)))) (let ((_let_747 (ASSUME :args (_let_58)))) (let ((_let_748 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_749 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_750 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_751 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_752 (ASSUME :args (_let_53)))) (let ((_let_753 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_754 (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_51 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_755 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_756 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.vanishes (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5)) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat K3) N2)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N2))) R5)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_757 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO :args (_let_47 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5)) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_235021 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K3))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_235021)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 BOUND_VARIABLE_235021)))) R5))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_758 (ASSUME :args (_let_46)))) (let ((_let_759 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO :args (_let_45 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.positive2 (lambda ((X2 tptp.real)) (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235444 tptp.nat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5)) (not (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_235444) N2)) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X2) N2)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_760 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_761 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_762 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.cr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X2) X2) (= Y (@ tptp.real2 X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_763 (ASSUME :args (_let_41)))) (let ((_let_764 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_765 (ASSUME :args (_let_39)))) (let ((_let_766 (EQ_RESOLVE (SYMM (ASSUME :args (_let_33))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.cr_real tptp.pcr_real) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_767 (ASSUME :args (_let_24)))) (let ((_let_768 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_769 (ASSUME :args (_let_16)))) (let ((_let_770 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X2 tptp.real)) (or (not (@ (@ tptp.member_real X2) X6)) (@ (@ tptp.ord_less_eq_real X2) Z2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_771 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y))) (and (not (= tptp.zero_zero_int _let_1)) (not (= tptp.zero_zero_int _let_2)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_772 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int X2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_773 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.inverse_inverse_rat (@ _let_3 (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int _let_1)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_774 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_775 (ASSUME :args (_let_6)))) (let ((_let_776 (ASSUME :args (_let_5)))) (let ((_let_777 (AND_INTRO (EQ_RESOLVE (SYMM (ASSUME :args (_let_2))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args ((= tptp.id_nat tptp.semiri1316708129612266289at_nat) SB_DEFAULT SBA_FIXPOINT))) _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504))) (let ((_let_778 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_777 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((U3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_2 (@ (@ tptp.plus_plus_int _let_1) (@ (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X2)))) _let_1)))) (let ((_let_3 (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat tptp.deg) _let_3)))) (let ((_let_5 (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) (@ tptp.numeral_numeral_int tptp.one)))))) (let ((_let_6 (@ (@ tptp.divide_divide_nat tptp.xa) _let_4))) (or (not (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_6)) U3)) (not (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat U3)) (@ tptp.some_nat (@ (@ tptp.minus_minus_nat tptp.xa) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ (@ _let_5 _let_6) _let_2)) (@ (@ _let_5 _let_4) _let_2)))))))))))))))) _let_503))) (PREPROCESS :args ((= _let_503 _let_502))))))) (let ((_let_779 (or))) (let ((_let_780 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_778) :args (_let_502))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_502) _let_500))) (REFL :args (_let_501)) :args _let_779)) _let_778 :args (_let_501 true _let_500)))) (let ((_let_781 (REFL :args (_let_499)))) (let ((_let_782 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_499 1)) (CONG _let_781 (MACRO_SR_PRED_INTRO :args ((= (not _let_495) _let_491))) :args _let_779)) :args ((or _let_491 _let_499))) _let_780 :args (_let_491 true _let_499)))) (let ((_let_783 (ho_4292 k_4304 _let_492))) (let ((_let_784 (ho_4293 _let_783 _let_489))) (let ((_let_785 (not _let_784))) (let ((_let_786 (= _let_785 _let_493))) (let ((_let_787 (not _let_493))) (let ((_let_788 (forall ((B5 tptp.nat) (A5 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 B5))) (let ((_let_2 (ho_4290 k_4289 A5))) (= (not (ho_4293 (ho_4292 k_4304 _let_1) _let_2)) (ho_4293 (ho_4292 k_4291 _let_2) _let_1))))))) (let ((_let_789 (EQ_RESOLVE (ASSUME :args (_let_379)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504) :args (_let_379 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B5 tptp.nat) (A5 tptp.nat)) (let ((_let_1 (@ tptp.some_nat A5))) (let ((_let_2 (@ tptp.some_nat B5))) (= (@ (@ tptp.vEBT_VEBT_less _let_1) _let_2) (not (@ (@ tptp.vEBT_VEBT_lesseq _let_2) _let_1)))))) _let_788))))))) (let ((_let_790 (_let_788))) (let ((_let_791 (= _let_492 (ho_9423 k_9422 _let_496)))) (let ((_let_792 (not _let_791))) (let ((_let_793 (ho_4288 (ho_5602 k_9157 _let_496) _let_483))) (let ((_let_794 (not _let_793))) (let ((_let_795 (or _let_794 _let_792 _let_498 _let_784))) (let ((_let_796 (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (let ((_let_1 (ho_4290 k_4289 Mini))) (or (not (ho_4288 (ho_5602 k_9157 T) N)) (not (= _let_1 (ho_9423 k_9422 T))) (not (ho_4288 (ho_5602 k_9441 T) X)) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 X))))))) (let ((_let_797 (EQ_RESOLVE (ASSUME :args (_let_469)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_469 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_510 :args ((forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (or (not (@ (@ tptp.vEBT_invar_vebt T) N)) (not (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini))) (not (@ (@ tptp.vEBT_vebt_member T) X)) (@ (@ tptp.ord_less_eq_nat Mini) X))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.some_nat Mini))) (or (not (@ (@ tptp.vEBT_invar_vebt T) N)) (not (= (@ tptp.vEBT_vebt_mint T) _let_1)) (not (@ (@ tptp.vEBT_vebt_member T) X)) (@ (@ tptp.vEBT_VEBT_lesseq _let_1) (@ tptp.some_nat X))))) _let_796))))))) (let ((_let_798 (@ _let_428 _let_156))) (let ((_let_799 (@ (@ tptp.power_power_nat _let_156) _let_798))) (let ((_let_800 (@ (@ tptp.divide_divide_nat tptp.xa) _let_799))) (let ((_let_801 (@ _let_433 _let_800))) (let ((_let_802 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_786)) :args ((or _let_785 _let_787 (not _let_786)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_795)) :args ((or _let_792 _let_794 _let_498 _let_784 (not _let_795)))) (EQ_RESOLVE (ASSUME :args (_let_475)) (TRANS (MACRO_SR_EQ_INTRO _let_777 :args (_let_475 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_474 (@ tptp.vEBT_vebt_mint _let_801)) _let_791))))) (EQ_RESOLVE (ASSUME :args (_let_470)) (TRANS (MACRO_SR_EQ_INTRO _let_777 :args (_let_470 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ tptp.vEBT_invar_vebt _let_801) _let_798) _let_793))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_499 0)) (CONG _let_781 (MACRO_SR_PRED_INTRO :args ((= (not _let_498) _let_497))) :args _let_779)) :args ((or _let_497 _let_499))) _let_780 :args (_let_497 true _let_499)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_797 :args (_let_496 _let_483 tptp.minilow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10445 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_796))) _let_797 :args (_let_795 false _let_796)) :args (_let_784 false _let_791 false _let_793 false _let_497 false _let_795)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_789 :args (tptp.minilow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10445 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_790)) _let_789 :args (_let_786 false _let_788)) :args (_let_787 false _let_784 false _let_786)))) (let ((_let_803 (not _let_494))) (let ((_let_804 (ho_4293 _let_783 _let_488))) (let ((_let_805 (and _let_804 _let_803))) (let ((_let_806 (ho_4293 (ho_4292 k_4304 _let_488) _let_492))) (let ((_let_807 (not _let_806))) (let ((_let_808 (= _let_807 _let_805))) (let ((_let_809 (not _let_805))) (let ((_let_810 (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (ho_4290 k_4289 A))) (let ((_let_2 (ho_4290 k_4289 B))) (= (not (ho_4293 (ho_4292 k_4304 _let_1) _let_2)) (and (ho_4293 (ho_4292 k_4304 _let_2) _let_1) (not (= A B))))))))) (let ((_let_811 (EQ_RESOLVE (ASSUME :args (_let_358)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_358 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_564 :args ((forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= A B))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.some_nat B))) (let ((_let_2 (@ tptp.some_nat A))) (= (and (@ (@ tptp.vEBT_VEBT_lesseq _let_1) _let_2) (not (= A B))) (not (@ (@ tptp.vEBT_VEBT_lesseq _let_2) _let_1)))))) _let_810))))))) (let ((_let_812 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_9906 x z) (ho_9906 y z)))) (= x y))))) (let ((_let_813 (forall ((x |u_(-> tptp.list_complex tptp.nat tptp.complex tptp.complex Bool)|) (y |u_(-> tptp.list_complex tptp.nat tptp.complex tptp.complex Bool)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_9207 x z) (ho_9207 y z)))) (= x y))))) (let ((_let_814 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_complex)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_complex)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_9900 x z) (ho_9900 y z)))) (= x y))))) (let ((_let_815 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_5479 x z) (ho_5479 y z)))) (= x y))))) (let ((_let_816 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_complex)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_complex)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_9899 x z) (ho_9899 y z)))) (= x y))))) (let ((_let_817 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_nat)_ tptp.produc8763457246119570046nteger tptp.set_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_nat)_ tptp.produc8763457246119570046nteger tptp.set_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_nat)|)) (= (ho_9883 x z) (ho_9883 y z)))) (= x y))))) (let ((_let_818 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_9881 x z) (ho_9881 y z)))) (= x y))))) (let ((_let_819 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_nat)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_nat)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_9884 x z) (ho_9884 y z)))) (= x y))))) (let ((_let_820 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_8918 x z) (ho_8918 y z)))) (= x y))))) (let ((_let_821 (forall ((x |u_(-> tptp.int tptp.real Bool)|) (y |u_(-> tptp.int tptp.real Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_9106 x z) (ho_9106 y z)))) (= x y))))) (let ((_let_822 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)_ tptp.product_prod_int_int tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)_ tptp.product_prod_int_int tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)|)) (= (ho_9878 x z) (ho_9878 y z)))) (= x y))))) (let ((_let_823 (forall ((x |u_(-> tptp.int tptp.int tptp.set_complex)|) (y |u_(-> tptp.int tptp.int tptp.set_complex)|)) (or (not (forall ((z tptp.int)) (= (ho_9871 x z) (ho_9871 y z)))) (= x y))))) (let ((_let_824 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.real)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.real)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_9917 x z) (ho_9917 y z)))) (= x y))))) (let ((_let_825 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_int)_ tptp.product_prod_int_int tptp.set_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_int)_ tptp.product_prod_int_int tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_int)|)) (= (ho_9869 x z) (ho_9869 y z)))) (= x y))))) (let ((_let_826 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_real)_ tptp.product_prod_int_int tptp.set_real)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_real)_ tptp.product_prod_int_int tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_real)|)) (= (ho_9865 x z) (ho_9865 y z)))) (= x y))))) (let ((_let_827 (forall ((x |u_(-> tptp.int tptp.int tptp.set_real)|) (y |u_(-> tptp.int tptp.int tptp.set_real)|)) (or (not (forall ((z tptp.int)) (= (ho_9863 x z) (ho_9863 y z)))) (= x y))))) (let ((_let_828 (forall ((x |u_(-> tptp.int tptp.set_nat)|) (y |u_(-> tptp.int tptp.set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_9862 x z) (ho_9862 y z)))) (= x y))))) (let ((_let_829 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_nat)|) (y |u_(-> tptp.product_prod_int_int tptp.set_nat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_9861 x z) (ho_9861 y z)))) (= x y))))) (let ((_let_830 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10273 x z) (ho_10273 y z)))) (= x y))))) (let ((_let_831 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ tptp.produc2285326912895808259nt_int Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ tptp.produc2285326912895808259nt_int Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9855 x z) (ho_9855 y z)))) (= x y))))) (let ((_let_832 (forall ((x |u_(-> tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9849 x z) (ho_9849 y z)))) (= x y))))) (let ((_let_833 (forall ((x |u_(-> tptp.list_o Bool Bool)|) (y |u_(-> tptp.list_o Bool Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_5153 x z) (ho_5153 y z)))) (= x y))))) (let ((_let_834 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_9841 x z) (ho_9841 y z)))) (= x y))))) (let ((_let_835 (forall ((x |u_(-> tptp.option_nat tptp.option_num Bool)|) (y |u_(-> tptp.option_nat tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9456 x z) (ho_9456 y z)))) (= x y))))) (let ((_let_836 (forall ((x |u_(-> _u_(-> tptp.complex tptp.code_integer)_ tptp.set_complex tptp.code_integer)|) (y |u_(-> _u_(-> tptp.complex tptp.code_integer)_ tptp.set_complex tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.code_integer)|)) (= (ho_9834 x z) (ho_9834 y z)))) (= x y))))) (let ((_let_837 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_9831 x z) (ho_9831 y z)))) (= x y))))) (let ((_let_838 (forall ((x |u_(-> tptp.set_complex tptp.set_complex tptp.set_complex)|) (y |u_(-> tptp.set_complex tptp.set_complex tptp.set_complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9822 x z) (ho_9822 y z)))) (= x y))))) (let ((_let_839 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10389 x z) (ho_10389 y z)))) (= x y))))) (let ((_let_840 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.set_real tptp.complex)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.set_real tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_9819 x z) (ho_9819 y z)))) (= x y))))) (let ((_let_841 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.set_int tptp.complex)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.set_int tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_9816 x z) (ho_9816 y z)))) (= x y))))) (let ((_let_842 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_5998 x z) (ho_5998 y z)))) (= x y))))) (let ((_let_843 (forall ((x |u_(-> tptp.num tptp.product_prod_num_num)|) (y |u_(-> tptp.num tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.num)) (= (ho_9814 x z) (ho_9814 y z)))) (= x y))))) (let ((_let_844 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_10087 x z) (ho_10087 y z)))) (= x y))))) (let ((_let_845 (forall ((x |u_(-> tptp.set_complex tptp.real)|) (y |u_(-> tptp.set_complex tptp.real)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9811 x z) (ho_9811 y z)))) (= x y))))) (let ((_let_846 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_9804 x z) (ho_9804 y z)))) (= x y))))) (let ((_let_847 (forall ((x |u_(-> tptp.complex tptp.int)|) (y |u_(-> tptp.complex tptp.int)|)) (or (not (forall ((z tptp.complex)) (= (ho_9799 x z) (ho_9799 y z)))) (= x y))))) (let ((_let_848 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9312 x z) (ho_9312 y z)))) (= x y))))) (let ((_let_849 (forall ((x |u_(-> tptp.set_complex tptp.int)|) (y |u_(-> tptp.set_complex tptp.int)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9802 x z) (ho_9802 y z)))) (= x y))))) (let ((_let_850 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4198 x z) (ho_4198 y z)))) (= x y))))) (let ((_let_851 (forall ((x |u_(-> tptp.produc7773217078559923341nt_int tptp.set_nat)|) (y |u_(-> tptp.produc7773217078559923341nt_int tptp.set_nat)|)) (or (not (forall ((z tptp.produc7773217078559923341nt_int)) (= (ho_9904 x z) (ho_9904 y z)))) (= x y))))) (let ((_let_852 (forall ((x |u_(-> tptp.set_real tptp.int)|) (y |u_(-> tptp.set_real tptp.int)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9798 x z) (ho_9798 y z)))) (= x y))))) (let ((_let_853 (forall ((x |u_(-> tptp.set_int tptp.int)|) (y |u_(-> tptp.set_int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8565 x z) (ho_8565 y z)))) (= x y))))) (let ((_let_854 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_7773 x z) (ho_7773 y z)))) (= x y))))) (let ((_let_855 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.set_complex tptp.nat)|) (y |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.set_complex tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat)|)) (= (ho_9794 x z) (ho_9794 y z)))) (= x y))))) (let ((_let_856 (forall ((x |u_(-> tptp.set_Pr9222295170931077689nt_int _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr9222295170931077689nt_int _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr9222295170931077689nt_int)) (= (ho_7731 x z) (ho_7731 y z)))) (= x y))))) (let ((_let_857 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_9791 x z) (ho_9791 y z)))) (= x y))))) (let ((_let_858 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.set_real tptp.nat)|) (y |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.set_real tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat)|)) (= (ho_9788 x z) (ho_9788 y z)))) (= x y))))) (let ((_let_859 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.rat)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_9785 x z) (ho_9785 y z)))) (= x y))))) (let ((_let_860 (forall ((x |u_(-> tptp.set_complex tptp.rat)|) (y |u_(-> tptp.set_complex tptp.rat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9786 x z) (ho_9786 y z)))) (= x y))))) (let ((_let_861 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_5243 x z) (ho_5243 y z)))) (= x y))))) (let ((_let_862 (forall ((x |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_9665 x z) (ho_9665 y z)))) (= x y))))) (let ((_let_863 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_9781 x z) (ho_9781 y z)))) (= x y))))) (let ((_let_864 (forall ((x |u_(-> Bool tptp.real)|) (y |u_(-> Bool tptp.real)|)) (or (not (forall ((z Bool)) (= (ho_9776 x z) (ho_9776 y z)))) (= x y))))) (let ((_let_865 (forall ((x |u_(-> tptp.real tptp.real tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_6976 x z) (ho_6976 y z)))) (= x y))))) (let ((_let_866 (forall ((x |u_(-> Bool tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_9772 x z) (ho_9772 y z)))) (= x y))))) (let ((_let_867 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_9759 x z) (ho_9759 y z)))) (= x y))))) (let ((_let_868 (forall ((x |u_(-> tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_9760 x z) (ho_9760 y z)))) (= x y))))) (let ((_let_869 (forall ((x |u_(-> _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|) (y |u_(-> _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.nat)|)) (= (ho_9755 x z) (ho_9755 y z)))) (= x y))))) (let ((_let_870 (forall ((x |u_(-> tptp.set_int tptp.rat)|) (y |u_(-> tptp.set_int tptp.rat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9782 x z) (ho_9782 y z)))) (= x y))))) (let ((_let_871 (forall ((x |u_(-> tptp.num tptp.num Bool)|) (y |u_(-> tptp.num tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_5279 x z) (ho_5279 y z)))) (= x y))))) (let ((_let_872 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.option4927543243414619207at_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.option4927543243414619207at_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_9753 x z) (ho_9753 y z)))) (= x y))))) (let ((_let_873 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8828 x z) (ho_8828 y z)))) (= x y))))) (let ((_let_874 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.option_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.option_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_9751 x z) (ho_9751 y z)))) (= x y))))) (let ((_let_875 (forall ((x |u_(-> tptp.int tptp.num)|) (y |u_(-> tptp.int tptp.num)|)) (or (not (forall ((z tptp.int)) (= (ho_9748 x z) (ho_9748 y z)))) (= x y))))) (let ((_let_876 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.produc3447558737645232053on_num tptp.produc1193250871479095198on_num)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.produc3447558737645232053on_num tptp.produc1193250871479095198on_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_9508 x z) (ho_9508 y z)))) (= x y))))) (let ((_let_877 (forall ((x |u_(-> tptp.num tptp.rat)|) (y |u_(-> tptp.num tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_9747 x z) (ho_9747 y z)))) (= x y))))) (let ((_let_878 (forall ((x |u_(-> Bool tptp.rat)|) (y |u_(-> Bool tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_9774 x z) (ho_9774 y z)))) (= x y))))) (let ((_let_879 (forall ((x |u_(-> tptp.rat tptp.num)|) (y |u_(-> tptp.rat tptp.num)|)) (or (not (forall ((z tptp.rat)) (= (ho_9744 x z) (ho_9744 y z)))) (= x y))))) (let ((_let_880 (forall ((x |u_(-> tptp.list_o tptp.list_P3126845725202233233VEBT_o)|) (y |u_(-> tptp.list_o tptp.list_P3126845725202233233VEBT_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9648 x z) (ho_9648 y z)))) (= x y))))) (let ((_let_881 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5510 x z) (ho_5510 y z)))) (= x y))))) (let ((_let_882 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_10437 x z) (ho_10437 y z)))) (= x y))))) (let ((_let_883 (forall ((x |u_(-> tptp.produc7773217078559923341nt_int Bool)|) (y |u_(-> tptp.produc7773217078559923341nt_int Bool)|)) (or (not (forall ((z tptp.produc7773217078559923341nt_int)) (= (ho_9742 x z) (ho_9742 y z)))) (= x y))))) (let ((_let_884 (forall ((x |u_(-> tptp.produc2285326912895808259nt_int Bool)|) (y |u_(-> tptp.produc2285326912895808259nt_int Bool)|)) (or (not (forall ((z tptp.produc2285326912895808259nt_int)) (= (ho_9741 x z) (ho_9741 y z)))) (= x y))))) (let ((_let_885 (forall ((x |u_(-> tptp.produc1908205239877642774nteger Bool)|) (y |u_(-> tptp.produc1908205239877642774nteger Bool)|)) (or (not (forall ((z tptp.produc1908205239877642774nteger)) (= (ho_9740 x z) (ho_9740 y z)))) (= x y))))) (let ((_let_886 (forall ((x |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat)|) (y |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat)|)) (or (not (forall ((z tptp.list_P7333126701944960589_nat_o)) (= (ho_9738 x z) (ho_9738 y z)))) (= x y))))) (let ((_let_887 (forall ((x |u_(-> tptp.list_P5647936690300460905T_VEBT tptp.nat)|) (y |u_(-> tptp.list_P5647936690300460905T_VEBT tptp.nat)|)) (or (not (forall ((z tptp.list_P5647936690300460905T_VEBT)) (= (ho_9736 x z) (ho_9736 y z)))) (= x y))))) (let ((_let_888 (forall ((x |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat)|) (y |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat)|)) (or (not (forall ((z tptp.list_P3795440434834930179_o_int)) (= (ho_9734 x z) (ho_9734 y z)))) (= x y))))) (let ((_let_889 (forall ((x |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat)|) (y |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P6285523579766656935_o_nat)) (= (ho_9732 x z) (ho_9732 y z)))) (= x y))))) (let ((_let_890 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9457 x z) (ho_9457 y z)))) (= x y))))) (let ((_let_891 (forall ((x |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat)|) (y |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat)|)) (or (not (forall ((z tptp.list_P4002435161011370285od_o_o)) (= (ho_9730 x z) (ho_9730 y z)))) (= x y))))) (let ((_let_892 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_4489 x z) (ho_4489 y z)))) (= x y))))) (let ((_let_893 (forall ((x |u_(-> tptp.list_P7495141550334521929T_VEBT tptp.nat)|) (y |u_(-> tptp.list_P7495141550334521929T_VEBT tptp.nat)|)) (or (not (forall ((z tptp.list_P7495141550334521929T_VEBT)) (= (ho_9728 x z) (ho_9728 y z)))) (= x y))))) (let ((_let_894 (forall ((x |u_(-> tptp.list_P4547456442757143711BT_int tptp.nat)|) (y |u_(-> tptp.list_P4547456442757143711BT_int tptp.nat)|)) (or (not (forall ((z tptp.list_P4547456442757143711BT_int)) (= (ho_9726 x z) (ho_9726 y z)))) (= x y))))) (let ((_let_895 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8834 x z) (ho_8834 y z)))) (= x y))))) (let ((_let_896 (forall ((x |u_(-> tptp.list_P7037539587688870467BT_nat tptp.nat)|) (y |u_(-> tptp.list_P7037539587688870467BT_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P7037539587688870467BT_nat)) (= (ho_9724 x z) (ho_9724 y z)))) (= x y))))) (let ((_let_897 (forall ((x |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat tptp.product_prod_nat_o)|) (y |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.list_P7333126701944960589_nat_o)) (= (ho_9717 x z) (ho_9717 y z)))) (= x y))))) (let ((_let_898 (forall ((x |u_(-> tptp.list_nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|) (y |u_(-> tptp.list_nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9714 x z) (ho_9714 y z)))) (= x y))))) (let ((_let_899 (forall ((x |u_(-> tptp.list_nat tptp.list_VEBT_VEBT tptp.list_P5647936690300460905T_VEBT)|) (y |u_(-> tptp.list_nat tptp.list_VEBT_VEBT tptp.list_P5647936690300460905T_VEBT)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9705 x z) (ho_9705 y z)))) (= x y))))) (let ((_let_900 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.produc8025551001238799321T_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.produc8025551001238799321T_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9703 x z) (ho_9703 y z)))) (= x y))))) (let ((_let_901 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_6564 x z) (ho_6564 y z)))) (= x y))))) (let ((_let_902 (forall ((x |u_(-> tptp.list_o tptp.list_int tptp.list_P3795440434834930179_o_int)|) (y |u_(-> tptp.list_o tptp.list_int tptp.list_P3795440434834930179_o_int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9696 x z) (ho_9696 y z)))) (= x y))))) (let ((_let_903 (forall ((x |u_(-> tptp.int tptp.product_prod_o_int)|) (y |u_(-> tptp.int tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.int)) (= (ho_9694 x z) (ho_9694 y z)))) (= x y))))) (let ((_let_904 (forall ((x |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z tptp.list_P6285523579766656935_o_nat)) (= (ho_9691 x z) (ho_9691 y z)))) (= x y))))) (let ((_let_905 (forall ((x |u_(-> tptp.list_real tptp.real Bool)|) (y |u_(-> tptp.list_real tptp.real Bool)|)) (or (not (forall ((z tptp.list_real)) (= (ho_8598 x z) (ho_8598 y z)))) (= x y))))) (let ((_let_906 (forall ((x |u_(-> tptp.list_o tptp.list_nat tptp.list_P6285523579766656935_o_nat)|) (y |u_(-> tptp.list_o tptp.list_nat tptp.list_P6285523579766656935_o_nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9688 x z) (ho_9688 y z)))) (= x y))))) (let ((_let_907 (forall ((x |u_(-> tptp.list_complex tptp.complex Bool)|) (y |u_(-> tptp.list_complex tptp.complex Bool)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_5161 x z) (ho_5161 y z)))) (= x y))))) (let ((_let_908 (forall ((x |u_(-> tptp.list_nat tptp.list_P6285523579766656935_o_nat)|) (y |u_(-> tptp.list_nat tptp.list_P6285523579766656935_o_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9689 x z) (ho_9689 y z)))) (= x y))))) (let ((_let_909 (forall ((x |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat tptp.product_prod_o_o)|) (y |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat tptp.product_prod_o_o)|)) (or (not (forall ((z tptp.list_P4002435161011370285od_o_o)) (= (ho_9682 x z) (ho_9682 y z)))) (= x y))))) (let ((_let_910 (forall ((x |u_(-> tptp.list_o tptp.list_o tptp.list_P4002435161011370285od_o_o)|) (y |u_(-> tptp.list_o tptp.list_o tptp.list_P4002435161011370285od_o_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9679 x z) (ho_9679 y z)))) (= x y))))) (let ((_let_911 (forall ((x |u_(-> tptp.list_o tptp.list_P4002435161011370285od_o_o)|) (y |u_(-> tptp.list_o tptp.list_P4002435161011370285od_o_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9680 x z) (ho_9680 y z)))) (= x y))))) (let ((_let_912 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_o)|) (y |u_(-> tptp.nat tptp.product_prod_o_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_9683 x z) (ho_9683 y z)))) (= x y))))) (let ((_let_913 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_6192 x z) (ho_6192 y z)))) (= x y))))) (let ((_let_914 (forall ((x |u_(-> Bool tptp.product_prod_o_o)|) (y |u_(-> Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_9677 x z) (ho_9677 y z)))) (= x y))))) (let ((_let_915 (forall ((x |u_(-> tptp.list_P7495141550334521929T_VEBT tptp.nat tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> tptp.list_P7495141550334521929T_VEBT tptp.nat tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z tptp.list_P7495141550334521929T_VEBT)) (= (ho_9673 x z) (ho_9673 y z)))) (= x y))))) (let ((_let_916 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_8855 x z) (ho_8855 y z)))) (= x y))))) (let ((_let_917 (forall ((x |u_(-> tptp.list_o tptp.list_VEBT_VEBT tptp.list_P7495141550334521929T_VEBT)|) (y |u_(-> tptp.list_o tptp.list_VEBT_VEBT tptp.list_P7495141550334521929T_VEBT)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9670 x z) (ho_9670 y z)))) (= x y))))) (let ((_let_918 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_P7495141550334521929T_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_P7495141550334521929T_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9671 x z) (ho_9671 y z)))) (= x y))))) (let ((_let_919 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10383 x z) (ho_10383 y z)))) (= x y))))) (let ((_let_920 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_int tptp.list_P4547456442757143711BT_int)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_int tptp.list_P4547456442757143711BT_int)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9661 x z) (ho_9661 y z)))) (= x y))))) (let ((_let_921 (forall ((x |u_(-> tptp.list_int tptp.list_P4547456442757143711BT_int)|) (y |u_(-> tptp.list_int tptp.list_P4547456442757143711BT_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9662 x z) (ho_9662 y z)))) (= x y))))) (let ((_let_922 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4448 x z) (ho_4448 y z)))) (= x y))))) (let ((_let_923 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.int tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.vEBT_VEBT tptp.int tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9658 x z) (ho_9658 y z)))) (= x y))))) (let ((_let_924 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_complex)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_complex)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_9896 x z) (ho_9896 y z)))) (= x y))))) (let ((_let_925 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_9119 x z) (ho_9119 y z)))) (= x y))))) (let ((_let_926 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_9891 x z) (ho_9891 y z)))) (= x y))))) (let ((_let_927 (forall ((x |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|) (y |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_9651 x z) (ho_9651 y z)))) (= x y))))) (let ((_let_928 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9635 x z) (ho_9635 y z)))) (= x y))))) (let ((_let_929 (forall ((x |u_(-> tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_9626 x z) (ho_9626 y z)))) (= x y))))) (let ((_let_930 (forall ((x |u_(-> tptp.set_Pr1281608226676607948nteger _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.set_Pr1281608226676607948nteger _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.set_Pr1281608226676607948nteger)) (= (ho_7742 x z) (ho_7742 y z)))) (= x y))))) (let ((_let_931 (forall ((x |u_(-> tptp.set_real tptp.set_real tptp.set_real)|) (y |u_(-> tptp.set_real tptp.set_real tptp.set_real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9622 x z) (ho_9622 y z)))) (= x y))))) (let ((_let_932 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_8553 x z) (ho_8553 y z)))) (= x y))))) (let ((_let_933 (forall ((x |u_(-> tptp.list_o tptp.set_list_o Bool)|) (y |u_(-> tptp.list_o tptp.set_list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9612 x z) (ho_9612 y z)))) (= x y))))) (let ((_let_934 (forall ((x |u_(-> tptp.set_set_int tptp.set_set_int Bool)|) (y |u_(-> tptp.set_set_int tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_9597 x z) (ho_9597 y z)))) (= x y))))) (let ((_let_935 (forall ((x |u_(-> tptp.real tptp.set_real)|) (y |u_(-> tptp.real tptp.set_real)|)) (or (not (forall ((z tptp.real)) (= (ho_9595 x z) (ho_9595 y z)))) (= x y))))) (let ((_let_936 (forall ((x |u_(-> tptp.set_num Bool)|) (y |u_(-> tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_9592 x z) (ho_9592 y z)))) (= x y))))) (let ((_let_937 (forall ((x |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|) (y |u_(-> _u_(-> tptp.real tptp.int)_ tptp.set_real tptp.int)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int)|)) (= (ho_9797 x z) (ho_9797 y z)))) (= x y))))) (let ((_let_938 (forall ((x |u_(-> tptp.rat tptp.set_rat Bool)|) (y |u_(-> tptp.rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_9585 x z) (ho_9585 y z)))) (= x y))))) (let ((_let_939 (forall ((x |u_(-> tptp.set_real tptp.code_integer)|) (y |u_(-> tptp.set_real tptp.code_integer)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9829 x z) (ho_9829 y z)))) (= x y))))) (let ((_let_940 (forall ((x |u_(-> tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_9586 x z) (ho_9586 y z)))) (= x y))))) (let ((_let_941 (forall ((x |u_(-> tptp.set_int tptp.nat)|) (y |u_(-> tptp.set_int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9792 x z) (ho_9792 y z)))) (= x y))))) (let ((_let_942 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10381 x z) (ho_10381 y z)))) (= x y))))) (let ((_let_943 (forall ((x |u_(-> tptp.rat tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_9582 x z) (ho_9582 y z)))) (= x y))))) (let ((_let_944 (forall ((x |u_(-> tptp.set_int tptp.set_set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9580 x z) (ho_9580 y z)))) (= x y))))) (let ((_let_945 (forall ((x |u_(-> tptp.set_int tptp.set_set_int)|) (y |u_(-> tptp.set_int tptp.set_set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9578 x z) (ho_9578 y z)))) (= x y))))) (let ((_let_946 (forall ((x |u_(-> _u_(-> tptp.complex tptp.int)_ tptp.set_complex tptp.int)|) (y |u_(-> _u_(-> tptp.complex tptp.int)_ tptp.set_complex tptp.int)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.int)|)) (= (ho_9801 x z) (ho_9801 y z)))) (= x y))))) (let ((_let_947 (forall ((x |u_(-> _u_(-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)_ tptp.produc9072475918466114483BT_nat Bool)|) (y |u_(-> _u_(-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)_ tptp.produc9072475918466114483BT_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)|)) (= (ho_9574 x z) (ho_9574 y z)))) (= x y))))) (let ((_let_948 (forall ((x |u_(-> tptp.product_prod_int_int tptp.produc7773217078559923341nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.produc7773217078559923341nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_7724 x z) (ho_7724 y z)))) (= x y))))) (let ((_let_949 (forall ((x |u_(-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)|) (y |u_(-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)|)) (or (not (forall ((z tptp.produc9072475918466114483BT_nat)) (= (ho_9572 x z) (ho_9572 y z)))) (= x y))))) (let ((_let_950 (forall ((x |u_(-> tptp.produc9072475918466114483BT_nat Bool)|) (y |u_(-> tptp.produc9072475918466114483BT_nat Bool)|)) (or (not (forall ((z tptp.produc9072475918466114483BT_nat)) (= (ho_9575 x z) (ho_9575 y z)))) (= x y))))) (let ((_let_951 (forall ((x |u_(-> tptp.set_set_int Bool)|) (y |u_(-> tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_9569 x z) (ho_9569 y z)))) (= x y))))) (let ((_let_952 (forall ((x |u_(-> tptp.produc1193250871479095198on_num Bool)|) (y |u_(-> tptp.produc1193250871479095198on_num Bool)|)) (or (not (forall ((z tptp.produc1193250871479095198on_num)) (= (ho_10018 x z) (ho_10018 y z)))) (= x y))))) (let ((_let_953 (forall ((x |u_(-> _u_(-> tptp.set_complex Bool)_ tptp.set_set_complex)|) (y |u_(-> _u_(-> tptp.set_complex Bool)_ tptp.set_set_complex)|)) (or (not (forall ((z |u_(-> tptp.set_complex Bool)|)) (= (ho_9563 x z) (ho_9563 y z)))) (= x y))))) (let ((_let_954 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_9096 x z) (ho_9096 y z)))) (= x y))))) (let ((_let_955 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_set_nat)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_9559 x z) (ho_9559 y z)))) (= x y))))) (let ((_let_956 (forall ((x |u_(-> tptp.option_num tptp.nat)|) (y |u_(-> tptp.option_num tptp.nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9557 x z) (ho_9557 y z)))) (= x y))))) (let ((_let_957 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9555 x z) (ho_9555 y z)))) (= x y))))) (let ((_let_958 (forall ((x |u_(-> tptp.set_list_int Bool)|) (y |u_(-> tptp.set_list_int Bool)|)) (or (not (forall ((z tptp.set_list_int)) (= (ho_9551 x z) (ho_9551 y z)))) (= x y))))) (let ((_let_959 (forall ((x |u_(-> tptp.real tptp.int Bool)|) (y |u_(-> tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_4673 x z) (ho_4673 y z)))) (= x y))))) (let ((_let_960 (forall ((x |u_(-> _u_(-> tptp.list_int Bool)_ tptp.set_list_int)|) (y |u_(-> _u_(-> tptp.list_int Bool)_ tptp.set_list_int)|)) (or (not (forall ((z |u_(-> tptp.list_int Bool)|)) (= (ho_9549 x z) (ho_9549 y z)))) (= x y))))) (let ((_let_961 (forall ((x |u_(-> _u_(-> tptp.list_o Bool)_ tptp.set_list_o)|) (y |u_(-> _u_(-> tptp.list_o Bool)_ tptp.set_list_o)|)) (or (not (forall ((z |u_(-> tptp.list_o Bool)|)) (= (ho_9543 x z) (ho_9543 y z)))) (= x y))))) (let ((_let_962 (forall ((x |u_(-> _u_(-> tptp.list_VEBT_VEBT Bool)_ tptp.set_list_VEBT_VEBT)|) (y |u_(-> _u_(-> tptp.list_VEBT_VEBT Bool)_ tptp.set_list_VEBT_VEBT)|)) (or (not (forall ((z |u_(-> tptp.list_VEBT_VEBT Bool)|)) (= (ho_9539 x z) (ho_9539 y z)))) (= x y))))) (let ((_let_963 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_9531 x z) (ho_9531 y z)))) (= x y))))) (let ((_let_964 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_9533 x z) (ho_9533 y z)))) (= x y))))) (let ((_let_965 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat tptp.produc9072475918466114483BT_nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat tptp.produc9072475918466114483BT_nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9528 x z) (ho_9528 y z)))) (= x y))))) (let ((_let_966 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9526 x z) (ho_9526 y z)))) (= x y))))) (let ((_let_967 (forall ((x |u_(-> Bool tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> Bool tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_9521 x z) (ho_9521 y z)))) (= x y))))) (let ((_let_968 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.produc6121120109295599847at_nat tptp.produc5491161045314408544at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.produc6121120109295599847at_nat tptp.produc5491161045314408544at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_9514 x z) (ho_9514 y z)))) (= x y))))) (let ((_let_969 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.produc4953844613479565601on_nat tptp.produc2233624965454879586on_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.produc4953844613479565601on_nat tptp.produc2233624965454879586on_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_9511 x z) (ho_9511 y z)))) (= x y))))) (let ((_let_970 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_5649 x z) (ho_5649 y z)))) (= x y))))) (let ((_let_971 (forall ((x |u_(-> tptp.produc3447558737645232053on_num tptp.produc1193250871479095198on_num)|) (y |u_(-> tptp.produc3447558737645232053on_num tptp.produc1193250871479095198on_num)|)) (or (not (forall ((z tptp.produc3447558737645232053on_num)) (= (ho_9509 x z) (ho_9509 y z)))) (= x y))))) (let ((_let_972 (forall ((x |u_(-> tptp.option_num tptp.option_num tptp.produc3447558737645232053on_num)|) (y |u_(-> tptp.option_num tptp.option_num tptp.produc3447558737645232053on_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9505 x z) (ho_9505 y z)))) (= x y))))) (let ((_let_973 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.produc6121120109295599847at_nat tptp.produc5542196010084753463at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.produc6121120109295599847at_nat tptp.produc5542196010084753463at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_9502 x z) (ho_9502 y z)))) (= x y))))) (let ((_let_974 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.produc6121120109295599847at_nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.produc6121120109295599847at_nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9500 x z) (ho_9500 y z)))) (= x y))))) (let ((_let_975 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10314 x z) (ho_10314 y z)))) (= x y))))) (let ((_let_976 (forall ((x |u_(-> tptp.set_num tptp.set_num Bool)|) (y |u_(-> tptp.set_num tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_9601 x z) (ho_9601 y z)))) (= x y))))) (let ((_let_977 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_8825 x z) (ho_8825 y z)))) (= x y))))) (let ((_let_978 (forall ((x |u_(-> tptp.produc4953844613479565601on_nat tptp.produc8306885398267862888on_nat)|) (y |u_(-> tptp.produc4953844613479565601on_nat tptp.produc8306885398267862888on_nat)|)) (or (not (forall ((z tptp.produc4953844613479565601on_nat)) (= (ho_9497 x z) (ho_9497 y z)))) (= x y))))) (let ((_let_979 (forall ((x |u_(-> tptp.set_rat tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_9599 x z) (ho_9599 y z)))) (= x y))))) (let ((_let_980 (forall ((x |u_(-> tptp.option_nat tptp.produc4953844613479565601on_nat)|) (y |u_(-> tptp.option_nat tptp.produc4953844613479565601on_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9494 x z) (ho_9494 y z)))) (= x y))))) (let ((_let_981 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9489 x z) (ho_9489 y z)))) (= x y))))) (let ((_let_982 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_8160 x z) (ho_8160 y z)))) (= x y))))) (let ((_let_983 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6250 x z) (ho_6250 y z)))) (= x y))))) (let ((_let_984 (forall ((x |u_(-> tptp.option_nat tptp.nat)|) (y |u_(-> tptp.option_nat tptp.nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9478 x z) (ho_9478 y z)))) (= x y))))) (let ((_let_985 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_9474 x z) (ho_9474 y z)))) (= x y))))) (let ((_let_986 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_9470 x z) (ho_9470 y z)))) (= x y))))) (let ((_let_987 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat tptp.option_nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9468 x z) (ho_9468 y z)))) (= x y))))) (let ((_let_988 (forall ((x |u_(-> tptp.option_num tptp.option_num Bool)|) (y |u_(-> tptp.option_num tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9462 x z) (ho_9462 y z)))) (= x y))))) (let ((_let_989 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8824 x z) (ho_8824 y z)))) (= x y))))) (let ((_let_990 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_6410 x z) (ho_6410 y z)))) (= x y))))) (let ((_let_991 (forall ((x |u_(-> tptp.option_num tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option_num tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9461 x z) (ho_9461 y z)))) (= x y))))) (let ((_let_992 (forall ((x |u_(-> tptp.num _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|) (y |u_(-> tptp.num _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_4239 x z) (ho_4239 y z)))) (= x y))))) (let ((_let_993 (forall ((x |u_(-> tptp.option_num tptp.option_nat Bool)|) (y |u_(-> tptp.option_num tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9460 x z) (ho_9460 y z)))) (= x y))))) (let ((_let_994 (forall ((x |u_(-> tptp.num tptp.complex)|) (y |u_(-> tptp.num tptp.complex)|)) (or (not (forall ((z tptp.num)) (= (ho_4701 x z) (ho_4701 y z)))) (= x y))))) (let ((_let_995 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9458 x z) (ho_9458 y z)))) (= x y))))) (let ((_let_996 (forall ((x |u_(-> tptp.set_real tptp.rat)|) (y |u_(-> tptp.set_real tptp.rat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9779 x z) (ho_9779 y z)))) (= x y))))) (let ((_let_997 (forall ((x |u_(-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9455 x z) (ho_9455 y z)))) (= x y))))) (let ((_let_998 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_8625 x z) (ho_8625 y z)))) (= x y))))) (let ((_let_999 (forall ((x |u_(-> tptp.int tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4723 x z) (ho_4723 y z)))) (= x y))))) (let ((_let_1000 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_9450 x z) (ho_9450 y z)))) (= x y))))) (let ((_let_1001 (forall ((x |u_(-> tptp.num tptp.extended_enat)|) (y |u_(-> tptp.num tptp.extended_enat)|)) (or (not (forall ((z tptp.num)) (= (ho_9448 x z) (ho_9448 y z)))) (= x y))))) (let ((_let_1002 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.option_nat tptp.option_nat tptp.option_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.option_nat tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_9444 x z) (ho_9444 y z)))) (= x y))))) (let ((_let_1003 (forall ((x |u_(-> tptp.option_nat tptp.option_nat tptp.option_nat)|) (y |u_(-> tptp.option_nat tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9445 x z) (ho_9445 y z)))) (= x y))))) (let ((_let_1004 (forall ((x |u_(-> tptp.set_list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_9434 x z) (ho_9434 y z)))) (= x y))))) (let ((_let_1005 (forall ((x |u_(-> tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9415 x z) (ho_9415 y z)))) (= x y))))) (let ((_let_1006 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4596 x z) (ho_4596 y z)))) (= x y))))) (let ((_let_1007 (forall ((x |u_(-> tptp.option_num Bool)|) (y |u_(-> tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9411 x z) (ho_9411 y z)))) (= x y))))) (let ((_let_1008 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8840 x z) (ho_8840 y z)))) (= x y))))) (let ((_let_1009 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9355 x z) (ho_9355 y z)))) (= x y))))) (let ((_let_1010 (forall ((x |u_(-> tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9349 x z) (ho_9349 y z)))) (= x y))))) (let ((_let_1011 (forall ((x |u_(-> tptp.list_int tptp.list_int Bool)|) (y |u_(-> tptp.list_int tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9346 x z) (ho_9346 y z)))) (= x y))))) (let ((_let_1012 (forall ((x |u_(-> tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4636 x z) (ho_4636 y z)))) (= x y))))) (let ((_let_1013 (forall ((x |u_(-> tptp.list_real tptp.nat tptp.real tptp.list_real)|) (y |u_(-> tptp.list_real tptp.nat tptp.real tptp.list_real)|)) (or (not (forall ((z tptp.list_real)) (= (ho_9213 x z) (ho_9213 y z)))) (= x y))))) (let ((_let_1014 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9311 x z) (ho_9311 y z)))) (= x y))))) (let ((_let_1015 (forall ((x |u_(-> tptp.nat tptp.list_o tptp.nat Bool Bool)|) (y |u_(-> tptp.nat tptp.list_o tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9305 x z) (ho_9305 y z)))) (= x y))))) (let ((_let_1016 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.list_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9301 x z) (ho_9301 y z)))) (= x y))))) (let ((_let_1017 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_real)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_real)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_9890 x z) (ho_9890 y z)))) (= x y))))) (let ((_let_1018 (forall ((x |u_(-> tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_10201 x z) (ho_10201 y z)))) (= x y))))) (let ((_let_1019 (forall ((x |u_(-> tptp.nat tptp.list_int tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.list_int tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9297 x z) (ho_9297 y z)))) (= x y))))) (let ((_let_1020 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_9292 x z) (ho_9292 y z)))) (= x y))))) (let ((_let_1021 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4245 x z) (ho_4245 y z)))) (= x y))))) (let ((_let_1022 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_real)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_real)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_9889 x z) (ho_9889 y z)))) (= x y))))) (let ((_let_1023 (forall ((x |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|) (y |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (or (not (forall ((z tptp.product_prod_num_num)) (= (ho_9955 x z) (ho_9955 y z)))) (= x y))))) (let ((_let_1024 (forall ((x |u_(-> tptp.nat tptp.list_complex Bool)|) (y |u_(-> tptp.nat tptp.list_complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9254 x z) (ho_9254 y z)))) (= x y))))) (let ((_let_1025 (forall ((x |u_(-> tptp.list_int tptp.list_P3795440434834930179_o_int)|) (y |u_(-> tptp.list_int tptp.list_P3795440434834930179_o_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9697 x z) (ho_9697 y z)))) (= x y))))) (let ((_let_1026 (forall ((x |u_(-> tptp.complex tptp.real)|) (y |u_(-> tptp.complex tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_4769 x z) (ho_4769 y z)))) (= x y))))) (let ((_let_1027 (forall ((x |u_(-> tptp.list_complex Bool)|) (y |u_(-> tptp.list_complex Bool)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_9255 x z) (ho_9255 y z)))) (= x y))))) (let ((_let_1028 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_9895 x z) (ho_9895 y z)))) (= x y))))) (let ((_let_1029 (forall ((x |u_(-> tptp.nat tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9248 x z) (ho_9248 y z)))) (= x y))))) (let ((_let_1030 (forall ((x |u_(-> tptp.set_o Bool)|) (y |u_(-> tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_9239 x z) (ho_9239 y z)))) (= x y))))) (let ((_let_1031 (forall ((x |u_(-> tptp.nat tptp.list_int Bool)|) (y |u_(-> tptp.nat tptp.list_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9231 x z) (ho_9231 y z)))) (= x y))))) (let ((_let_1032 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_int)|) (y |u_(-> tptp.nat tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_9700 x z) (ho_9700 y z)))) (= x y))))) (let ((_let_1033 (forall ((x |u_(-> tptp.list_int Bool)|) (y |u_(-> tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9232 x z) (ho_9232 y z)))) (= x y))))) (let ((_let_1034 (forall ((x |u_(-> tptp.list_real tptp.nat tptp.real tptp.real Bool)|) (y |u_(-> tptp.list_real tptp.nat tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.list_real)) (= (ho_9211 x z) (ho_9211 y z)))) (= x y))))) (let ((_let_1035 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9205 x z) (ho_9205 y z)))) (= x y))))) (let ((_let_1036 (forall ((x |u_(-> tptp.list_o tptp.nat Bool tptp.list_o)|) (y |u_(-> tptp.list_o tptp.nat Bool tptp.list_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9199 x z) (ho_9199 y z)))) (= x y))))) (let ((_let_1037 (forall ((x |u_(-> tptp.nat Bool tptp.list_o)|) (y |u_(-> tptp.nat Bool tptp.list_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_9200 x z) (ho_9200 y z)))) (= x y))))) (let ((_let_1038 (forall ((x |u_(-> tptp.nat Bool Bool Bool)|) (y |u_(-> tptp.nat Bool Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9197 x z) (ho_9197 y z)))) (= x y))))) (let ((_let_1039 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9194 x z) (ho_9194 y z)))) (= x y))))) (let ((_let_1040 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8850 x z) (ho_8850 y z)))) (= x y))))) (let ((_let_1041 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_9911 x z) (ho_9911 y z)))) (= x y))))) (let ((_let_1042 (forall ((x |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.produc7773217078559923341nt_int)|) (y |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.produc7773217078559923341nt_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.option6357759511663192854e_term)|)) (= (ho_7723 x z) (ho_7723 y z)))) (= x y))))) (let ((_let_1043 (forall ((x |u_(-> tptp.list_P7413028617227757229T_VEBT tptp.nat)|) (y |u_(-> tptp.list_P7413028617227757229T_VEBT tptp.nat)|)) (or (not (forall ((z tptp.list_P7413028617227757229T_VEBT)) (= (ho_9720 x z) (ho_9720 y z)))) (= x y))))) (let ((_let_1044 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.list_int tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9188 x z) (ho_9188 y z)))) (= x y))))) (let ((_let_1045 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.complex tptp.nat)|) (y |u_(-> _u_(-> tptp.complex tptp.nat)_ tptp.complex tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat)|)) (= (ho_8406 x z) (ho_8406 y z)))) (= x y))))) (let ((_let_1046 (forall ((x |u_(-> Bool Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_9166 x z) (ho_9166 y z)))) (= x y))))) (let ((_let_1047 (forall ((x |u_(-> tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_9589 x z) (ho_9589 y z)))) (= x y))))) (let ((_let_1048 (forall ((x |u_(-> tptp.set_list_o Bool)|) (y |u_(-> tptp.set_list_o Bool)|)) (or (not (forall ((z tptp.set_list_o)) (= (ho_9545 x z) (ho_9545 y z)))) (= x y))))) (let ((_let_1049 (forall ((x |u_(-> Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_9167 x z) (ho_9167 y z)))) (= x y))))) (let ((_let_1050 (forall ((x |u_(-> tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_5897 x z) (ho_5897 y z)))) (= x y))))) (let ((_let_1051 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.option4927543243414619207at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.option4927543243414619207at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_9159 x z) (ho_9159 y z)))) (= x y))))) (let ((_let_1052 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_5202 x z) (ho_5202 y z)))) (= x y))))) (let ((_let_1053 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9164 x z) (ho_9164 y z)))) (= x y))))) (let ((_let_1054 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_7381 x z) (ho_7381 y z)))) (= x y))))) (let ((_let_1055 (forall ((x |u_(-> tptp.set_nat tptp.code_integer)|) (y |u_(-> tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_9826 x z) (ho_9826 y z)))) (= x y))))) (let ((_let_1056 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.rat)|)) (= (ho_8057 x z) (ho_8057 y z)))) (= x y))))) (let ((_let_1057 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9143 x z) (ho_9143 y z)))) (= x y))))) (let ((_let_1058 (forall ((x |u_(-> tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_9583 x z) (ho_9583 y z)))) (= x y))))) (let ((_let_1059 (forall ((x |u_(-> tptp.set_list_complex Bool)|) (y |u_(-> tptp.set_list_complex Bool)|)) (or (not (forall ((z tptp.set_list_complex)) (= (ho_9537 x z) (ho_9537 y z)))) (= x y))))) (let ((_let_1060 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real Bool)|)) (= (ho_9144 x z) (ho_9144 y z)))) (= x y))))) (let ((_let_1061 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9943 x z) (ho_9943 y z)))) (= x y))))) (let ((_let_1062 (forall ((x |u_(-> tptp.set_complex tptp.nat)|) (y |u_(-> tptp.set_complex tptp.nat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9795 x z) (ho_9795 y z)))) (= x y))))) (let ((_let_1063 (forall ((x |u_(-> tptp.real tptp.num)|) (y |u_(-> tptp.real tptp.num)|)) (or (not (forall ((z tptp.real)) (= (ho_9749 x z) (ho_9749 y z)))) (= x y))))) (let ((_let_1064 (forall ((x |u_(-> tptp.code_integer Bool tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.code_integer Bool tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4608 x z) (ho_4608 y z)))) (= x y))))) (let ((_let_1065 (forall ((x |u_(-> Bool tptp.product_prod_nat_o)|) (y |u_(-> Bool tptp.product_prod_nat_o)|)) (or (not (forall ((z Bool)) (= (ho_9712 x z) (ho_9712 y z)))) (= x y))))) (let ((_let_1066 (forall ((x |u_(-> tptp.num tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_9588 x z) (ho_9588 y z)))) (= x y))))) (let ((_let_1067 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real Bool)_ tptp.real tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real Bool)_ tptp.real tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real Bool)|)) (= (ho_9141 x z) (ho_9141 y z)))) (= x y))))) (let ((_let_1068 (forall ((x |u_(-> _u_(-> tptp.option_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option_nat Bool)|)) (= (ho_9420 x z) (ho_9420 y z)))) (= x y))))) (let ((_let_1069 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_6076 x z) (ho_6076 y z)))) (= x y))))) (let ((_let_1070 (forall ((x |u_(-> tptp.real tptp.complex Bool)|) (y |u_(-> tptp.real tptp.complex Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_9134 x z) (ho_9134 y z)))) (= x y))))) (let ((_let_1071 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real Bool)|)) (= (ho_9131 x z) (ho_9131 y z)))) (= x y))))) (let ((_let_1072 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_7837 x z) (ho_7837 y z)))) (= x y))))) (let ((_let_1073 (forall ((x |u_(-> tptp.complex tptp.rat)|) (y |u_(-> tptp.complex tptp.rat)|)) (or (not (forall ((z tptp.complex)) (= (ho_9783 x z) (ho_9783 y z)))) (= x y))))) (let ((_let_1074 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_9117 x z) (ho_9117 y z)))) (= x y))))) (let ((_let_1075 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat Bool)_ tptp.nat tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.nat Bool)_ tptp.nat tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat Bool)|)) (= (ho_9112 x z) (ho_9112 y z)))) (= x y))))) (let ((_let_1076 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat Bool)|)) (= (ho_9110 x z) (ho_9110 y z)))) (= x y))))) (let ((_let_1077 (forall ((x |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.int tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int Bool)|)) (= (ho_9105 x z) (ho_9105 y z)))) (= x y))))) (let ((_let_1078 (forall ((x |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int Bool)|)) (= (ho_9103 x z) (ho_9103 y z)))) (= x y))))) (let ((_let_1079 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_9099 x z) (ho_9099 y z)))) (= x y))))) (let ((_let_1080 (forall ((x |u_(-> tptp.extended_enat Bool)|) (y |u_(-> tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_9055 x z) (ho_9055 y z)))) (= x y))))) (let ((_let_1081 (forall ((x |u_(-> tptp.product_prod_int_int tptp.rat Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_10337 x z) (ho_10337 y z)))) (= x y))))) (let ((_let_1082 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_9046 x z) (ho_9046 y z)))) (= x y))))) (let ((_let_1083 (forall ((x |u_(-> _u_(-> tptp.real tptp.int)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int)|)) (= (ho_9042 x z) (ho_9042 y z)))) (= x y))))) (let ((_let_1084 (forall ((x |u_(-> tptp.list_P4547456442757143711BT_int tptp.nat tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.list_P4547456442757143711BT_int tptp.nat tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.list_P4547456442757143711BT_int)) (= (ho_9664 x z) (ho_9664 y z)))) (= x y))))) (let ((_let_1085 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_9038 x z) (ho_9038 y z)))) (= x y))))) (let ((_let_1086 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10270 x z) (ho_10270 y z)))) (= x y))))) (let ((_let_1087 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_9032 x z) (ho_9032 y z)))) (= x y))))) (let ((_let_1088 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_4432 x z) (ho_4432 y z)))) (= x y))))) (let ((_let_1089 (forall ((x |u_(-> _u_(-> tptp.real tptp.real tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real tptp.real)|)) (= (ho_9023 x z) (ho_9023 y z)))) (= x y))))) (let ((_let_1090 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9024 x z) (ho_9024 y z)))) (= x y))))) (let ((_let_1091 (forall ((x |u_(-> tptp.real tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_9017 x z) (ho_9017 y z)))) (= x y))))) (let ((_let_1092 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.product_prod_int_int tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_9879 x z) (ho_9879 y z)))) (= x y))))) (let ((_let_1093 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10354 x z) (ho_10354 y z)))) (= x y))))) (let ((_let_1094 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9020 x z) (ho_9020 y z)))) (= x y))))) (let ((_let_1095 (forall ((x |u_(-> tptp.product_prod_int_int tptp.int)|) (y |u_(-> tptp.product_prod_int_int tptp.int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_4587 x z) (ho_4587 y z)))) (= x y))))) (let ((_let_1096 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10166 x z) (ho_10166 y z)))) (= x y))))) (let ((_let_1097 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9021 x z) (ho_9021 y z)))) (= x y))))) (let ((_let_1098 (forall ((x |u_(-> _u_(-> tptp.real tptp.real tptp.int)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real tptp.int)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real tptp.int)|)) (= (ho_9014 x z) (ho_9014 y z)))) (= x y))))) (let ((_let_1099 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9015 x z) (ho_9015 y z)))) (= x y))))) (let ((_let_1100 (forall ((x |u_(-> _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (= (ho_10373 x z) (ho_10373 y z)))) (= x y))))) (let ((_let_1101 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.nat tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9190 x z) (ho_9190 y z)))) (= x y))))) (let ((_let_1102 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9016 x z) (ho_9016 y z)))) (= x y))))) (let ((_let_1103 (forall ((x |u_(-> tptp.list_o Bool)|) (y |u_(-> tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9243 x z) (ho_9243 y z)))) (= x y))))) (let ((_let_1104 (forall ((x |u_(-> tptp.real tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_9007 x z) (ho_9007 y z)))) (= x y))))) (let ((_let_1105 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_6189 x z) (ho_6189 y z)))) (= x y))))) (let ((_let_1106 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9010 x z) (ho_9010 y z)))) (= x y))))) (let ((_let_1107 (forall ((x |u_(-> tptp.set_o tptp.set_o Bool)|) (y |u_(-> tptp.set_o tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_9238 x z) (ho_9238 y z)))) (= x y))))) (let ((_let_1108 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9005 x z) (ho_9005 y z)))) (= x y))))) (let ((_let_1109 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_5142 x z) (ho_5142 y z)))) (= x y))))) (let ((_let_1110 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_9908 x z) (ho_9908 y z)))) (= x y))))) (let ((_let_1111 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.nat)|)) (= (ho_9001 x z) (ho_9001 y z)))) (= x y))))) (let ((_let_1112 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_8457 x z) (ho_8457 y z)))) (= x y))))) (let ((_let_1113 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.set_nat tptp.set_complex Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.set_nat tptp.set_complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_10079 x z) (ho_10079 y z)))) (= x y))))) (let ((_let_1114 (forall ((x |u_(-> tptp.real tptp.nat tptp.int)|) (y |u_(-> tptp.real tptp.nat tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_8994 x z) (ho_8994 y z)))) (= x y))))) (let ((_let_1115 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8997 x z) (ho_8997 y z)))) (= x y))))) (let ((_let_1116 (forall ((x |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|) (y |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9529 x z) (ho_9529 y z)))) (= x y))))) (let ((_let_1117 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10384 x z) (ho_10384 y z)))) (= x y))))) (let ((_let_1118 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_8998 x z) (ho_8998 y z)))) (= x y))))) (let ((_let_1119 (forall ((x |u_(-> tptp.list_P5647936690300460905T_VEBT tptp.nat tptp.produc8025551001238799321T_VEBT)|) (y |u_(-> tptp.list_P5647936690300460905T_VEBT tptp.nat tptp.produc8025551001238799321T_VEBT)|)) (or (not (forall ((z tptp.list_P5647936690300460905T_VEBT)) (= (ho_9708 x z) (ho_9708 y z)))) (= x y))))) (let ((_let_1120 (forall ((x |u_(-> tptp.real tptp.nat tptp.complex)|) (y |u_(-> tptp.real tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_8989 x z) (ho_8989 y z)))) (= x y))))) (let ((_let_1121 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4258 x z) (ho_4258 y z)))) (= x y))))) (let ((_let_1122 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_8993 x z) (ho_8993 y z)))) (= x y))))) (let ((_let_1123 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_10409 x z) (ho_10409 y z)))) (= x y))))) (let ((_let_1124 (forall ((x |u_(-> tptp.real tptp.int tptp.real)|) (y |u_(-> tptp.real tptp.int tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_8984 x z) (ho_8984 y z)))) (= x y))))) (let ((_let_1125 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_9034 x z) (ho_9034 y z)))) (= x y))))) (let ((_let_1126 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10347 x z) (ho_10347 y z)))) (= x y))))) (let ((_let_1127 (forall ((x |u_(-> tptp.real tptp.int tptp.nat)|) (y |u_(-> tptp.real tptp.int tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_8978 x z) (ho_8978 y z)))) (= x y))))) (let ((_let_1128 (forall ((x |u_(-> tptp.rat tptp.nat)|) (y |u_(-> tptp.rat tptp.nat)|)) (or (not (forall ((z tptp.rat)) (= (ho_9745 x z) (ho_9745 y z)))) (= x y))))) (let ((_let_1129 (forall ((x |u_(-> tptp.int tptp.set_complex)|) (y |u_(-> tptp.int tptp.set_complex)|)) (or (not (forall ((z tptp.int)) (= (ho_9875 x z) (ho_9875 y z)))) (= x y))))) (let ((_let_1130 (forall ((x |u_(-> _u_(-> 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)|) (y |u_(-> _u_(-> 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)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_9846 x z) (ho_9846 y z)))) (= x y))))) (let ((_let_1131 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8981 x z) (ho_8981 y z)))) (= x y))))) (let ((_let_1132 (forall ((x |u_(-> tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8935 x z) (ho_8935 y z)))) (= x y))))) (let ((_let_1133 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ tptp.produc7773217078559923341nt_int Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ tptp.produc7773217078559923341nt_int Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9857 x z) (ho_9857 y z)))) (= x y))))) (let ((_let_1134 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8987 x z) (ho_8987 y z)))) (= x y))))) (let ((_let_1135 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_8549 x z) (ho_8549 y z)))) (= x y))))) (let ((_let_1136 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_8933 x z) (ho_8933 y z)))) (= x y))))) (let ((_let_1137 (forall ((x |u_(-> tptp.set_real tptp.set_real Bool)|) (y |u_(-> tptp.set_real tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8931 x z) (ho_8931 y z)))) (= x y))))) (let ((_let_1138 (forall ((x |u_(-> tptp.list_P7413028617227757229T_VEBT tptp.nat tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.list_P7413028617227757229T_VEBT tptp.nat tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.list_P7413028617227757229T_VEBT)) (= (ho_9641 x z) (ho_9641 y z)))) (= x y))))) (let ((_let_1139 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.code_integer tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.code_integer tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_6612 x z) (ho_6612 y z)))) (= x y))))) (let ((_let_1140 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8929 x z) (ho_8929 y z)))) (= x y))))) (let ((_let_1141 (forall ((x |u_(-> tptp.set_complex tptp.set_complex Bool)|) (y |u_(-> tptp.set_complex tptp.set_complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8926 x z) (ho_8926 y z)))) (= x y))))) (let ((_let_1142 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (= (ho_10413 x z) (ho_10413 y z)))) (= x y))))) (let ((_let_1143 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_8923 x z) (ho_8923 y z)))) (= x y))))) (let ((_let_1144 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_8921 x z) (ho_8921 y z)))) (= x y))))) (let ((_let_1145 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_10418 x z) (ho_10418 y z)))) (= x y))))) (let ((_let_1146 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_8914 x z) (ho_8914 y z)))) (= x y))))) (let ((_let_1147 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_8915 x z) (ho_8915 y z)))) (= x y))))) (let ((_let_1148 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6528 x z) (ho_6528 y z)))) (= x y))))) (let ((_let_1149 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_P7413028617227757229T_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_P7413028617227757229T_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9639 x z) (ho_9639 y z)))) (= x y))))) (let ((_let_1150 (forall ((x |u_(-> Bool Bool Bool)|) (y |u_(-> Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_5178 x z) (ho_5178 y z)))) (= x y))))) (let ((_let_1151 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8992 x z) (ho_8992 y z)))) (= x y))))) (let ((_let_1152 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_8912 x z) (ho_8912 y z)))) (= x y))))) (let ((_let_1153 (forall ((x |u_(-> tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4244 x z) (ho_4244 y z)))) (= x y))))) (let ((_let_1154 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9668 x z) (ho_9668 y z)))) (= x y))))) (let ((_let_1155 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.produc6121120109295599847at_nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.produc6121120109295599847at_nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9499 x z) (ho_9499 y z)))) (= x y))))) (let ((_let_1156 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_8811 x z) (ho_8811 y z)))) (= x y))))) (let ((_let_1157 (forall ((x |u_(-> tptp.set_complex _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> tptp.set_complex _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8908 x z) (ho_8908 y z)))) (= x y))))) (let ((_let_1158 (forall ((x |u_(-> tptp.num tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_4619 x z) (ho_4619 y z)))) (= x y))))) (let ((_let_1159 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8906 x z) (ho_8906 y z)))) (= x y))))) (let ((_let_1160 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_9825 x z) (ho_9825 y z)))) (= x y))))) (let ((_let_1161 (forall ((x |u_(-> tptp.list_nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_8902 x z) (ho_8902 y z)))) (= x y))))) (let ((_let_1162 (forall ((x |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.set_nat)|) (y |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.option6357759511663192854e_term)|)) (= (ho_9901 x z) (ho_9901 y z)))) (= x y))))) (let ((_let_1163 (forall ((x |u_(-> tptp.set_real tptp.complex)|) (y |u_(-> tptp.set_real tptp.complex)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9820 x z) (ho_9820 y z)))) (= x y))))) (let ((_let_1164 (forall ((x |u_(-> tptp.real tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4696 x z) (ho_4696 y z)))) (= x y))))) (let ((_let_1165 (forall ((x |u_(-> tptp.set_list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_8899 x z) (ho_8899 y z)))) (= x y))))) (let ((_let_1166 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_nat)_ tptp.product_prod_int_int tptp.set_nat)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_nat)_ tptp.product_prod_int_int tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_nat)|)) (= (ho_9860 x z) (ho_9860 y z)))) (= x y))))) (let ((_let_1167 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8894 x z) (ho_8894 y z)))) (= x y))))) (let ((_let_1168 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8854 x z) (ho_8854 y z)))) (= x y))))) (let ((_let_1169 (forall ((x |u_(-> Bool tptp.option_nat tptp.option_nat tptp.option_nat)|) (y |u_(-> Bool tptp.option_nat tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z Bool)) (= (ho_9483 x z) (ho_9483 y z)))) (= x y))))) (let ((_let_1170 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_8851 x z) (ho_8851 y z)))) (= x y))))) (let ((_let_1171 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_8209 x z) (ho_8209 y z)))) (= x y))))) (let ((_let_1172 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5457 x z) (ho_5457 y z)))) (= x y))))) (let ((_let_1173 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_8848 x z) (ho_8848 y z)))) (= x y))))) (let ((_let_1174 (forall ((x |u_(-> tptp.nat tptp.option_num)|) (y |u_(-> tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_4300 x z) (ho_4300 y z)))) (= x y))))) (let ((_let_1175 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8843 x z) (ho_8843 y z)))) (= x y))))) (let ((_let_1176 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_P7413028617227757229T_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_P7413028617227757229T_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9638 x z) (ho_9638 y z)))) (= x y))))) (let ((_let_1177 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_8844 x z) (ho_8844 y z)))) (= x y))))) (let ((_let_1178 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_8841 x z) (ho_8841 y z)))) (= x y))))) (let ((_let_1179 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_8835 x z) (ho_8835 y z)))) (= x y))))) (let ((_let_1180 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_9472 x z) (ho_9472 y z)))) (= x y))))) (let ((_let_1181 (forall ((x |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9310 x z) (ho_9310 y z)))) (= x y))))) (let ((_let_1182 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_6539 x z) (ho_6539 y z)))) (= x y))))) (let ((_let_1183 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_9030 x z) (ho_9030 y z)))) (= x y))))) (let ((_let_1184 (forall ((x |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.int)) (= (ho_9659 x z) (ho_9659 y z)))) (= x y))))) (let ((_let_1185 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_5629 x z) (ho_5629 y z)))) (= x y))))) (let ((_let_1186 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8817 x z) (ho_8817 y z)))) (= x y))))) (let ((_let_1187 (forall ((x |u_(-> tptp.complex Bool)|) (y |u_(-> tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_5127 x z) (ho_5127 y z)))) (= x y))))) (let ((_let_1188 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8813 x z) (ho_8813 y z)))) (= x y))))) (let ((_let_1189 (forall ((x |u_(-> tptp.set_o tptp.nat tptp.list_o Bool)|) (y |u_(-> tptp.set_o tptp.nat tptp.list_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_9241 x z) (ho_9241 y z)))) (= x y))))) (let ((_let_1190 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.real)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.real)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8804 x z) (ho_8804 y z)))) (= x y))))) (let ((_let_1191 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_7767 x z) (ho_7767 y z)))) (= x y))))) (let ((_let_1192 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_8805 x z) (ho_8805 y z)))) (= x y))))) (let ((_let_1193 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_8802 x z) (ho_8802 y z)))) (= x y))))) (let ((_let_1194 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6165 x z) (ho_6165 y z)))) (= x y))))) (let ((_let_1195 (forall ((x |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|) (y |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8797 x z) (ho_8797 y z)))) (= x y))))) (let ((_let_1196 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_real)_ tptp.produc8763457246119570046nteger tptp.set_real)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_real)_ tptp.produc8763457246119570046nteger tptp.set_real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_real)|)) (= (ho_9888 x z) (ho_9888 y z)))) (= x y))))) (let ((_let_1197 (forall ((x |u_(-> tptp.produc4953844613479565601on_nat tptp.produc2233624965454879586on_nat)|) (y |u_(-> tptp.produc4953844613479565601on_nat tptp.produc2233624965454879586on_nat)|)) (or (not (forall ((z tptp.produc4953844613479565601on_nat)) (= (ho_9512 x z) (ho_9512 y z)))) (= x y))))) (let ((_let_1198 (forall ((x |u_(-> tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_7888 x z) (ho_7888 y z)))) (= x y))))) (let ((_let_1199 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8790 x z) (ho_8790 y z)))) (= x y))))) (let ((_let_1200 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_8791 x z) (ho_8791 y z)))) (= x y))))) (let ((_let_1201 (forall ((x |u_(-> tptp.rat tptp.real)|) (y |u_(-> tptp.rat tptp.real)|)) (or (not (forall ((z tptp.rat)) (= (ho_7347 x z) (ho_7347 y z)))) (= x y))))) (let ((_let_1202 (forall ((x |u_(-> Bool tptp.extended_enat tptp.extended_enat tptp.extended_enat)|) (y |u_(-> Bool tptp.extended_enat tptp.extended_enat tptp.extended_enat)|)) (or (not (forall ((z Bool)) (= (ho_8694 x z) (ho_8694 y z)))) (= x y))))) (let ((_let_1203 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat tptp.extended_enat)|) (y |u_(-> tptp.extended_enat tptp.extended_enat tptp.extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_8690 x z) (ho_8690 y z)))) (= x y))))) (let ((_let_1204 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6633 x z) (ho_6633 y z)))) (= x y))))) (let ((_let_1205 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat)|) (y |u_(-> tptp.extended_enat tptp.extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_8691 x z) (ho_8691 y z)))) (= x y))))) (let ((_let_1206 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_8919 x z) (ho_8919 y z)))) (= x y))))) (let ((_let_1207 (forall ((x |u_(-> tptp.nat tptp.real tptp.list_real)|) (y |u_(-> tptp.nat tptp.real tptp.list_real)|)) (or (not (forall ((z tptp.nat)) (= (ho_8642 x z) (ho_8642 y z)))) (= x y))))) (let ((_let_1208 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_4531 x z) (ho_4531 y z)))) (= x y))))) (let ((_let_1209 (forall ((x |u_(-> tptp.set_VEBT_VEBT tptp.nat tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_VEBT_VEBT tptp.nat tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_VEBT_VEBT)) (= (ho_9247 x z) (ho_9247 y z)))) (= x y))))) (let ((_let_1210 (forall ((x |u_(-> tptp.real tptp.list_real)|) (y |u_(-> tptp.real tptp.list_real)|)) (or (not (forall ((z tptp.real)) (= (ho_8643 x z) (ho_8643 y z)))) (= x y))))) (let ((_let_1211 (forall ((x |u_(-> tptp.nat tptp.real tptp.real Bool)|) (y |u_(-> tptp.nat tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_8640 x z) (ho_8640 y z)))) (= x y))))) (let ((_let_1212 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_5547 x z) (ho_5547 y z)))) (= x y))))) (let ((_let_1213 (forall ((x |u_(-> tptp.nat tptp.complex tptp.list_complex)|) (y |u_(-> tptp.nat tptp.complex tptp.list_complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_8637 x z) (ho_8637 y z)))) (= x y))))) (let ((_let_1214 (forall ((x |u_(-> tptp.produc6121120109295599847at_nat tptp.produc5542196010084753463at_nat)|) (y |u_(-> tptp.produc6121120109295599847at_nat tptp.produc5542196010084753463at_nat)|)) (or (not (forall ((z tptp.produc6121120109295599847at_nat)) (= (ho_9503 x z) (ho_9503 y z)))) (= x y))))) (let ((_let_1215 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_8928 x z) (ho_8928 y z)))) (= x y))))) (let ((_let_1216 (forall ((x |u_(-> tptp.complex tptp.list_complex)|) (y |u_(-> tptp.complex tptp.list_complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_8638 x z) (ho_8638 y z)))) (= x y))))) (let ((_let_1217 (forall ((x |u_(-> tptp.nat tptp.complex tptp.complex Bool)|) (y |u_(-> tptp.nat tptp.complex tptp.complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_8634 x z) (ho_8634 y z)))) (= x y))))) (let ((_let_1218 (forall ((x |u_(-> tptp.num tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_5064 x z) (ho_5064 y z)))) (= x y))))) (let ((_let_1219 (forall ((x |u_(-> tptp.complex tptp.complex Bool)|) (y |u_(-> tptp.complex tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_8635 x z) (ho_8635 y z)))) (= x y))))) (let ((_let_1220 (forall ((x |u_(-> tptp.nat tptp.int tptp.list_int)|) (y |u_(-> tptp.nat tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_8632 x z) (ho_8632 y z)))) (= x y))))) (let ((_let_1221 (forall ((x |u_(-> tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_8630 x z) (ho_8630 y z)))) (= x y))))) (let ((_let_1222 (forall ((x |u_(-> Bool tptp.list_o)|) (y |u_(-> Bool tptp.list_o)|)) (or (not (forall ((z Bool)) (= (ho_9201 x z) (ho_9201 y z)))) (= x y))))) (let ((_let_1223 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_8622 x z) (ho_8622 y z)))) (= x y))))) (let ((_let_1224 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9192 x z) (ho_9192 y z)))) (= x y))))) (let ((_let_1225 (forall ((x |u_(-> tptp.list_real tptp.nat tptp.real)|) (y |u_(-> tptp.list_real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.list_real)) (= (ho_8602 x z) (ho_8602 y z)))) (= x y))))) (let ((_let_1226 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8847 x z) (ho_8847 y z)))) (= x y))))) (let ((_let_1227 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8794 x z) (ho_8794 y z)))) (= x y))))) (let ((_let_1228 (forall ((x |u_(-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.int tptp.int tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_9876 x z) (ho_9876 y z)))) (= x y))))) (let ((_let_1229 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_8567 x z) (ho_8567 y z)))) (= x y))))) (let ((_let_1230 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_4208 x z) (ho_4208 y z)))) (= x y))))) (let ((_let_1231 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ tptp.produc3447558737645232053on_num tptp.produc7036089656553540234on_num)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ tptp.produc3447558737645232053on_num tptp.produc7036089656553540234on_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_9517 x z) (ho_9517 y z)))) (= x y))))) (let ((_let_1232 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_8568 x z) (ho_8568 y z)))) (= x y))))) (let ((_let_1233 (forall ((x |u_(-> Bool tptp.set_o Bool)|) (y |u_(-> Bool tptp.set_o Bool)|)) (or (not (forall ((z Bool)) (= (ho_9476 x z) (ho_9476 y z)))) (= x y))))) (let ((_let_1234 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_8564 x z) (ho_8564 y z)))) (= x y))))) (let ((_let_1235 (forall ((x |u_(-> _u_(-> Bool Bool)_ tptp.set_o)|) (y |u_(-> _u_(-> Bool Bool)_ tptp.set_o)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_9236 x z) (ho_9236 y z)))) (= x y))))) (let ((_let_1236 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8557 x z) (ho_8557 y z)))) (= x y))))) (let ((_let_1237 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_complex)_ tptp.produc8763457246119570046nteger tptp.set_complex)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_complex)_ tptp.produc8763457246119570046nteger tptp.set_complex)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_complex)|)) (= (ho_9898 x z) (ho_9898 y z)))) (= x y))))) (let ((_let_1238 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_8554 x z) (ho_8554 y z)))) (= x y))))) (let ((_let_1239 (forall ((x |u_(-> tptp.set_Pr8056137968301705908nteger _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.set_Pr8056137968301705908nteger _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.set_Pr8056137968301705908nteger)) (= (ho_7754 x z) (ho_7754 y z)))) (= x y))))) (let ((_let_1240 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8538 x z) (ho_8538 y z)))) (= x y))))) (let ((_let_1241 (forall ((x |u_(-> _u_(-> tptp.real tptp.code_integer)_ _u_(-> tptp.real tptp.code_integer)_ tptp.real tptp.code_integer)|) (y |u_(-> _u_(-> tptp.real tptp.code_integer)_ _u_(-> tptp.real tptp.code_integer)_ tptp.real tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.real tptp.code_integer)|)) (= (ho_8472 x z) (ho_8472 y z)))) (= x y))))) (let ((_let_1242 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (= (ho_10324 x z) (ho_10324 y z)))) (= x y))))) (let ((_let_1243 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.real)|)) (= (ho_9004 x z) (ho_9004 y z)))) (= x y))))) (let ((_let_1244 (forall ((x |u_(-> _u_(-> tptp.real tptp.code_integer)_ tptp.real tptp.code_integer)|) (y |u_(-> _u_(-> tptp.real tptp.code_integer)_ tptp.real tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.real tptp.code_integer)|)) (= (ho_8473 x z) (ho_8473 y z)))) (= x y))))) (let ((_let_1245 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_4309 x z) (ho_4309 y z)))) (= x y))))) (let ((_let_1246 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_real)|) (y |u_(-> tptp.product_prod_int_int tptp.set_real)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_9866 x z) (ho_9866 y z)))) (= x y))))) (let ((_let_1247 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_8469 x z) (ho_8469 y z)))) (= x y))))) (let ((_let_1248 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4287 x z) (ho_4287 y z)))) (= x y))))) (let ((_let_1249 (forall ((x |u_(-> tptp.option_num tptp.produc3447558737645232053on_num)|) (y |u_(-> tptp.option_num tptp.produc3447558737645232053on_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_9506 x z) (ho_9506 y z)))) (= x y))))) (let ((_let_1250 (forall ((x |u_(-> _u_(-> tptp.complex tptp.code_integer)_ _u_(-> tptp.complex tptp.code_integer)_ tptp.complex tptp.code_integer)|) (y |u_(-> _u_(-> tptp.complex tptp.code_integer)_ _u_(-> tptp.complex tptp.code_integer)_ tptp.complex tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.code_integer)|)) (= (ho_8465 x z) (ho_8465 y z)))) (= x y))))) (let ((_let_1251 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10280 x z) (ho_10280 y z)))) (= x y))))) (let ((_let_1252 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.int)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.int)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.int)|)) (= (ho_8996 x z) (ho_8996 y z)))) (= x y))))) (let ((_let_1253 (forall ((x |u_(-> _u_(-> tptp.complex tptp.code_integer)_ tptp.complex tptp.code_integer)|) (y |u_(-> _u_(-> tptp.complex tptp.code_integer)_ tptp.complex tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.code_integer)|)) (= (ho_8466 x z) (ho_8466 y z)))) (= x y))))) (let ((_let_1254 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_10412 x z) (ho_10412 y z)))) (= x y))))) (let ((_let_1255 (forall ((x |u_(-> tptp.complex tptp.code_integer)|) (y |u_(-> tptp.complex tptp.code_integer)|)) (or (not (forall ((z tptp.complex)) (= (ho_8463 x z) (ho_8463 y z)))) (= x y))))) (let ((_let_1256 (forall ((x |u_(-> _u_(-> tptp.list_complex Bool)_ tptp.set_list_complex)|) (y |u_(-> _u_(-> tptp.list_complex Bool)_ tptp.set_list_complex)|)) (or (not (forall ((z |u_(-> tptp.list_complex Bool)|)) (= (ho_9535 x z) (ho_9535 y z)))) (= x y))))) (let ((_let_1257 (forall ((x |u_(-> tptp.set_set_complex Bool)|) (y |u_(-> tptp.set_set_complex Bool)|)) (or (not (forall ((z tptp.set_set_complex)) (= (ho_9565 x z) (ho_9565 y z)))) (= x y))))) (let ((_let_1258 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.int tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9138 x z) (ho_9138 y z)))) (= x y))))) (let ((_let_1259 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_8454 x z) (ho_8454 y z)))) (= x y))))) (let ((_let_1260 (forall ((x |u_(-> tptp.real tptp.nat Bool)|) (y |u_(-> tptp.real tptp.nat Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_9123 x z) (ho_9123 y z)))) (= x y))))) (let ((_let_1261 (forall ((x |u_(-> tptp.real tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_8451 x z) (ho_8451 y z)))) (= x y))))) (let ((_let_1262 (forall ((x |u_(-> tptp.list_P7037539587688870467BT_nat tptp.nat tptp.produc9072475918466114483BT_nat)|) (y |u_(-> tptp.list_P7037539587688870467BT_nat tptp.nat tptp.produc9072475918466114483BT_nat)|)) (or (not (forall ((z tptp.list_P7037539587688870467BT_nat)) (= (ho_9656 x z) (ho_9656 y z)))) (= x y))))) (let ((_let_1263 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_6252 x z) (ho_6252 y z)))) (= x y))))) (let ((_let_1264 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8820 x z) (ho_8820 y z)))) (= x y))))) (let ((_let_1265 (forall ((x |u_(-> tptp.num tptp.nat)|) (y |u_(-> tptp.num tptp.nat)|)) (or (not (forall ((z tptp.num)) (= (ho_8410 x z) (ho_8410 y z)))) (= x y))))) (let ((_let_1266 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat tptp.vEBT_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9464 x z) (ho_9464 y z)))) (= x y))))) (let ((_let_1267 (forall ((x |u_(-> _u_(-> tptp.complex tptp.nat)_ _u_(-> tptp.complex tptp.nat)_ tptp.complex tptp.nat)|) (y |u_(-> _u_(-> tptp.complex tptp.nat)_ _u_(-> tptp.complex tptp.nat)_ tptp.complex tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.nat)|)) (= (ho_8405 x z) (ho_8405 y z)))) (= x y))))) (let ((_let_1268 (forall ((x |u_(-> tptp.complex tptp.nat)|) (y |u_(-> tptp.complex tptp.nat)|)) (or (not (forall ((z tptp.complex)) (= (ho_8403 x z) (ho_8403 y z)))) (= x y))))) (let ((_let_1269 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_5992 x z) (ho_5992 y z)))) (= x y))))) (let ((_let_1270 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_8401 x z) (ho_8401 y z)))) (= x y))))) (let ((_let_1271 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_8402 x z) (ho_8402 y z)))) (= x y))))) (let ((_let_1272 (forall ((x |u_(-> tptp.set_int tptp.nat tptp.list_int Bool)|) (y |u_(-> tptp.set_int tptp.nat tptp.list_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9230 x z) (ho_9230 y z)))) (= x y))))) (let ((_let_1273 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_8378 x z) (ho_8378 y z)))) (= x y))))) (let ((_let_1274 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_8258 x z) (ho_8258 y z)))) (= x y))))) (let ((_let_1275 (forall ((x |u_(-> tptp.set_int tptp.int tptp.int)|) (y |u_(-> tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8569 x z) (ho_8569 y z)))) (= x y))))) (let ((_let_1276 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_10431 x z) (ho_10431 y z)))) (= x y))))) (let ((_let_1277 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_8259 x z) (ho_8259 y z)))) (= x y))))) (let ((_let_1278 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_8255 x z) (ho_8255 y z)))) (= x y))))) (let ((_let_1279 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_P5647936690300460905T_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_P5647936690300460905T_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9706 x z) (ho_9706 y z)))) (= x y))))) (let ((_let_1280 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_5414 x z) (ho_5414 y z)))) (= x y))))) (let ((_let_1281 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ tptp.produc8763457246119570046nteger Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ tptp.produc8763457246119570046nteger Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9851 x z) (ho_9851 y z)))) (= x y))))) (let ((_let_1282 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_8162 x z) (ho_8162 y z)))) (= x y))))) (let ((_let_1283 (forall ((x |u_(-> Bool _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> Bool _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_5254 x z) (ho_5254 y z)))) (= x y))))) (let ((_let_1284 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_real)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_9886 x z) (ho_9886 y z)))) (= x y))))) (let ((_let_1285 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8783 x z) (ho_8783 y z)))) (= x y))))) (let ((_let_1286 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.int)|)) (= (ho_8158 x z) (ho_8158 y z)))) (= x y))))) (let ((_let_1287 (forall ((x |u_(-> Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z Bool)) (= (ho_5790 x z) (ho_5790 y z)))) (= x y))))) (let ((_let_1288 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_8103 x z) (ho_8103 y z)))) (= x y))))) (let ((_let_1289 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.complex)_ tptp.product_prod_nat_nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.complex)_ tptp.product_prod_nat_nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.complex)|)) (= (ho_8071 x z) (ho_8071 y z)))) (= x y))))) (let ((_let_1290 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.product_prod_nat_nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.product_prod_nat_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_8068 x z) (ho_8068 y z)))) (= x y))))) (let ((_let_1291 (forall ((x |u_(-> tptp.nat tptp.complex tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_4750 x z) (ho_4750 y z)))) (= x y))))) (let ((_let_1292 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.real)|)) (= (ho_8065 x z) (ho_8065 y z)))) (= x y))))) (let ((_let_1293 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_4756 x z) (ho_4756 y z)))) (= x y))))) (let ((_let_1294 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_8061 x z) (ho_8061 y z)))) (= x y))))) (let ((_let_1295 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_5088 x z) (ho_5088 y z)))) (= x y))))) (let ((_let_1296 (forall ((x |u_(-> tptp.list_o tptp.nat Bool)|) (y |u_(-> tptp.list_o tptp.nat Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_5158 x z) (ho_5158 y z)))) (= x y))))) (let ((_let_1297 (forall ((x |u_(-> tptp.set_int tptp.complex)|) (y |u_(-> tptp.set_int tptp.complex)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9817 x z) (ho_9817 y z)))) (= x y))))) (let ((_let_1298 (forall ((x |u_(-> tptp.list_o tptp.list_P7333126701944960589_nat_o)|) (y |u_(-> tptp.list_o tptp.list_P7333126701944960589_nat_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9715 x z) (ho_9715 y z)))) (= x y))))) (let ((_let_1299 (forall ((x |u_(-> tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_4220 x z) (ho_4220 y z)))) (= x y))))) (let ((_let_1300 (forall ((x |u_(-> tptp.complex tptp.real Bool)|) (y |u_(-> tptp.complex tptp.real Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_5659 x z) (ho_5659 y z)))) (= x y))))) (let ((_let_1301 (forall ((x |u_(-> tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4487 x z) (ho_4487 y z)))) (= x y))))) (let ((_let_1302 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8534 x z) (ho_8534 y z)))) (= x y))))) (let ((_let_1303 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_4213 x z) (ho_4213 y z)))) (= x y))))) (let ((_let_1304 (forall ((x |u_(-> tptp.list_nat tptp.nat Bool)|) (y |u_(-> tptp.list_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_5151 x z) (ho_5151 y z)))) (= x y))))) (let ((_let_1305 (forall ((x |u_(-> tptp.list_int tptp.int Bool)|) (y |u_(-> tptp.list_int tptp.int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_5149 x z) (ho_5149 y z)))) (= x y))))) (let ((_let_1306 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_5993 x z) (ho_5993 y z)))) (= x y))))) (let ((_let_1307 (forall ((x |u_(-> tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_5139 x z) (ho_5139 y z)))) (= x y))))) (let ((_let_1308 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6709 x z) (ho_6709 y z)))) (= x y))))) (let ((_let_1309 (forall ((x |u_(-> Bool tptp.vEBT_VEBT tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> Bool tptp.vEBT_VEBT tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_9667 x z) (ho_9667 y z)))) (= x y))))) (let ((_let_1310 (forall ((x |u_(-> tptp.nat tptp.list_o Bool)|) (y |u_(-> tptp.nat tptp.list_o Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9242 x z) (ho_9242 y z)))) (= x y))))) (let ((_let_1311 (forall ((x |u_(-> tptp.set_complex tptp.complex Bool)|) (y |u_(-> tptp.set_complex tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_5126 x z) (ho_5126 y z)))) (= x y))))) (let ((_let_1312 (forall ((x |u_(-> tptp.nat tptp.num tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5828 x z) (ho_5828 y z)))) (= x y))))) (let ((_let_1313 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.real tptp.nat)|) (y |u_(-> _u_(-> tptp.real tptp.nat)_ tptp.real tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat)|)) (= (ho_7998 x z) (ho_7998 y z)))) (= x y))))) (let ((_let_1314 (forall ((x |u_(-> tptp.option_nat tptp.option_nat)|) (y |u_(-> tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9446 x z) (ho_9446 y z)))) (= x y))))) (let ((_let_1315 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int Bool)|) (y |u_(-> tptp.list_int tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9298 x z) (ho_9298 y z)))) (= x y))))) (let ((_let_1316 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_8476 x z) (ho_8476 y z)))) (= x y))))) (let ((_let_1317 (forall ((x |u_(-> tptp.list_P3126845725202233233VEBT_o tptp.nat tptp.produc334124729049499915VEBT_o)|) (y |u_(-> tptp.list_P3126845725202233233VEBT_o tptp.nat tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z tptp.list_P3126845725202233233VEBT_o)) (= (ho_9650 x z) (ho_9650 y z)))) (= x y))))) (let ((_let_1318 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_5094 x z) (ho_5094 y z)))) (= x y))))) (let ((_let_1319 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (= (ho_4200 x z) (ho_4200 y z)))) (= x y))))) (let ((_let_1320 (forall ((x |u_(-> tptp.set_real Bool)|) (y |u_(-> tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_5136 x z) (ho_5136 y z)))) (= x y))))) (let ((_let_1321 (forall ((x |u_(-> tptp.set_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_VEBT_VEBT)) (= (ho_5608 x z) (ho_5608 y z)))) (= x y))))) (let ((_let_1322 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.rat)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_9778 x z) (ho_9778 y z)))) (= x y))))) (let ((_let_1323 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_9114 x z) (ho_9114 y z)))) (= x y))))) (let ((_let_1324 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4814 x z) (ho_4814 y z)))) (= x y))))) (let ((_let_1325 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.set_VEBT_VEBT Bool)|) (y |u_(-> tptp.vEBT_VEBT tptp.set_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_5607 x z) (ho_5607 y z)))) (= x y))))) (let ((_let_1326 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_8821 x z) (ho_8821 y z)))) (= x y))))) (let ((_let_1327 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_8118 x z) (ho_8118 y z)))) (= x y))))) (let ((_let_1328 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4615 x z) (ho_4615 y z)))) (= x y))))) (let ((_let_1329 (forall ((x |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.option6357759511663192854e_term)|)) (= (ho_7721 x z) (ho_7721 y z)))) (= x y))))) (let ((_let_1330 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_4858 x z) (ho_4858 y z)))) (= x y))))) (let ((_let_1331 (forall ((x |u_(-> Bool tptp.option_num tptp.option_num tptp.option_num)|) (y |u_(-> Bool tptp.option_num tptp.option_num tptp.option_num)|)) (or (not (forall ((z Bool)) (= (ho_4229 x z) (ho_4229 y z)))) (= x y))))) (let ((_let_1332 (forall ((x |u_(-> tptp.real tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_9012 x z) (ho_9012 y z)))) (= x y))))) (let ((_let_1333 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4837 x z) (ho_4837 y z)))) (= x y))))) (let ((_let_1334 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_4824 x z) (ho_4824 y z)))) (= x y))))) (let ((_let_1335 (forall ((x |u_(-> tptp.real tptp.real tptp.set_real)|) (y |u_(-> tptp.real tptp.real tptp.set_real)|)) (or (not (forall ((z tptp.real)) (= (ho_9594 x z) (ho_9594 y z)))) (= x y))))) (let ((_let_1336 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_4825 x z) (ho_4825 y z)))) (= x y))))) (let ((_let_1337 (forall ((x |u_(-> tptp.vEBT_VEBT Bool tptp.produc334124729049499915VEBT_o)|) (y |u_(-> tptp.vEBT_VEBT Bool tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9644 x z) (ho_9644 y z)))) (= x y))))) (let ((_let_1338 (forall ((x |u_(-> tptp.int tptp.nat tptp.real)|) (y |u_(-> tptp.int tptp.nat tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_7280 x z) (ho_7280 y z)))) (= x y))))) (let ((_let_1339 (forall ((x |u_(-> tptp.produc6121120109295599847at_nat tptp.produc5491161045314408544at_nat)|) (y |u_(-> tptp.produc6121120109295599847at_nat tptp.produc5491161045314408544at_nat)|)) (or (not (forall ((z tptp.produc6121120109295599847at_nat)) (= (ho_9515 x z) (ho_9515 y z)))) (= x y))))) (let ((_let_1340 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8787 x z) (ho_8787 y z)))) (= x y))))) (let ((_let_1341 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_8164 x z) (ho_8164 y z)))) (= x y))))) (let ((_let_1342 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4211 x z) (ho_4211 y z)))) (= x y))))) (let ((_let_1343 (forall ((x |u_(-> tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_VEBT_VEBT)) (= (ho_9245 x z) (ho_9245 y z)))) (= x y))))) (let ((_let_1344 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_4796 x z) (ho_4796 y z)))) (= x y))))) (let ((_let_1345 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_6175 x z) (ho_6175 y z)))) (= x y))))) (let ((_let_1346 (forall ((x |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.real tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real Bool)|)) (= (ho_9136 x z) (ho_9136 y z)))) (= x y))))) (let ((_let_1347 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.real tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.real tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_9102 x z) (ho_9102 y z)))) (= x y))))) (let ((_let_1348 (forall ((x |u_(-> tptp.real tptp.int tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.int tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7279 x z) (ho_7279 y z)))) (= x y))))) (let ((_let_1349 (forall ((x |u_(-> tptp.nat tptp.rat tptp.real)|) (y |u_(-> tptp.nat tptp.rat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7346 x z) (ho_7346 y z)))) (= x y))))) (let ((_let_1350 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4815 x z) (ho_4815 y z)))) (= x y))))) (let ((_let_1351 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4799 x z) (ho_4799 y z)))) (= x y))))) (let ((_let_1352 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4337 x z) (ho_4337 y z)))) (= x y))))) (let ((_let_1353 (forall ((x |u_(-> tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4777 x z) (ho_4777 y z)))) (= x y))))) (let ((_let_1354 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_8988 x z) (ho_8988 y z)))) (= x y))))) (let ((_let_1355 (forall ((x |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_9674 x z) (ho_9674 y z)))) (= x y))))) (let ((_let_1356 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4766 x z) (ho_4766 y z)))) (= x y))))) (let ((_let_1357 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4793 x z) (ho_4793 y z)))) (= x y))))) (let ((_let_1358 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_4828 x z) (ho_4828 y z)))) (= x y))))) (let ((_let_1359 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_10427 x z) (ho_10427 y z)))) (= x y))))) (let ((_let_1360 (forall ((x |u_(-> tptp.complex tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4778 x z) (ho_4778 y z)))) (= x y))))) (let ((_let_1361 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ tptp.set_complex)|) (y |u_(-> _u_(-> tptp.complex Bool)_ tptp.set_complex)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_9251 x z) (ho_9251 y z)))) (= x y))))) (let ((_let_1362 (forall ((x |u_(-> tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_4771 x z) (ho_4771 y z)))) (= x y))))) (let ((_let_1363 (forall ((x |u_(-> _u_(-> tptp.real tptp.real tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real tptp.nat)|)) (= (ho_9019 x z) (ho_9019 y z)))) (= x y))))) (let ((_let_1364 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_7151 x z) (ho_7151 y z)))) (= x y))))) (let ((_let_1365 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_4810 x z) (ho_4810 y z)))) (= x y))))) (let ((_let_1366 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (= (ho_4446 x z) (ho_4446 y z)))) (= x y))))) (let ((_let_1367 (forall ((x |u_(-> tptp.set_int Bool)|) (y |u_(-> tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_5117 x z) (ho_5117 y z)))) (= x y))))) (let ((_let_1368 (forall ((x |u_(-> tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_4709 x z) (ho_4709 y z)))) (= x y))))) (let ((_let_1369 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (= (ho_4207 x z) (ho_4207 y z)))) (= x y))))) (let ((_let_1370 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_10433 x z) (ho_10433 y z)))) (= x y))))) (let ((_let_1371 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_8097 x z) (ho_8097 y z)))) (= x y))))) (let ((_let_1372 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT tptp.produc8025551001238799321T_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT tptp.produc8025551001238799321T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_9702 x z) (ho_9702 y z)))) (= x y))))) (let ((_let_1373 (forall ((x |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4744 x z) (ho_4744 y z)))) (= x y))))) (let ((_let_1374 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_P3126845725202233233VEBT_o)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_P3126845725202233233VEBT_o)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9647 x z) (ho_9647 y z)))) (= x y))))) (let ((_let_1375 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_9036 x z) (ho_9036 y z)))) (= x y))))) (let ((_let_1376 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_4310 x z) (ho_4310 y z)))) (= x y))))) (let ((_let_1377 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_8924 x z) (ho_8924 y z)))) (= x y))))) (let ((_let_1378 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_4501 x z) (ho_4501 y z)))) (= x y))))) (let ((_let_1379 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_int)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_int)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_9894 x z) (ho_9894 y z)))) (= x y))))) (let ((_let_1380 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_5120 x z) (ho_5120 y z)))) (= x y))))) (let ((_let_1381 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_4468 x z) (ho_4468 y z)))) (= x y))))) (let ((_let_1382 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6255 x z) (ho_6255 y z)))) (= x y))))) (let ((_let_1383 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_5084 x z) (ho_5084 y z)))) (= x y))))) (let ((_let_1384 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_8127 x z) (ho_8127 y z)))) (= x y))))) (let ((_let_1385 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_4296 x z) (ho_4296 y z)))) (= x y))))) (let ((_let_1386 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4736 x z) (ho_4736 y z)))) (= x y))))) (let ((_let_1387 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_4726 x z) (ho_4726 y z)))) (= x y))))) (let ((_let_1388 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4718 x z) (ho_4718 y z)))) (= x y))))) (let ((_let_1389 (forall ((x |u_(-> tptp.nat tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4715 x z) (ho_4715 y z)))) (= x y))))) (let ((_let_1390 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_5095 x z) (ho_5095 y z)))) (= x y))))) (let ((_let_1391 (forall ((x |u_(-> tptp.nat tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4492 x z) (ho_4492 y z)))) (= x y))))) (let ((_let_1392 (forall ((x |u_(-> tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_5370 x z) (ho_5370 y z)))) (= x y))))) (let ((_let_1393 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.real tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.real tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4807 x z) (ho_4807 y z)))) (= x y))))) (let ((_let_1394 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_6075 x z) (ho_6075 y z)))) (= x y))))) (let ((_let_1395 (forall ((x |u_(-> tptp.nat Bool tptp.product_prod_nat_o)|) (y |u_(-> tptp.nat Bool tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_9711 x z) (ho_9711 y z)))) (= x y))))) (let ((_let_1396 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8561 x z) (ho_8561 y z)))) (= x y))))) (let ((_let_1397 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4712 x z) (ho_4712 y z)))) (= x y))))) (let ((_let_1398 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_5154 x z) (ho_5154 y z)))) (= x y))))) (let ((_let_1399 (forall ((x |u_(-> tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4625 x z) (ho_4625 y z)))) (= x y))))) (let ((_let_1400 (forall ((x |u_(-> tptp.int tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_4315 x z) (ho_4315 y z)))) (= x y))))) (let ((_let_1401 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.set_Pr1261947904930325089at_nat tptp.complex)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.set_Pr1261947904930325089at_nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.complex)|)) (= (ho_9913 x z) (ho_9913 y z)))) (= x y))))) (let ((_let_1402 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.int tptp.nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.int tptp.nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_9116 x z) (ho_9116 y z)))) (= x y))))) (let ((_let_1403 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_5205 x z) (ho_5205 y z)))) (= x y))))) (let ((_let_1404 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (= (ho_5640 x z) (ho_5640 y z)))) (= x y))))) (let ((_let_1405 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_5201 x z) (ho_5201 y z)))) (= x y))))) (let ((_let_1406 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4627 x z) (ho_4627 y z)))) (= x y))))) (let ((_let_1407 (forall ((x |u_(-> tptp.set_complex tptp.nat tptp.list_complex Bool)|) (y |u_(-> tptp.set_complex tptp.nat tptp.list_complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9253 x z) (ho_9253 y z)))) (= x y))))) (let ((_let_1408 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.real)|)) (= (ho_4851 x z) (ho_4851 y z)))) (= x y))))) (let ((_let_1409 (forall ((x |u_(-> tptp.num tptp.num tptp.int Bool)|) (y |u_(-> tptp.num tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_5970 x z) (ho_5970 y z)))) (= x y))))) (let ((_let_1410 (forall ((x |u_(-> tptp.produc3447558737645232053on_num tptp.produc7036089656553540234on_num)|) (y |u_(-> tptp.produc3447558737645232053on_num tptp.produc7036089656553540234on_num)|)) (or (not (forall ((z tptp.produc3447558737645232053on_num)) (= (ho_9518 x z) (ho_9518 y z)))) (= x y))))) (let ((_let_1411 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_10362 x z) (ho_10362 y z)))) (= x y))))) (let ((_let_1412 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_8550 x z) (ho_8550 y z)))) (= x y))))) (let ((_let_1413 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4623 x z) (ho_4623 y z)))) (= x y))))) (let ((_let_1414 (forall ((x |u_(-> tptp.complex tptp.nat tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4720 x z) (ho_4720 y z)))) (= x y))))) (let ((_let_1415 (forall ((x |u_(-> Bool tptp.num tptp.num tptp.num)|) (y |u_(-> Bool tptp.num tptp.num tptp.num)|)) (or (not (forall ((z Bool)) (= (ho_4621 x z) (ho_4621 y z)))) (= x y))))) (let ((_let_1416 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat Bool)|)) (= (ho_9126 x z) (ho_9126 y z)))) (= x y))))) (let ((_let_1417 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.complex tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_4818 x z) (ho_4818 y z)))) (= x y))))) (let ((_let_1418 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.nat tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_5476 x z) (ho_5476 y z)))) (= x y))))) (let ((_let_1419 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4338 x z) (ho_4338 y z)))) (= x y))))) (let ((_let_1420 (forall ((x |u_(-> tptp.produc8763457246119570046nteger Bool)|) (y |u_(-> tptp.produc8763457246119570046nteger Bool)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_9739 x z) (ho_9739 y z)))) (= x y))))) (let ((_let_1421 (forall ((x |u_(-> tptp.nat tptp.real tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.real tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4747 x z) (ho_4747 y z)))) (= x y))))) (let ((_let_1422 (forall ((x |u_(-> tptp.int tptp.set_int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_5899 x z) (ho_5899 y z)))) (= x y))))) (let ((_let_1423 (forall ((x |u_(-> Bool tptp.rat tptp.rat tptp.rat)|) (y |u_(-> Bool tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_5050 x z) (ho_5050 y z)))) (= x y))))) (let ((_let_1424 (forall ((x |u_(-> tptp.code_integer tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.code_integer tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4606 x z) (ho_4606 y z)))) (= x y))))) (let ((_let_1425 (forall ((x |u_(-> tptp.set_nat tptp.int)|) (y |u_(-> tptp.set_nat tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_6080 x z) (ho_6080 y z)))) (= x y))))) (let ((_let_1426 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9686 x z) (ho_9686 y z)))) (= x y))))) (let ((_let_1427 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_9757 x z) (ho_9757 y z)))) (= x y))))) (let ((_let_1428 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_num)|) (y |u_(-> tptp.num tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.num)) (= (ho_5586 x z) (ho_5586 y z)))) (= x y))))) (let ((_let_1429 (forall ((x |u_(-> tptp.list_P3126845725202233233VEBT_o tptp.nat)|) (y |u_(-> tptp.list_P3126845725202233233VEBT_o tptp.nat)|)) (or (not (forall ((z tptp.list_P3126845725202233233VEBT_o)) (= (ho_9722 x z) (ho_9722 y z)))) (= x y))))) (let ((_let_1430 (forall ((x |u_(-> Bool tptp.int tptp.int tptp.int)|) (y |u_(-> Bool tptp.int tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_4593 x z) (ho_4593 y z)))) (= x y))))) (let ((_let_1431 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9488 x z) (ho_9488 y z)))) (= x y))))) (let ((_let_1432 (forall ((x |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4427 x z) (ho_4427 y z)))) (= x y))))) (let ((_let_1433 (forall ((x |u_(-> tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9249 x z) (ho_9249 y z)))) (= x y))))) (let ((_let_1434 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_4581 x z) (ho_4581 y z)))) (= x y))))) (let ((_let_1435 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_8798 x z) (ho_8798 y z)))) (= x y))))) (let ((_let_1436 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_complex)_ tptp.product_prod_int_int tptp.set_complex)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_complex)_ tptp.product_prod_int_int tptp.set_complex)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_complex)|)) (= (ho_9873 x z) (ho_9873 y z)))) (= x y))))) (let ((_let_1437 (forall ((x |u_(-> tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_4582 x z) (ho_4582 y z)))) (= x y))))) (let ((_let_1438 (forall ((x |u_(-> tptp.int tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.int tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_9880 x z) (ho_9880 y z)))) (= x y))))) (let ((_let_1439 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_4760 x z) (ho_4760 y z)))) (= x y))))) (let ((_let_1440 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.real)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_4506 x z) (ho_4506 y z)))) (= x y))))) (let ((_let_1441 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9302 x z) (ho_9302 y z)))) (= x y))))) (let ((_let_1442 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4578 x z) (ho_4578 y z)))) (= x y))))) (let ((_let_1443 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.real)|)) (= (ho_6186 x z) (ho_6186 y z)))) (= x y))))) (let ((_let_1444 (forall ((x |u_(-> tptp.char tptp.nat)|) (y |u_(-> tptp.char tptp.nat)|)) (or (not (forall ((z tptp.char)) (= (ho_10173 x z) (ho_10173 y z)))) (= x y))))) (let ((_let_1445 (forall ((x |u_(-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z Bool)) (= (ho_4574 x z) (ho_4574 y z)))) (= x y))))) (let ((_let_1446 (forall ((x |u_(-> tptp.option_num tptp.option_num tptp.option_num)|) (y |u_(-> tptp.option_num tptp.option_num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4230 x z) (ho_4230 y z)))) (= x y))))) (let ((_let_1447 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_4447 x z) (ho_4447 y z)))) (= x y))))) (let ((_let_1448 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_4575 x z) (ho_4575 y z)))) (= x y))))) (let ((_let_1449 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_4576 x z) (ho_4576 y z)))) (= x y))))) (let ((_let_1450 (forall ((x |u_(-> tptp.real tptp.num tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.num tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7289 x z) (ho_7289 y z)))) (= x y))))) (let ((_let_1451 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_4833 x z) (ho_4833 y z)))) (= x y))))) (let ((_let_1452 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_5061 x z) (ho_5061 y z)))) (= x y))))) (let ((_let_1453 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.complex tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.complex tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_9109 x z) (ho_9109 y z)))) (= x y))))) (let ((_let_1454 (forall ((x |u_(-> Bool tptp.list_int tptp.list_int tptp.list_int)|) (y |u_(-> Bool tptp.list_int tptp.list_int tptp.list_int)|)) (or (not (forall ((z Bool)) (= (ho_5398 x z) (ho_5398 y z)))) (= x y))))) (let ((_let_1455 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_5092 x z) (ho_5092 y z)))) (= x y))))) (let ((_let_1456 (forall ((x |u_(-> tptp.nat tptp.num tptp.product_prod_nat_num)|) (y |u_(-> tptp.nat tptp.num tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_5585 x z) (ho_5585 y z)))) (= x y))))) (let ((_let_1457 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_5090 x z) (ho_5090 y z)))) (= x y))))) (let ((_let_1458 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4233 x z) (ho_4233 y z)))) (= x y))))) (let ((_let_1459 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_6520 x z) (ho_6520 y z)))) (= x y))))) (let ((_let_1460 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4463 x z) (ho_4463 y z)))) (= x y))))) (let ((_let_1461 (forall ((x |u_(-> tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_5114 x z) (ho_5114 y z)))) (= x y))))) (let ((_let_1462 (forall ((x |u_(-> tptp.product_prod_nat_num tptp.option_num)|) (y |u_(-> tptp.product_prod_nat_num tptp.option_num)|)) (or (not (forall ((z tptp.product_prod_nat_num)) (= (ho_5589 x z) (ho_5589 y z)))) (= x y))))) (let ((_let_1463 (forall ((x |u_(-> tptp.list_int tptp.nat)|) (y |u_(-> tptp.list_int tptp.nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_4638 x z) (ho_4638 y z)))) (= x y))))) (let ((_let_1464 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4209 x z) (ho_4209 y z)))) (= x y))))) (let ((_let_1465 (forall ((x |u_(-> tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4703 x z) (ho_4703 y z)))) (= x y))))) (let ((_let_1466 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)|)) (= (ho_4256 x z) (ho_4256 y z)))) (= x y))))) (let ((_let_1467 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5349 x z) (ho_5349 y z)))) (= x y))))) (let ((_let_1468 (forall ((x |u_(-> tptp.real _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> tptp.real _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_7578 x z) (ho_7578 y z)))) (= x y))))) (let ((_let_1469 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_8453 x z) (ho_8453 y z)))) (= x y))))) (let ((_let_1470 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_4268 x z) (ho_4268 y z)))) (= x y))))) (let ((_let_1471 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_6980 x z) (ho_6980 y z)))) (= x y))))) (let ((_let_1472 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_4548 x z) (ho_4548 y z)))) (= x y))))) (let ((_let_1473 (forall ((x |u_(-> tptp.rat tptp.product_prod_int_int)|) (y |u_(-> tptp.rat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.rat)) (= (ho_4437 x z) (ho_4437 y z)))) (= x y))))) (let ((_let_1474 (forall ((x |u_(-> tptp.list_o tptp.list_o Bool)|) (y |u_(-> tptp.list_o tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9352 x z) (ho_9352 y z)))) (= x y))))) (let ((_let_1475 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6716 x z) (ho_6716 y z)))) (= x y))))) (let ((_let_1476 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_9487 x z) (ho_9487 y z)))) (= x y))))) (let ((_let_1477 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4604 x z) (ho_4604 y z)))) (= x y))))) (let ((_let_1478 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_4537 x z) (ho_4537 y z)))) (= x y))))) (let ((_let_1479 (forall ((x |u_(-> Bool tptp.nat)|) (y |u_(-> Bool tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_4591 x z) (ho_4591 y z)))) (= x y))))) (let ((_let_1480 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_4264 x z) (ho_4264 y z)))) (= x y))))) (let ((_let_1481 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_5800 x z) (ho_5800 y z)))) (= x y))))) (let ((_let_1482 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (= (ho_10274 x z) (ho_10274 y z)))) (= x y))))) (let ((_let_1483 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_4445 x z) (ho_4445 y z)))) (= x y))))) (let ((_let_1484 (forall ((x |u_(-> tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4458 x z) (ho_4458 y z)))) (= x y))))) (let ((_let_1485 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.nat tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_4272 x z) (ho_4272 y z)))) (= x y))))) (let ((_let_1486 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat)|) (y |u_(-> tptp.real tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_8999 x z) (ho_8999 y z)))) (= x y))))) (let ((_let_1487 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_4834 x z) (ho_4834 y z)))) (= x y))))) (let ((_let_1488 (forall ((x |u_(-> tptp.real tptp.nat tptp.rat)|) (y |u_(-> tptp.real tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_4253 x z) (ho_4253 y z)))) (= x y))))) (let ((_let_1489 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_8458 x z) (ho_8458 y z)))) (= x y))))) (let ((_let_1490 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4821 x z) (ho_4821 y z)))) (= x y))))) (let ((_let_1491 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (= (ho_9978 x z) (ho_9978 y z)))) (= x y))))) (let ((_let_1492 (forall ((x |u_(-> tptp.option_num tptp.num)|) (y |u_(-> tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4241 x z) (ho_4241 y z)))) (= x y))))) (let ((_let_1493 (forall ((x |u_(-> tptp.nat tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_4721 x z) (ho_4721 y z)))) (= x y))))) (let ((_let_1494 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9146 x z) (ho_9146 y z)))) (= x y))))) (let ((_let_1495 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_9006 x z) (ho_9006 y z)))) (= x y))))) (let ((_let_1496 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_6373 x z) (ho_6373 y z)))) (= x y))))) (let ((_let_1497 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10330 x z) (ho_10330 y z)))) (= x y))))) (let ((_let_1498 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_4536 x z) (ho_4536 y z)))) (= x y))))) (let ((_let_1499 (forall ((x |u_(-> Bool tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> Bool tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z Bool)) (= (ho_9685 x z) (ho_9685 y z)))) (= x y))))) (let ((_let_1500 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.real tptp.nat Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.real tptp.nat Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_9125 x z) (ho_9125 y z)))) (= x y))))) (let ((_let_1501 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4260 x z) (ho_4260 y z)))) (= x y))))) (let ((_let_1502 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6372 x z) (ho_6372 y z)))) (= x y))))) (let ((_let_1503 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_9840 x z) (ho_9840 y z)))) (= x y))))) (let ((_let_1504 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_5086 x z) (ho_5086 y z)))) (= x y))))) (let ((_let_1505 (forall ((x |u_(-> tptp.list_o tptp.nat Bool Bool Bool)|) (y |u_(-> tptp.list_o tptp.nat Bool Bool Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9196 x z) (ho_9196 y z)))) (= x y))))) (let ((_let_1506 (forall ((x |u_(-> tptp.list_int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_5399 x z) (ho_5399 y z)))) (= x y))))) (let ((_let_1507 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_7766 x z) (ho_7766 y z)))) (= x y))))) (let ((_let_1508 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_5096 x z) (ho_5096 y z)))) (= x y))))) (let ((_let_1509 (forall ((x |u_(-> tptp.complex tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_4705 x z) (ho_4705 y z)))) (= x y))))) (let ((_let_1510 (forall ((x |u_(-> tptp.set_nat tptp.set_real)|) (y |u_(-> tptp.set_nat tptp.set_real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_5542 x z) (ho_5542 y z)))) (= x y))))) (let ((_let_1511 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4699 x z) (ho_4699 y z)))) (= x y))))) (let ((_let_1512 (forall ((x |u_(-> tptp.int tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4635 x z) (ho_4635 y z)))) (= x y))))) (let ((_let_1513 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_4257 x z) (ho_4257 y z)))) (= x y))))) (let ((_let_1514 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (= (ho_10387 x z) (ho_10387 y z)))) (= x y))))) (let ((_let_1515 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_5087 x z) (ho_5087 y z)))) (= x y))))) (let ((_let_1516 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_6984 x z) (ho_6984 y z)))) (= x y))))) (let ((_let_1517 (forall ((x |u_(-> tptp.set_complex Bool)|) (y |u_(-> tptp.set_complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_5130 x z) (ho_5130 y z)))) (= x y))))) (let ((_let_1518 (forall ((x |u_(-> tptp.num tptp.nat tptp.option_num)|) (y |u_(-> tptp.num tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_4299 x z) (ho_4299 y z)))) (= x y))))) (let ((_let_1519 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.complex tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex tptp.real)|)) (= (ho_7356 x z) (ho_7356 y z)))) (= x y))))) (let ((_let_1520 (forall ((x |u_(-> tptp.list_real tptp.nat)|) (y |u_(-> tptp.list_real tptp.nat)|)) (or (not (forall ((z tptp.list_real)) (= (ho_8600 x z) (ho_8600 y z)))) (= x y))))) (let ((_let_1521 (forall ((x |u_(-> Bool tptp.int tptp.product_prod_o_int)|) (y |u_(-> Bool tptp.int tptp.product_prod_o_int)|)) (or (not (forall ((z Bool)) (= (ho_9693 x z) (ho_9693 y z)))) (= x y))))) (let ((_let_1522 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4249 x z) (ho_4249 y z)))) (= x y))))) (let ((_let_1523 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4572 x z) (ho_4572 y z)))) (= x y))))) (let ((_let_1524 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_4516 x z) (ho_4516 y z)))) (= x y))))) (let ((_let_1525 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_4439 x z) (ho_4439 y z)))) (= x y))))) (let ((_let_1526 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6683 x z) (ho_6683 y z)))) (= x y))))) (let ((_let_1527 (forall ((x |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real Bool)|)) (= (ho_9147 x z) (ho_9147 y z)))) (= x y))))) (let ((_let_1528 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (= (ho_4263 x z) (ho_4263 y z)))) (= x y))))) (let ((_let_1529 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9203 x z) (ho_9203 y z)))) (= x y))))) (let ((_let_1530 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc4953844613479565601on_nat tptp.produc8306885398267862888on_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc4953844613479565601on_nat tptp.produc8306885398267862888on_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_9496 x z) (ho_9496 y z)))) (= x y))))) (let ((_let_1531 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_5517 x z) (ho_5517 y z)))) (= x y))))) (let ((_let_1532 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.complex)|)) (= (ho_6171 x z) (ho_6171 y z)))) (= x y))))) (let ((_let_1533 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4265 x z) (ho_4265 y z)))) (= x y))))) (let ((_let_1534 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10325 x z) (ho_10325 y z)))) (= x y))))) (let ((_let_1535 (forall ((x |u_(-> tptp.set_complex tptp.complex)|) (y |u_(-> tptp.set_complex tptp.complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8558 x z) (ho_8558 y z)))) (= x y))))) (let ((_let_1536 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_10206 x z) (ho_10206 y z)))) (= x y))))) (let ((_let_1537 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_5994 x z) (ho_5994 y z)))) (= x y))))) (let ((_let_1538 (forall ((x |u_(-> tptp.int tptp.product_prod_nat_nat)|) (y |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_4204 x z) (ho_4204 y z)))) (= x y))))) (let ((_let_1539 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.rat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.rat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_8058 x z) (ho_8058 y z)))) (= x y))))) (let ((_let_1540 (forall ((x |u_(-> Bool tptp.real tptp.real tptp.real)|) (y |u_(-> Bool tptp.real tptp.real tptp.real)|)) (or (not (forall ((z Bool)) (= (ho_4277 x z) (ho_4277 y z)))) (= x y))))) (let ((_let_1541 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_8100 x z) (ho_8100 y z)))) (= x y))))) (let ((_let_1542 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5945 x z) (ho_5945 y z)))) (= x y))))) (let ((_let_1543 (forall ((x |u_(-> tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4560 x z) (ho_4560 y z)))) (= x y))))) (let ((_let_1544 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_6640 x z) (ho_6640 y z)))) (= x y))))) (let ((_let_1545 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4714 x z) (ho_4714 y z)))) (= x y))))) (let ((_let_1546 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_10122 x z) (ho_10122 y z)))) (= x y))))) (let ((_let_1547 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4334 x z) (ho_4334 y z)))) (= x y))))) (let ((_let_1548 (forall ((x |u_(-> tptp.set_complex tptp.set_complex)|) (y |u_(-> tptp.set_complex tptp.set_complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9823 x z) (ho_9823 y z)))) (= x y))))) (let ((_let_1549 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_10436 x z) (ho_10436 y z)))) (= x y))))) (let ((_let_1550 (forall ((x |u_(-> tptp.num tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_4629 x z) (ho_4629 y z)))) (= x y))))) (let ((_let_1551 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_8895 x z) (ho_8895 y z)))) (= x y))))) (let ((_let_1552 (forall ((x |u_(-> tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_4549 x z) (ho_4549 y z)))) (= x y))))) (let ((_let_1553 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_10340 x z) (ho_10340 y z)))) (= x y))))) (let ((_let_1554 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (= (ho_5628 x z) (ho_5628 y z)))) (= x y))))) (let ((_let_1555 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4409 x z) (ho_4409 y z)))) (= x y))))) (let ((_let_1556 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4251 x z) (ho_4251 y z)))) (= x y))))) (let ((_let_1557 (forall ((x |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|) (y |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_7752 x z) (ho_7752 y z)))) (= x y))))) (let ((_let_1558 (forall ((x |u_(-> tptp.int _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_6409 x z) (ho_6409 y z)))) (= x y))))) (let ((_let_1559 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.real tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.real tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_5403 x z) (ho_5403 y z)))) (= x y))))) (let ((_let_1560 (forall ((x |u_(-> tptp.real tptp.rat)|) (y |u_(-> tptp.real tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_8455 x z) (ho_8455 y z)))) (= x y))))) (let ((_let_1561 (forall ((x |u_(-> tptp.nat tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_6548 x z) (ho_6548 y z)))) (= x y))))) (let ((_let_1562 (forall ((x |u_(-> tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_4191 x z) (ho_4191 y z)))) (= x y))))) (let ((_let_1563 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_7755 x z) (ho_7755 y z)))) (= x y))))) (let ((_let_1564 (forall ((x |u_(-> tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4290 x z) (ho_4290 y z)))) (= x y))))) (let ((_let_1565 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_8788 x z) (ho_8788 y z)))) (= x y))))) (let ((_let_1566 (forall ((x |u_(-> tptp.real tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_5451 x z) (ho_5451 y z)))) (= x y))))) (let ((_let_1567 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_9991 x z) (ho_9991 y z)))) (= x y))))) (let ((_let_1568 (forall ((x |u_(-> tptp.nat tptp.product_prod_int_int)|) (y |u_(-> tptp.nat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_5726 x z) (ho_5726 y z)))) (= x y))))) (let ((_let_1569 (forall ((x |u_(-> tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_6530 x z) (ho_6530 y z)))) (= x y))))) (let ((_let_1570 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_9122 x z) (ho_9122 y z)))) (= x y))))) (let ((_let_1571 (forall ((x |u_(-> tptp.product_prod_int_int tptp.produc2285326912895808259nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.produc2285326912895808259nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_7735 x z) (ho_7735 y z)))) (= x y))))) (let ((_let_1572 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_4262 x z) (ho_4262 y z)))) (= x y))))) (let ((_let_1573 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.set_nat)_ tptp.produc7773217078559923341nt_int tptp.set_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.set_nat)_ tptp.produc7773217078559923341nt_int tptp.set_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.set_nat)|)) (= (ho_9903 x z) (ho_9903 y z)))) (= x y))))) (let ((_let_1574 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4216 x z) (ho_4216 y z)))) (= x y))))) (let ((_let_1575 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9452 x z) (ho_9452 y z)))) (= x y))))) (let ((_let_1576 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ tptp.produc1908205239877642774nteger Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ tptp.produc1908205239877642774nteger Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9853 x z) (ho_9853 y z)))) (= x y))))) (let ((_let_1577 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4215 x z) (ho_4215 y z)))) (= x y))))) (let ((_let_1578 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4597 x z) (ho_4597 y z)))) (= x y))))) (let ((_let_1579 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4288 x z) (ho_4288 y z)))) (= x y))))) (let ((_let_1580 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10334 x z) (ho_10334 y z)))) (= x y))))) (let ((_let_1581 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_4466 x z) (ho_4466 y z)))) (= x y))))) (let ((_let_1582 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_4206 x z) (ho_4206 y z)))) (= x y))))) (let ((_let_1583 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.real)|)) (= (ho_5523 x z) (ho_5523 y z)))) (= x y))))) (let ((_let_1584 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_8982 x z) (ho_8982 y z)))) (= x y))))) (let ((_let_1585 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_10355 x z) (ho_10355 y z)))) (= x y))))) (let ((_let_1586 (forall ((x |u_(-> tptp.nat tptp.num)|) (y |u_(-> tptp.nat tptp.num)|)) (or (not (forall ((z tptp.nat)) (= (ho_4225 x z) (ho_4225 y z)))) (= x y))))) (let ((_let_1587 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real Bool)_ tptp.real tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.real Bool)_ tptp.real tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real Bool)|)) (= (ho_9133 x z) (ho_9133 y z)))) (= x y))))) (let ((_let_1588 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_4441 x z) (ho_4441 y z)))) (= x y))))) (let ((_let_1589 (forall ((x |u_(-> tptp.complex tptp.set_complex Bool)|) (y |u_(-> tptp.complex tptp.set_complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_5129 x z) (ho_5129 y z)))) (= x y))))) (let ((_let_1590 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_4946 x z) (ho_4946 y z)))) (= x y))))) (let ((_let_1591 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4571 x z) (ho_4571 y z)))) (= x y))))) (let ((_let_1592 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10358 x z) (ho_10358 y z)))) (= x y))))) (let ((_let_1593 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_5611 x z) (ho_5611 y z)))) (= x y))))) (let ((_let_1594 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9928 x z) (ho_9928 y z)))) (= x y))))) (let ((_let_1595 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4552 x z) (ho_4552 y z)))) (= x y))))) (let ((_let_1596 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5440 x z) (ho_5440 y z)))) (= x y))))) (let ((_let_1597 (forall ((x |u_(-> Bool tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> Bool tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z Bool)) (= (ho_4430 x z) (ho_4430 y z)))) (= x y))))) (let ((_let_1598 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9002 x z) (ho_9002 y z)))) (= x y))))) (let ((_let_1599 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_6646 x z) (ho_6646 y z)))) (= x y))))) (let ((_let_1600 (forall ((x |u_(-> tptp.list_int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_5396 x z) (ho_5396 y z)))) (= x y))))) (let ((_let_1601 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_4234 x z) (ho_4234 y z)))) (= x y))))) (let ((_let_1602 (forall ((x |u_(-> tptp.complex tptp.nat Bool)|) (y |u_(-> tptp.complex tptp.nat Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_9107 x z) (ho_9107 y z)))) (= x y))))) (let ((_let_1603 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.nat)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.nat)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_4534 x z) (ho_4534 y z)))) (= x y))))) (let ((_let_1604 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_int)_ tptp.produc8763457246119570046nteger tptp.set_int)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_int)_ tptp.produc8763457246119570046nteger tptp.set_int)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.set_int)|)) (= (ho_9893 x z) (ho_9893 y z)))) (= x y))))) (let ((_let_1605 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_5186 x z) (ho_5186 y z)))) (= x y))))) (let ((_let_1606 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6636 x z) (ho_6636 y z)))) (= x y))))) (let ((_let_1607 (forall ((x |u_(-> tptp.product_prod_int_int tptp.rat)|) (y |u_(-> tptp.product_prod_int_int tptp.rat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_4434 x z) (ho_4434 y z)))) (= x y))))) (let ((_let_1608 (forall ((x |u_(-> tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_4532 x z) (ho_4532 y z)))) (= x y))))) (let ((_let_1609 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8560 x z) (ho_8560 y z)))) (= x y))))) (let ((_let_1610 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|)) (= (ho_5646 x z) (ho_5646 y z)))) (= x y))))) (let ((_let_1611 (forall ((x |u_(-> tptp.complex _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|) (y |u_(-> tptp.complex _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_5091 x z) (ho_5091 y z)))) (= x y))))) (let ((_let_1612 (forall ((x |u_(-> Bool tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_4569 x z) (ho_4569 y z)))) (= x y))))) (let ((_let_1613 (forall ((x |u_(-> tptp.nat tptp.int tptp.real)|) (y |u_(-> tptp.nat tptp.int tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7340 x z) (ho_7340 y z)))) (= x y))))) (let ((_let_1614 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4740 x z) (ho_4740 y z)))) (= x y))))) (let ((_let_1615 (forall ((x |u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)|) (y |u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)|)) (or (not (forall ((z tptp.produc6241069584506657477e_term)) (= (ho_7740 x z) (ho_7740 y z)))) (= x y))))) (let ((_let_1616 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_5062 x z) (ho_5062 y z)))) (= x y))))) (let ((_let_1617 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_9121 x z) (ho_9121 y z)))) (= x y))))) (let ((_let_1618 (forall ((x |u_(-> tptp.option_num tptp.option_num)|) (y |u_(-> tptp.option_num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4231 x z) (ho_4231 y z)))) (= x y))))) (let ((_let_1619 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_4240 x z) (ho_4240 y z)))) (= x y))))) (let ((_let_1620 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.product_prod_int_int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.product_prod_int_int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_9843 x z) (ho_9843 y z)))) (= x y))))) (let ((_let_1621 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_9027 x z) (ho_9027 y z)))) (= x y))))) (let ((_let_1622 (forall ((x |u_(-> tptp.nat tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_5854 x z) (ho_5854 y z)))) (= x y))))) (let ((_let_1623 (forall ((x |u_(-> tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_4273 x z) (ho_4273 y z)))) (= x y))))) (let ((_let_1624 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_5806 x z) (ho_5806 y z)))) (= x y))))) (let ((_let_1625 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_o)|) (y |u_(-> tptp.nat tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_9718 x z) (ho_9718 y z)))) (= x y))))) (let ((_let_1626 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_10403 x z) (ho_10403 y z)))) (= x y))))) (let ((_let_1627 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.nat tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_6006 x z) (ho_6006 y z)))) (= x y))))) (let ((_let_1628 (forall ((x |u_(-> tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4617 x z) (ho_4617 y z)))) (= x y))))) (let ((_let_1629 (forall ((x |u_(-> tptp.set_real tptp.set_real)|) (y |u_(-> tptp.set_real tptp.set_real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9623 x z) (ho_9623 y z)))) (= x y))))) (let ((_let_1630 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9532 x z) (ho_9532 y z)))) (= x y))))) (let ((_let_1631 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4303 x z) (ho_4303 y z)))) (= x y))))) (let ((_let_1632 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_num)|)) (= (ho_4527 x z) (ho_4527 y z)))) (= x y))))) (let ((_let_1633 (forall ((x |u_(-> tptp.list_nat tptp.list_P7037539587688870467BT_nat)|) (y |u_(-> tptp.list_nat tptp.list_P7037539587688870467BT_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_9654 x z) (ho_9654 y z)))) (= x y))))) (let ((_let_1634 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_9976 x z) (ho_9976 y z)))) (= x y))))) (let ((_let_1635 (forall ((x |u_(-> _u_(-> tptp.real tptp.int tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int tptp.nat)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int tptp.nat)|)) (= (ho_8980 x z) (ho_8980 y z)))) (= x y))))) (let ((_let_1636 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4605 x z) (ho_4605 y z)))) (= x y))))) (let ((_let_1637 (forall ((x |u_(-> tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_4196 x z) (ho_4196 y z)))) (= x y))))) (let ((_let_1638 (forall ((x |u_(-> tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_4193 x z) (ho_4193 y z)))) (= x y))))) (let ((_let_1639 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4564 x z) (ho_4564 y z)))) (= x y))))) (let ((_let_1640 (forall ((x |u_(-> tptp.filter_real Bool)|) (y |u_(-> tptp.filter_real Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_10188 x z) (ho_10188 y z)))) (= x y))))) (let ((_let_1641 (forall ((x |u_(-> tptp.real tptp.real tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_4782 x z) (ho_4782 y z)))) (= x y))))) (let ((_let_1642 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_4730 x z) (ho_4730 y z)))) (= x y))))) (let ((_let_1643 (forall ((x |u_(-> tptp.int tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_6529 x z) (ho_6529 y z)))) (= x y))))) (let ((_let_1644 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4302 x z) (ho_4302 y z)))) (= x y))))) (let ((_let_1645 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_5123 x z) (ho_5123 y z)))) (= x y))))) (let ((_let_1646 (forall ((x |u_(-> tptp.int tptp.complex)|) (y |u_(-> tptp.int tptp.complex)|)) (or (not (forall ((z tptp.int)) (= (ho_6177 x z) (ho_6177 y z)))) (= x y))))) (let ((_let_1647 (forall ((x |u_(-> tptp.list_o tptp.nat)|) (y |u_(-> tptp.list_o tptp.nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_5156 x z) (ho_5156 y z)))) (= x y))))) (let ((_let_1648 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9636 x z) (ho_9636 y z)))) (= x y))))) (let ((_let_1649 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_4351 x z) (ho_4351 y z)))) (= x y))))) (let ((_let_1650 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_5954 x z) (ho_5954 y z)))) (= x y))))) (let ((_let_1651 (forall ((x |u_(-> tptp.list_o tptp.nat Bool Bool)|) (y |u_(-> tptp.list_o tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_9306 x z) (ho_9306 y z)))) (= x y))))) (let ((_let_1652 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4295 x z) (ho_4295 y z)))) (= x y))))) (let ((_let_1653 (forall ((x |u_(-> tptp.real _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|) (y |u_(-> tptp.real _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_6416 x z) (ho_6416 y z)))) (= x y))))) (let ((_let_1654 (forall ((x |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|) (y |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8831 x z) (ho_8831 y z)))) (= x y))))) (let ((_let_1655 (forall ((x |u_(-> tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_4308 x z) (ho_4308 y z)))) (= x y))))) (let ((_let_1656 (forall ((x |u_(-> tptp.nat tptp.code_integer tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_6613 x z) (ho_6613 y z)))) (= x y))))) (let ((_let_1657 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_4335 x z) (ho_4335 y z)))) (= x y))))) (let ((_let_1658 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_6258 x z) (ho_6258 y z)))) (= x y))))) (let ((_let_1659 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_7378 x z) (ho_7378 y z)))) (= x y))))) (let ((_let_1660 (forall ((x |u_(-> tptp.num tptp.code_integer)|) (y |u_(-> tptp.num tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_4562 x z) (ho_4562 y z)))) (= x y))))) (let ((_let_1661 (forall ((x |u_(-> Bool Bool tptp.product_prod_o_o)|) (y |u_(-> Bool Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_9676 x z) (ho_9676 y z)))) (= x y))))) (let ((_let_1662 (forall ((x |u_(-> tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4316 x z) (ho_4316 y z)))) (= x y))))) (let ((_let_1663 (forall ((x |u_(-> Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z Bool)) (= (ho_5060 x z) (ho_5060 y z)))) (= x y))))) (let ((_let_1664 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8555 x z) (ho_8555 y z)))) (= x y))))) (let ((_let_1665 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.nat tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_4708 x z) (ho_4708 y z)))) (= x y))))) (let ((_let_1666 (forall ((x |u_(-> _u_(-> tptp.option4927543243414619207at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option4927543243414619207at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option4927543243414619207at_nat Bool)|)) (= (ho_9417 x z) (ho_9417 y z)))) (= x y))))) (let ((_let_1667 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ _u_(-> tptp.real tptp.rat)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_8795 x z) (ho_8795 y z)))) (= x y))))) (let ((_let_1668 (forall ((x |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|) (y |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|)) (or (not (forall ((z |u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)|)) (= (ho_7746 x z) (ho_7746 y z)))) (= x y))))) (let ((_let_1669 (forall ((x |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (y |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_4613 x z) (ho_4613 y z)))) (= x y))))) (let ((_let_1670 (forall ((x |u_(-> tptp.set_complex tptp.code_integer)|) (y |u_(-> tptp.set_complex tptp.code_integer)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_9835 x z) (ho_9835 y z)))) (= x y))))) (let ((_let_1671 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_9625 x z) (ho_9625 y z)))) (= x y))))) (let ((_let_1672 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_8623 x z) (ho_8623 y z)))) (= x y))))) (let ((_let_1673 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ tptp.nat tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.real)_ tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.real)|)) (= (ho_5521 x z) (ho_5521 y z)))) (= x y))))) (let ((_let_1674 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_5820 x z) (ho_5820 y z)))) (= x y))))) (let ((_let_1675 (forall ((x |u_(-> tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_4779 x z) (ho_4779 y z)))) (= x y))))) (let ((_let_1676 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.set_complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.set_complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_9810 x z) (ho_9810 y z)))) (= x y))))) (let ((_let_1677 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_6669 x z) (ho_6669 y z)))) (= x y))))) (let ((_let_1678 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6645 x z) (ho_6645 y z)))) (= x y))))) (let ((_let_1679 (forall ((x |u_(-> tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_8653 x z) (ho_8653 y z)))) (= x y))))) (let ((_let_1680 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_10352 x z) (ho_10352 y z)))) (= x y))))) (let ((_let_1681 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4512 x z) (ho_4512 y z)))) (= x y))))) (let ((_let_1682 (forall ((x |u_(-> tptp.real tptp.nat tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_6521 x z) (ho_6521 y z)))) (= x y))))) (let ((_let_1683 (forall ((x |u_(-> tptp.real tptp.real tptp.int Bool)|) (y |u_(-> tptp.real tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_5964 x z) (ho_5964 y z)))) (= x y))))) (let ((_let_1684 (forall ((x |u_(-> tptp.set_int tptp.real)|) (y |u_(-> tptp.set_int tptp.real)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9808 x z) (ho_9808 y z)))) (= x y))))) (let ((_let_1685 (forall ((x |u_(-> tptp.list_complex tptp.nat tptp.complex tptp.list_complex)|) (y |u_(-> tptp.list_complex tptp.nat tptp.complex tptp.list_complex)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_9209 x z) (ho_9209 y z)))) (= x y))))) (let ((_let_1686 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat Bool)_ tptp.nat tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat Bool)_ tptp.nat tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat Bool)|)) (= (ho_9128 x z) (ho_9128 y z)))) (= x y))))) (let ((_let_1687 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_10002 x z) (ho_10002 y z)))) (= x y))))) (let ((_let_1688 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4269 x z) (ho_4269 y z)))) (= x y))))) (let ((_let_1689 (forall ((x |u_(-> tptp.option_nat tptp.option_nat Bool)|) (y |u_(-> tptp.option_nat tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_4292 x z) (ho_4292 y z)))) (= x y))))) (let ((_let_1690 (forall ((x |u_(-> tptp.set_nat tptp.real)|) (y |u_(-> tptp.set_nat tptp.real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_4519 x z) (ho_4519 y z)))) (= x y))))) (let ((_let_1691 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.real)_ _u_(-> tptp.int tptp.real)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_8810 x z) (ho_8810 y z)))) (= x y))))) (let ((_let_1692 (forall ((x |u_(-> tptp.set_Pr1281608226676607948nteger Bool)|) (y |u_(-> tptp.set_Pr1281608226676607948nteger Bool)|)) (or (not (forall ((z tptp.set_Pr1281608226676607948nteger)) (= (ho_7750 x z) (ho_7750 y z)))) (= x y))))) (let ((_let_1693 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_4457 x z) (ho_4457 y z)))) (= x y))))) (let ((_let_1694 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_8468 x z) (ho_8468 y z)))) (= x y))))) (let ((_let_1695 (forall ((x |u_(-> tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_4428 x z) (ho_4428 y z)))) (= x y))))) (let ((_let_1696 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5083 x z) (ho_5083 y z)))) (= x y))))) (let ((_let_1697 (forall ((x |u_(-> Bool tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> Bool tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z Bool)) (= (ho_5378 x z) (ho_5378 y z)))) (= x y))))) (let ((_let_1698 (forall ((x |u_(-> tptp.num tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_4227 x z) (ho_4227 y z)))) (= x y))))) (let ((_let_1699 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (= (ho_10351 x z) (ho_10351 y z)))) (= x y))))) (let ((_let_1700 (forall ((x |u_(-> tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4464 x z) (ho_4464 y z)))) (= x y))))) (let ((_let_1701 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4408 x z) (ho_4408 y z)))) (= x y))))) (let ((_let_1702 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real Bool)_ tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_8905 x z) (ho_8905 y z)))) (= x y))))) (let ((_let_1703 (forall ((x |u_(-> tptp.int tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_5250 x z) (ho_5250 y z)))) (= x y))))) (let ((_let_1704 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4473 x z) (ho_4473 y z)))) (= x y))))) (let ((_let_1705 (forall ((x |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)|)) (= (ho_7732 x z) (ho_7732 y z)))) (= x y))))) (let ((_let_1706 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_nat tptp.list_P7037539587688870467BT_nat)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_nat tptp.list_P7037539587688870467BT_nat)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9653 x z) (ho_9653 y z)))) (= x y))))) (let ((_let_1707 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4486 x z) (ho_4486 y z)))) (= x y))))) (let ((_let_1708 (forall ((x |u_(-> tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_4584 x z) (ho_4584 y z)))) (= x y))))) (let ((_let_1709 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4717 x z) (ho_4717 y z)))) (= x y))))) (let ((_let_1710 (forall ((x |u_(-> tptp.set_nat tptp.rat)|) (y |u_(-> tptp.set_nat tptp.rat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_6089 x z) (ho_6089 y z)))) (= x y))))) (let ((_let_1711 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10316 x z) (ho_10316 y z)))) (= x y))))) (let ((_let_1712 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_5478 x z) (ho_5478 y z)))) (= x y))))) (let ((_let_1713 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_num_num)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.num)) (= (ho_9813 x z) (ho_9813 y z)))) (= x y))))) (let ((_let_1714 (forall ((x |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_9642 x z) (ho_9642 y z)))) (= x y))))) (let ((_let_1715 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_4508 x z) (ho_4508 y z)))) (= x y))))) (let ((_let_1716 (forall ((x |u_(-> tptp.rat tptp.int)|) (y |u_(-> tptp.rat tptp.int)|)) (or (not (forall ((z tptp.rat)) (= (ho_9746 x z) (ho_9746 y z)))) (= x y))))) (let ((_let_1717 (forall ((x |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.produc2285326912895808259nt_int)|) (y |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int tptp.produc2285326912895808259nt_int)|)) (or (not (forall ((z |u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)|)) (= (ho_7734 x z) (ho_7734 y z)))) (= x y))))) (let ((_let_1718 (forall ((x |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|) (y |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8827 x z) (ho_8827 y z)))) (= x y))))) (let ((_let_1719 (forall ((x |u_(-> tptp.complex _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.complex)|) (y |u_(-> tptp.complex _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_6413 x z) (ho_6413 y z)))) (= x y))))) (let ((_let_1720 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_4526 x z) (ho_4526 y z)))) (= x y))))) (let ((_let_1721 (forall ((x |u_(-> tptp.set_real tptp.real)|) (y |u_(-> tptp.set_real tptp.real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9805 x z) (ho_9805 y z)))) (= x y))))) (let ((_let_1722 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ tptp.int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_6193 x z) (ho_6193 y z)))) (= x y))))) (let ((_let_1723 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5544 x z) (ho_5544 y z)))) (= x y))))) (let ((_let_1724 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.set_nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.set_nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_9885 x z) (ho_9885 y z)))) (= x y))))) (let ((_let_1725 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10367 x z) (ho_10367 y z)))) (= x y))))) (let ((_let_1726 (forall ((x |u_(-> tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4566 x z) (ho_4566 y z)))) (= x y))))) (let ((_let_1727 (forall ((x |u_(-> _u_(-> tptp.real tptp.code_integer)_ tptp.set_real tptp.code_integer)|) (y |u_(-> _u_(-> tptp.real tptp.code_integer)_ tptp.set_real tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.real tptp.code_integer)|)) (= (ho_9828 x z) (ho_9828 y z)))) (= x y))))) (let ((_let_1728 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_6414 x z) (ho_6414 y z)))) (= x y))))) (let ((_let_1729 (forall ((x |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real Bool)_ tptp.real tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real Bool)|)) (= (ho_9149 x z) (ho_9149 y z)))) (= x y))))) (let ((_let_1730 (forall ((x |u_(-> tptp.option_nat tptp.option_nat tptp.produc4953844613479565601on_nat)|) (y |u_(-> tptp.option_nat tptp.option_nat tptp.produc4953844613479565601on_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_9493 x z) (ho_9493 y z)))) (= x y))))) (let ((_let_1731 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.complex)_ tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.complex)|)) (= (ho_6172 x z) (ho_6172 y z)))) (= x y))))) (let ((_let_1732 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_8166 x z) (ho_8166 y z)))) (= x y))))) (let ((_let_1733 (forall ((x |u_(-> tptp.option_nat Bool)|) (y |u_(-> tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_4293 x z) (ho_4293 y z)))) (= x y))))) (let ((_let_1734 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.option_nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.option_nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9423 x z) (ho_9423 y z)))) (= x y))))) (let ((_let_1735 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_7764 x z) (ho_7764 y z)))) (= x y))))) (let ((_let_1736 (forall ((x |u_(-> tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4567 x z) (ho_4567 y z)))) (= x y))))) (let ((_let_1737 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_4297 x z) (ho_4297 y z)))) (= x y))))) (let ((_let_1738 (forall ((x |u_(-> tptp.list_complex tptp.nat)|) (y |u_(-> tptp.list_complex tptp.nat)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_5163 x z) (ho_5163 y z)))) (= x y))))) (let ((_let_1739 (forall ((x |u_(-> tptp.list_complex tptp.nat tptp.complex)|) (y |u_(-> tptp.list_complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_5165 x z) (ho_5165 y z)))) (= x y))))) (let ((_let_1740 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6427 x z) (ho_6427 y z)))) (= x y))))) (let ((_let_1741 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.nat Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.complex)|)) (= (ho_8991 x z) (ho_8991 y z)))) (= x y))))) (let ((_let_1742 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_8911 x z) (ho_8911 y z)))) (= x y))))) (let ((_let_1743 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat tptp.rat)|)) (= (ho_10345 x z) (ho_10345 y z)))) (= x y))))) (let ((_let_1744 (forall ((x |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|) (y |u_(-> tptp.set_complex _u_(-> tptp.complex tptp.real)_ _u_(-> tptp.complex tptp.real)_ tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8801 x z) (ho_8801 y z)))) (= x y))))) (let ((_let_1745 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ tptp.int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_6180 x z) (ho_6180 y z)))) (= x y))))) (let ((_let_1746 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_9910 x z) (ho_9910 y z)))) (= x y))))) (let ((_let_1747 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10415 x z) (ho_10415 y z)))) (= x y))))) (let ((_let_1748 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_8062 x z) (ho_8062 y z)))) (= x y))))) (let ((_let_1749 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.product_prod_nat_nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_5200 x z) (ho_5200 y z)))) (= x y))))) (let ((_let_1750 (forall ((x |u_(-> tptp.nat tptp.num tptp.option_num)|) (y |u_(-> tptp.nat tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_4236 x z) (ho_4236 y z)))) (= x y))))) (let ((_let_1751 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_5210 x z) (ho_5210 y z)))) (= x y))))) (let ((_let_1752 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_7352 x z) (ho_7352 y z)))) (= x y))))) (let ((_let_1753 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6538 x z) (ho_6538 y z)))) (= x y))))) (let ((_let_1754 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_4406 x z) (ho_4406 y z)))) (= x y))))) (let ((_let_1755 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_complex)|) (y |u_(-> tptp.product_prod_int_int tptp.set_complex)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_9874 x z) (ho_9874 y z)))) (= x y))))) (let ((_let_1756 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_9973 x z) (ho_9973 y z)))) (= x y))))) (let ((_let_1757 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|)) (= (ho_5795 x z) (ho_5795 y z)))) (= x y))))) (let ((_let_1758 (forall ((x |u_(-> tptp.set_complex tptp.complex tptp.complex)|) (y |u_(-> tptp.set_complex tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_8562 x z) (ho_8562 y z)))) (= x y))))) (let ((_let_1759 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_8256 x z) (ho_8256 y z)))) (= x y))))) (let ((_let_1760 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_5260 x z) (ho_5260 y z)))) (= x y))))) (let ((_let_1761 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_4219 x z) (ho_4219 y z)))) (= x y))))) (let ((_let_1762 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_5268 x z) (ho_5268 y z)))) (= x y))))) (let ((_let_1763 (forall ((x |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_9162 x z) (ho_9162 y z)))) (= x y))))) (let ((_let_1764 (forall ((x |u_(-> tptp.num Bool)|) (y |u_(-> tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_5280 x z) (ho_5280 y z)))) (= x y))))) (let ((_let_1765 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6723 x z) (ho_6723 y z)))) (= x y))))) (let ((_let_1766 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.list_VEBT_VEBT tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.vEBT_VEBT tptp.list_VEBT_VEBT tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_5610 x z) (ho_5610 y z)))) (= x y))))) (let ((_let_1767 (forall ((x |u_(-> tptp.num tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_5284 x z) (ho_5284 y z)))) (= x y))))) (let ((_let_1768 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_5317 x z) (ho_5317 y z)))) (= x y))))) (let ((_let_1769 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_set_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9577 x z) (ho_9577 y z)))) (= x y))))) (let ((_let_1770 (forall ((x |u_(-> tptp.set_nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_5346 x z) (ho_5346 y z)))) (= x y))))) (let ((_let_1771 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.option_num Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.option_num Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9459 x z) (ho_9459 y z)))) (= x y))))) (let ((_let_1772 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_5351 x z) (ho_5351 y z)))) (= x y))))) (let ((_let_1773 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_8377 x z) (ho_8377 y z)))) (= x y))))) (let ((_let_1774 (forall ((x |u_(-> tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5350 x z) (ho_5350 y z)))) (= x y))))) (let ((_let_1775 (forall ((x |u_(-> tptp.set_int tptp.code_integer)|) (y |u_(-> tptp.set_int tptp.code_integer)|)) (or (not (forall ((z tptp.set_int)) (= (ho_9832 x z) (ho_9832 y z)))) (= x y))))) (let ((_let_1776 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.int)|) (y |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_4202 x z) (ho_4202 y z)))) (= x y))))) (let ((_let_1777 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_5375 x z) (ho_5375 y z)))) (= x y))))) (let ((_let_1778 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.real)|) (y |u_(-> tptp.set_nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8551 x z) (ho_8551 y z)))) (= x y))))) (let ((_let_1779 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.num)_ tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.num)_ tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.num)|)) (= (ho_5799 x z) (ho_5799 y z)))) (= x y))))) (let ((_let_1780 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_5390 x z) (ho_5390 y z)))) (= x y))))) (let ((_let_1781 (forall ((x |u_(-> tptp.set_Pr1872883991513573699nt_int Bool)|) (y |u_(-> tptp.set_Pr1872883991513573699nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr1872883991513573699nt_int)) (= (ho_7727 x z) (ho_7727 y z)))) (= x y))))) (let ((_let_1782 (forall ((x |u_(-> tptp.num tptp.int Bool)|) (y |u_(-> tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_5968 x z) (ho_5968 y z)))) (= x y))))) (let ((_let_1783 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_5379 x z) (ho_5379 y z)))) (= x y))))) (let ((_let_1784 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_6434 x z) (ho_6434 y z)))) (= x y))))) (let ((_let_1785 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4491 x z) (ho_4491 y z)))) (= x y))))) (let ((_let_1786 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5389 x z) (ho_5389 y z)))) (= x y))))) (let ((_let_1787 (forall ((x |u_(-> Bool tptp.produc6271795597528267376eger_o)|) (y |u_(-> Bool tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z Bool)) (= (ho_4609 x z) (ho_4609 y z)))) (= x y))))) (let ((_let_1788 (forall ((x |u_(-> tptp.int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_5395 x z) (ho_5395 y z)))) (= x y))))) (let ((_let_1789 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_7770 x z) (ho_7770 y z)))) (= x y))))) (let ((_let_1790 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4801 x z) (ho_4801 y z)))) (= x y))))) (let ((_let_1791 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4348 x z) (ho_4348 y z)))) (= x y))))) (let ((_let_1792 (forall ((x |u_(-> tptp.int tptp.code_integer)|) (y |u_(-> tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.int)) (= (ho_5809 x z) (ho_5809 y z)))) (= x y))))) (let ((_let_1793 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9480 x z) (ho_9480 y z)))) (= x y))))) (let ((_let_1794 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_8818 x z) (ho_8818 y z)))) (= x y))))) (let ((_let_1795 (forall ((x |u_(-> tptp.set_Pr1281608226676607948nteger tptp.set_Pr1281608226676607948nteger Bool)|) (y |u_(-> tptp.set_Pr1281608226676607948nteger tptp.set_Pr1281608226676607948nteger Bool)|)) (or (not (forall ((z tptp.set_Pr1281608226676607948nteger)) (= (ho_9936 x z) (ho_9936 y z)))) (= x y))))) (let ((_let_1796 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat)|)) (= (ho_4440 x z) (ho_4440 y z)))) (= x y))))) (let ((_let_1797 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_9989 x z) (ho_9989 y z)))) (= x y))))) (let ((_let_1798 (forall ((x |u_(-> tptp.int tptp.set_int Bool)|) (y |u_(-> tptp.int tptp.set_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_5116 x z) (ho_5116 y z)))) (= x y))))) (let ((_let_1799 (forall ((x |u_(-> tptp.set_Pr2522554150109002629et_int Bool)|) (y |u_(-> tptp.set_Pr2522554150109002629et_int Bool)|)) (or (not (forall ((z tptp.set_Pr2522554150109002629et_int)) (= (ho_10039 x z) (ho_10039 y z)))) (= x y))))) (let ((_let_1800 (forall ((x |u_(-> tptp.set_list_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_list_VEBT_VEBT)) (= (ho_9541 x z) (ho_9541 y z)))) (= x y))))) (let ((_let_1801 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_7821 x z) (ho_7821 y z)))) (= x y))))) (let ((_let_1802 (forall ((x |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z tptp.produc4471711990508489141at_nat)) (= (ho_10005 x z) (ho_10005 y z)))) (= x y))))) (let ((_let_1803 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (= (ho_10123 x z) (ho_10123 y z)))) (= x y))))) (let ((_let_1804 (forall ((x |u_(-> Bool tptp.set_int tptp.set_int tptp.set_int)|) (y |u_(-> Bool tptp.set_int tptp.set_int tptp.set_int)|)) (or (not (forall ((z Bool)) (= (ho_5901 x z) (ho_5901 y z)))) (= x y))))) (let ((_let_1805 (forall ((x |u_(-> tptp.set_real tptp.nat)|) (y |u_(-> tptp.set_real tptp.nat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_9789 x z) (ho_9789 y z)))) (= x y))))) (let ((_let_1806 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10386 x z) (ho_10386 y z)))) (= x y))))) (let ((_let_1807 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_5729 x z) (ho_5729 y z)))) (= x y))))) (let ((_let_1808 (forall ((x |u_(-> tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_8903 x z) (ho_8903 y z)))) (= x y))))) (let ((_let_1809 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real tptp.real)_ tptp.real tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real tptp.real)|)) (= (ho_5482 x z) (ho_5482 y z)))) (= x y))))) (let ((_let_1810 (forall ((x |u_(-> tptp.nat tptp.produc8025551001238799321T_VEBT)|) (y |u_(-> tptp.nat tptp.produc8025551001238799321T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_9709 x z) (ho_9709 y z)))) (= x y))))) (let ((_let_1811 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.set_int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_5550 x z) (ho_5550 y z)))) (= x y))))) (let ((_let_1812 (forall ((x |u_(-> tptp.int tptp.nat Bool)|) (y |u_(-> tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_5533 x z) (ho_5533 y z)))) (= x y))))) (let ((_let_1813 (forall ((x |u_(-> tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_4767 x z) (ho_4767 y z)))) (= x y))))) (let ((_let_1814 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.set_real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_5541 x z) (ho_5541 y z)))) (= x y))))) (let ((_let_1815 (forall ((x |u_(-> tptp.set_int tptp.set_int)|) (y |u_(-> tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_5551 x z) (ho_5551 y z)))) (= x y))))) (let ((_let_1816 (forall ((x |u_(-> _u_(-> tptp.nat tptp.num tptp.option_num)_ tptp.product_prod_nat_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.num tptp.option_num)_ tptp.product_prod_nat_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.num tptp.option_num)|)) (= (ho_5588 x z) (ho_5588 y z)))) (= x y))))) (let ((_let_1817 (forall ((x |u_(-> Bool tptp.int)|) (y |u_(-> Bool tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_5598 x z) (ho_5598 y z)))) (= x y))))) (let ((_let_1818 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat Bool)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_5602 x z) (ho_5602 y z)))) (= x y))))) (let ((_let_1819 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_5209 x z) (ho_5209 y z)))) (= x y))))) (let ((_let_1820 (forall ((x |u_(-> tptp.nat tptp.set_int)|) (y |u_(-> tptp.nat tptp.set_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_7388 x z) (ho_7388 y z)))) (= x y))))) (let ((_let_1821 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_5650 x z) (ho_5650 y z)))) (= x y))))) (let ((_let_1822 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_5645 x z) (ho_5645 y z)))) (= x y))))) (let ((_let_1823 (forall ((x |u_(-> tptp.nat tptp.complex Bool)|) (y |u_(-> tptp.nat tptp.complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5661 x z) (ho_5661 y z)))) (= x y))))) (let ((_let_1824 (forall ((x |u_(-> tptp.int tptp.int tptp.set_nat)|) (y |u_(-> tptp.int tptp.int tptp.set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_9858 x z) (ho_9858 y z)))) (= x y))))) (let ((_let_1825 (forall ((x |u_(-> tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_4442 x z) (ho_4442 y z)))) (= x y))))) (let ((_let_1826 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex Bool)|) (y |u_(-> tptp.complex tptp.nat tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_5663 x z) (ho_5663 y z)))) (= x y))))) (let ((_let_1827 (forall ((x |u_(-> tptp.real tptp.filter_real)|) (y |u_(-> tptp.real tptp.filter_real)|)) (or (not (forall ((z tptp.real)) (= (ho_10194 x z) (ho_10194 y z)))) (= x y))))) (let ((_let_1828 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.complex tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9130 x z) (ho_9130 y z)))) (= x y))))) (let ((_let_1829 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_5725 x z) (ho_5725 y z)))) (= x y))))) (let ((_let_1830 (forall ((x |u_(-> tptp.produc8306885398267862888on_nat Bool)|) (y |u_(-> tptp.produc8306885398267862888on_nat Bool)|)) (or (not (forall ((z tptp.produc8306885398267862888on_nat)) (= (ho_10023 x z) (ho_10023 y z)))) (= x y))))) (let ((_let_1831 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ tptp.set_int tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ tptp.set_int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_9807 x z) (ho_9807 y z)))) (= x y))))) (let ((_let_1832 (forall ((x |u_(-> tptp.set_Pr1872883991513573699nt_int _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr1872883991513573699nt_int _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr1872883991513573699nt_int)) (= (ho_7720 x z) (ho_7720 y z)))) (= x y))))) (let ((_let_1833 (forall ((x |u_(-> tptp.list_int tptp.set_list_int Bool)|) (y |u_(-> tptp.list_int tptp.set_list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_9614 x z) (ho_9614 y z)))) (= x y))))) (let ((_let_1834 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4725 x z) (ho_4725 y z)))) (= x y))))) (let ((_let_1835 (forall ((x |u_(-> tptp.set_Pr8056137968301705908nteger Bool)|) (y |u_(-> tptp.set_Pr8056137968301705908nteger Bool)|)) (or (not (forall ((z tptp.set_Pr8056137968301705908nteger)) (= (ho_7761 x z) (ho_7761 y z)))) (= x y))))) (let ((_let_1836 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.nat tptp.int Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.nat tptp.int Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_9098 x z) (ho_9098 y z)))) (= x y))))) (let ((_let_1837 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.set_list_nat)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.set_list_nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_9454 x z) (ho_9454 y z)))) (= x y))))) (let ((_let_1838 (forall ((x |u_(-> tptp.rat tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.rat tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.rat)) (= (ho_5736 x z) (ho_5736 y z)))) (= x y))))) (let ((_let_1839 (forall ((x |u_(-> _u_(-> tptp.option_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option_num Bool)|)) (= (ho_9413 x z) (ho_9413 y z)))) (= x y))))) (let ((_let_1840 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_9975 x z) (ho_9975 y z)))) (= x y))))) (let ((_let_1841 (forall ((x |u_(-> tptp.complex tptp.nat tptp.real)|) (y |u_(-> tptp.complex tptp.nat tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_5759 x z) (ho_5759 y z)))) (= x y))))) (let ((_let_1842 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.rat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat tptp.real)|)) (= (ho_7349 x z) (ho_7349 y z)))) (= x y))))) (let ((_let_1843 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real tptp.complex)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_6183 x z) (ho_6183 y z)))) (= x y))))) (let ((_let_1844 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5773 x z) (ho_5773 y z)))) (= x y))))) (let ((_let_1845 (forall ((x |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc6271795597528267376eger_o)) (= (ho_5791 x z) (ho_5791 y z)))) (= x y))))) (let ((_let_1846 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_9040 x z) (ho_9040 y z)))) (= x y))))) (let ((_let_1847 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int)|) (y |u_(-> tptp.list_int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_4640 x z) (ho_4640 y z)))) (= x y))))) (let ((_let_1848 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_5788 x z) (ho_5788 y z)))) (= x y))))) (let ((_let_1849 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_8897 x z) (ho_8897 y z)))) (= x y))))) (let ((_let_1850 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_10000 x z) (ho_10000 y z)))) (= x y))))) (let ((_let_1851 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)_ tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)_ tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o)|)) (= (ho_5787 x z) (ho_5787 y z)))) (= x y))))) (let ((_let_1852 (forall ((x |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc6271795597528267376eger_o)) (= (ho_5792 x z) (ho_5792 y z)))) (= x y))))) (let ((_let_1853 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (= (ho_10284 x z) (ho_10284 y z)))) (= x y))))) (let ((_let_1854 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6166 x z) (ho_6166 y z)))) (= x y))))) (let ((_let_1855 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat)_ _u_(-> tptp.real Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat)|)) (= (ho_9044 x z) (ho_9044 y z)))) (= x y))))) (let ((_let_1856 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_5796 x z) (ho_5796 y z)))) (= x y))))) (let ((_let_1857 (forall ((x |u_(-> _u_(-> tptp.real tptp.int tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.int tptp.real)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.int Bool)_ tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int tptp.real)|)) (= (ho_8986 x z) (ho_8986 y z)))) (= x y))))) (let ((_let_1858 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_8909 x z) (ho_8909 y z)))) (= x y))))) (let ((_let_1859 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_5813 x z) (ho_5813 y z)))) (= x y))))) (let ((_let_1860 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6244 x z) (ho_6244 y z)))) (= x y))))) (let ((_let_1861 (forall ((x |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_5812 x z) (ho_5812 y z)))) (= x y))))) (let ((_let_1862 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_5815 x z) (ho_5815 y z)))) (= x y))))) (let ((_let_1863 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_8626 x z) (ho_8626 y z)))) (= x y))))) (let ((_let_1864 (forall ((x |u_(-> tptp.complex _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> tptp.complex _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_7580 x z) (ho_7580 y z)))) (= x y))))) (let ((_let_1865 (forall ((x |u_(-> tptp.num tptp.nat Bool)|) (y |u_(-> tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_5829 x z) (ho_5829 y z)))) (= x y))))) (let ((_let_1866 (forall ((x |u_(-> Bool tptp.produc334124729049499915VEBT_o)|) (y |u_(-> Bool tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z Bool)) (= (ho_9645 x z) (ho_9645 y z)))) (= x y))))) (let ((_let_1867 (forall ((x |u_(-> tptp.int tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_5896 x z) (ho_5896 y z)))) (= x y))))) (let ((_let_1868 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.real)|)) (= (ho_7342 x z) (ho_7342 y z)))) (= x y))))) (let ((_let_1869 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_5902 x z) (ho_5902 y z)))) (= x y))))) (let ((_let_1870 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_9522 x z) (ho_9522 y z)))) (= x y))))) (let ((_let_1871 (forall ((x |u_(-> Bool tptp.complex tptp.complex tptp.complex)|) (y |u_(-> Bool tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z Bool)) (= (ho_4775 x z) (ho_4775 y z)))) (= x y))))) (let ((_let_1872 (forall ((x |u_(-> tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5920 x z) (ho_5920 y z)))) (= x y))))) (let ((_let_1873 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10393 x z) (ho_10393 y z)))) (= x y))))) (let ((_let_1874 (forall ((x |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat tptp.product_prod_o_int)|) (y |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.list_P3795440434834930179_o_int)) (= (ho_9699 x z) (ho_9699 y z)))) (= x y))))) (let ((_let_1875 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_9011 x z) (ho_9011 y z)))) (= x y))))) (let ((_let_1876 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_5927 x z) (ho_5927 y z)))) (= x y))))) (let ((_let_1877 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_6406 x z) (ho_6406 y z)))) (= x y))))) (let ((_let_1878 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_4804 x z) (ho_4804 y z)))) (= x y))))) (let ((_let_1879 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_4255 x z) (ho_4255 y z)))) (= x y))))) (let ((_let_1880 (forall ((x |u_(-> tptp.real tptp.int tptp.int Bool)|) (y |u_(-> tptp.real tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_5949 x z) (ho_5949 y z)))) (= x y))))) (let ((_let_1881 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_int)|) (y |u_(-> tptp.product_prod_int_int tptp.set_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_9870 x z) (ho_9870 y z)))) (= x y))))) (let ((_let_1882 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10294 x z) (ho_10294 y z)))) (= x y))))) (let ((_let_1883 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_5997 x z) (ho_5997 y z)))) (= x y))))) (let ((_let_1884 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6001 x z) (ho_6001 y z)))) (= x y))))) (let ((_let_1885 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_9847 x z) (ho_9847 y z)))) (= x y))))) (let ((_let_1886 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat tptp.rat)|)) (= (ho_6011 x z) (ho_6011 y z)))) (= x y))))) (let ((_let_1887 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex tptp.complex)_ tptp.nat tptp.nat tptp.complex tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex tptp.complex)_ tptp.nat tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex tptp.complex)|)) (= (ho_6017 x z) (ho_6017 y z)))) (= x y))))) (let ((_let_1888 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_9234 x z) (ho_9234 y z)))) (= x y))))) (let ((_let_1889 (forall ((x |u_(-> tptp.set_real tptp.real Bool)|) (y |u_(-> tptp.set_real tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_5133 x z) (ho_5133 y z)))) (= x y))))) (let ((_let_1890 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_5141 x z) (ho_5141 y z)))) (= x y))))) (let ((_let_1891 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_6079 x z) (ho_6079 y z)))) (= x y))))) (let ((_let_1892 (forall ((x |u_(-> tptp.num tptp.set_num Bool)|) (y |u_(-> tptp.num tptp.set_num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_9591 x z) (ho_9591 y z)))) (= x y))))) (let ((_let_1893 (forall ((x |u_(-> tptp.set_complex tptp.produc8064648209034914857omplex)|) (y |u_(-> tptp.set_complex tptp.produc8064648209034914857omplex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_10043 x z) (ho_10043 y z)))) (= x y))))) (let ((_let_1894 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_6084 x z) (ho_6084 y z)))) (= x y))))) (let ((_let_1895 (forall ((x |u_(-> tptp.produc8763457246119570046nteger tptp.set_Pr8056137968301705908nteger Bool)|) (y |u_(-> tptp.produc8763457246119570046nteger tptp.set_Pr8056137968301705908nteger Bool)|)) (or (not (forall ((z tptp.produc8763457246119570046nteger)) (= (ho_7760 x z) (ho_7760 y z)))) (= x y))))) (let ((_let_1896 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6088 x z) (ho_6088 y z)))) (= x y))))) (let ((_let_1897 (forall ((x |u_(-> tptp.produc1908205239877642774nteger tptp.set_Pr1281608226676607948nteger Bool)|) (y |u_(-> tptp.produc1908205239877642774nteger tptp.set_Pr1281608226676607948nteger Bool)|)) (or (not (forall ((z tptp.produc1908205239877642774nteger)) (= (ho_7749 x z) (ho_7749 y z)))) (= x y))))) (let ((_let_1898 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.complex)|) (y |u_(-> tptp.product_prod_nat_nat tptp.complex)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_6169 x z) (ho_6169 y z)))) (= x y))))) (let ((_let_1899 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_5122 x z) (ho_5122 y z)))) (= x y))))) (let ((_let_1900 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_6173 x z) (ho_6173 y z)))) (= x y))))) (let ((_let_1901 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_6176 x z) (ho_6176 y z)))) (= x y))))) (let ((_let_1902 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_6181 x z) (ho_6181 y z)))) (= x y))))) (let ((_let_1903 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat Bool)|) (y |u_(-> tptp.extended_enat tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_9054 x z) (ho_9054 y z)))) (= x y))))) (let ((_let_1904 (forall ((x |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.complex)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.complex)|)) (= (ho_6184 x z) (ho_6184 y z)))) (= x y))))) (let ((_let_1905 (forall ((x |u_(-> tptp.num tptp.real)|) (y |u_(-> tptp.num tptp.real)|)) (or (not (forall ((z tptp.num)) (= (ho_4247 x z) (ho_4247 y z)))) (= x y))))) (let ((_let_1906 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.product_prod_nat_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.real)|)) (= (ho_6187 x z) (ho_6187 y z)))) (= x y))))) (let ((_let_1907 (forall ((x |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|) (y |u_(-> _u_(-> tptp.complex tptp.real)_ tptp.complex tptp.real)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.real)|)) (= (ho_6190 x z) (ho_6190 y z)))) (= x y))))) (let ((_let_1908 (forall ((x |u_(-> tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_5196 x z) (ho_5196 y z)))) (= x y))))) (let ((_let_1909 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_10359 x z) (ho_10359 y z)))) (= x y))))) (let ((_let_1910 (forall ((x |u_(-> tptp.real tptp.code_integer)|) (y |u_(-> tptp.real tptp.code_integer)|)) (or (not (forall ((z tptp.real)) (= (ho_8470 x z) (ho_8470 y z)))) (= x y))))) (let ((_let_1911 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_6547 x z) (ho_6547 y z)))) (= x y))))) (let ((_let_1912 (forall ((x |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z |u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)|)) (= (ho_7743 x z) (ho_7743 y z)))) (= x y))))) (let ((_let_1913 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_6263 x z) (ho_6263 y z)))) (= x y))))) (let ((_let_1914 (forall ((x |u_(-> _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.complex)_ _u_(-> tptp.int tptp.complex)_ tptp.int tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.complex)|)) (= (ho_6179 x z) (ho_6179 y z)))) (= x y))))) (let ((_let_1915 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_6407 x z) (ho_6407 y z)))) (= x y))))) (let ((_let_1916 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_6376 x z) (ho_6376 y z)))) (= x y))))) (let ((_let_1917 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9163 x z) (ho_9163 y z)))) (= x y))))) (let ((_let_1918 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_7393 x z) (ho_7393 y z)))) (= x y))))) (let ((_let_1919 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_5441 x z) (ho_5441 y z)))) (= x y))))) (let ((_let_1920 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_4307 x z) (ho_4307 y z)))) (= x y))))) (let ((_let_1921 (forall ((x |u_(-> tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_7744 x z) (ho_7744 y z)))) (= x y))))) (let ((_let_1922 (forall ((x |u_(-> tptp.produc2285326912895808259nt_int tptp.set_Pr9222295170931077689nt_int Bool)|) (y |u_(-> tptp.produc2285326912895808259nt_int tptp.set_Pr9222295170931077689nt_int Bool)|)) (or (not (forall ((z tptp.produc2285326912895808259nt_int)) (= (ho_7737 x z) (ho_7737 y z)))) (= x y))))) (let ((_let_1923 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_8784 x z) (ho_8784 y z)))) (= x y))))) (let ((_let_1924 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_4431 x z) (ho_4431 y z)))) (= x y))))) (let ((_let_1925 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_5734 x z) (ho_5734 y z)))) (= x y))))) (let ((_let_1926 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_6424 x z) (ho_6424 y z)))) (= x y))))) (let ((_let_1927 (forall ((x |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|) (y |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|)) (or (not (forall ((z |u_(-> tptp.set_int Bool)|)) (= (ho_9567 x z) (ho_9567 y z)))) (= x y))))) (let ((_let_1928 (forall ((x |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.real Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real Bool)|)) (= (ho_9139 x z) (ho_9139 y z)))) (= x y))))) (let ((_let_1929 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6642 x z) (ho_6642 y z)))) (= x y))))) (let ((_let_1930 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_8001 x z) (ho_8001 y z)))) (= x y))))) (let ((_let_1931 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4551 x z) (ho_4551 y z)))) (= x y))))) (let ((_let_1932 (forall ((x |u_(-> tptp.set_nat tptp.complex)|) (y |u_(-> tptp.set_nat tptp.complex)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_6495 x z) (ho_6495 y z)))) (= x y))))) (let ((_let_1933 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_9610 x z) (ho_9610 y z)))) (= x y))))) (let ((_let_1934 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.set_nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.set_nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6494 x z) (ho_6494 y z)))) (= x y))))) (let ((_let_1935 (forall ((x |u_(-> tptp.complex tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_6497 x z) (ho_6497 y z)))) (= x y))))) (let ((_let_1936 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_6533 x z) (ho_6533 y z)))) (= x y))))) (let ((_let_1937 (forall ((x |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6540 x z) (ho_6540 y z)))) (= x y))))) (let ((_let_1938 (forall ((x |u_(-> tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_4318 x z) (ho_4318 y z)))) (= x y))))) (let ((_let_1939 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex tptp.nat tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6546 x z) (ho_6546 y z)))) (= x y))))) (let ((_let_1940 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.set_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_int)|)) (= (ho_7390 x z) (ho_7390 y z)))) (= x y))))) (let ((_let_1941 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_5648 x z) (ho_5648 y z)))) (= x y))))) (let ((_let_1942 (forall ((x |u_(-> tptp.nat tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_6561 x z) (ho_6561 y z)))) (= x y))))) (let ((_let_1943 (forall ((x |u_(-> _u_(-> tptp.vEBT_VEBT Bool)_ tptp.set_VEBT_VEBT)|) (y |u_(-> _u_(-> tptp.vEBT_VEBT Bool)_ tptp.set_VEBT_VEBT)|)) (or (not (forall ((z |u_(-> tptp.vEBT_VEBT Bool)|)) (= (ho_5605 x z) (ho_5605 y z)))) (= x y))))) (let ((_let_1944 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_6820 x z) (ho_6820 y z)))) (= x y))))) (let ((_let_1945 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_6620 x z) (ho_6620 y z)))) (= x y))))) (let ((_let_1946 (forall ((x |u_(-> tptp.int tptp.set_real)|) (y |u_(-> tptp.int tptp.set_real)|)) (or (not (forall ((z tptp.int)) (= (ho_9867 x z) (ho_9867 y z)))) (= x y))))) (let ((_let_1947 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_10323 x z) (ho_10323 y z)))) (= x y))))) (let ((_let_1948 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_6637 x z) (ho_6637 y z)))) (= x y))))) (let ((_let_1949 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_8814 x z) (ho_8814 y z)))) (= x y))))) (let ((_let_1950 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (= (ho_10421 x z) (ho_10421 y z)))) (= x y))))) (let ((_let_1951 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6641 x z) (ho_6641 y z)))) (= x y))))) (let ((_let_1952 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ _u_(-> tptp.complex tptp.complex)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_8832 x z) (ho_8832 y z)))) (= x y))))) (let ((_let_1953 (forall ((x |u_(-> tptp.num tptp.nat tptp.rat)|) (y |u_(-> tptp.num tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_8140 x z) (ho_8140 y z)))) (= x y))))) (let ((_let_1954 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_6702 x z) (ho_6702 y z)))) (= x y))))) (let ((_let_1955 (forall ((x |u_(-> tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_5376 x z) (ho_5376 y z)))) (= x y))))) (let ((_let_1956 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.rat)|)) (= (ho_10353 x z) (ho_10353 y z)))) (= x y))))) (let ((_let_1957 (forall ((x |u_(-> tptp.nat tptp.real Bool)|) (y |u_(-> tptp.nat tptp.real Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_6821 x z) (ho_6821 y z)))) (= x y))))) (let ((_let_1958 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_9981 x z) (ho_9981 y z)))) (= x y))))) (let ((_let_1959 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10424 x z) (ho_10424 y z)))) (= x y))))) (let ((_let_1960 (forall ((x |u_(-> tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_4611 x z) (ho_4611 y z)))) (= x y))))) (let ((_let_1961 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_9631 x z) (ho_9631 y z)))) (= x y))))) (let ((_let_1962 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.nat tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_6823 x z) (ho_6823 y z)))) (= x y))))) (let ((_let_1963 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_8475 x z) (ho_8475 y z)))) (= x y))))) (let ((_let_1964 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10320 x z) (ho_10320 y z)))) (= x y))))) (let ((_let_1965 (forall ((x |u_(-> tptp.set_int tptp.set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_7023 x z) (ho_7023 y z)))) (= x y))))) (let ((_let_1966 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_10410 x z) (ho_10410 y z)))) (= x y))))) (let ((_let_1967 (forall ((x |u_(-> tptp.num tptp.nat tptp.real)|) (y |u_(-> tptp.num tptp.nat tptp.real)|)) (or (not (forall ((z tptp.num)) (= (ho_7290 x z) (ho_7290 y z)))) (= x y))))) (let ((_let_1968 (forall ((x |u_(-> tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_9561 x z) (ho_9561 y z)))) (= x y))))) (let ((_let_1969 (forall ((x |u_(-> tptp.real tptp.filter_real Bool)|) (y |u_(-> tptp.real tptp.filter_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_10187 x z) (ho_10187 y z)))) (= x y))))) (let ((_let_1970 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_8900 x z) (ho_8900 y z)))) (= x y))))) (let ((_let_1971 (forall ((x |u_(-> tptp.num tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_5057 x z) (ho_5057 y z)))) (= x y))))) (let ((_let_1972 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.int)_ tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.int)_ tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.int)|)) (= (ho_5805 x z) (ho_5805 y z)))) (= x y))))) (let ((_let_1973 (forall ((x |u_(-> tptp.nat tptp.complex tptp.real)|) (y |u_(-> tptp.nat tptp.complex tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_7354 x z) (ho_7354 y z)))) (= x y))))) (let ((_let_1974 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10276 x z) (ho_10276 y z)))) (= x y))))) (let ((_let_1975 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_5643 x z) (ho_5643 y z)))) (= x y))))) (let ((_let_1976 (forall ((x |u_(-> _u_(-> tptp.nat tptp.num)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.num)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.num)|)) (= (ho_7384 x z) (ho_7384 y z)))) (= x y))))) (let ((_let_1977 (forall ((x |u_(-> tptp.real tptp.set_real Bool)|) (y |u_(-> tptp.real tptp.set_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_5135 x z) (ho_5135 y z)))) (= x y))))) (let ((_let_1978 (forall ((x |u_(-> tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_7995 x z) (ho_7995 y z)))) (= x y))))) (let ((_let_1979 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_7479 x z) (ho_7479 y z)))) (= x y))))) (let ((_let_1980 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.complex)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.complex)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_9914 x z) (ho_9914 y z)))) (= x y))))) (let ((_let_1981 (forall ((x |u_(-> tptp.int tptp.option6357759511663192854e_term)|) (y |u_(-> tptp.int tptp.option6357759511663192854e_term)|)) (or (not (forall ((z tptp.int)) (= (ho_7718 x z) (ho_7718 y z)))) (= x y))))) (let ((_let_1982 (forall ((x |u_(-> _u_(-> tptp.real tptp.real tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real tptp.complex)_ _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real tptp.complex)|)) (= (ho_9009 x z) (ho_9009 y z)))) (= x y))))) (let ((_let_1983 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.filter_real tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.filter_real tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_10199 x z) (ho_10199 y z)))) (= x y))))) (let ((_let_1984 (forall ((x |u_(-> tptp.nat Bool Bool)|) (y |u_(-> tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9307 x z) (ho_9307 y z)))) (= x y))))) (let ((_let_1985 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_4518 x z) (ho_4518 y z)))) (= x y))))) (let ((_let_1986 (forall ((x |u_(-> tptp.produc7773217078559923341nt_int tptp.set_Pr1872883991513573699nt_int Bool)|) (y |u_(-> tptp.produc7773217078559923341nt_int tptp.set_Pr1872883991513573699nt_int Bool)|)) (or (not (forall ((z tptp.produc7773217078559923341nt_int)) (= (ho_7726 x z) (ho_7726 y z)))) (= x y))))) (let ((_let_1987 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_4811 x z) (ho_4811 y z)))) (= x y))))) (let ((_let_1988 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_4838 x z) (ho_4838 y z)))) (= x y))))) (let ((_let_1989 (forall ((x |u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)|) (y |u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)|)) (or (not (forall ((z tptp.produc8551481072490612790e_term)) (= (ho_7729 x z) (ho_7729 y z)))) (= x y))))) (let ((_let_1990 (forall ((x |u_(-> tptp.list_int tptp.int tptp.int)|) (y |u_(-> tptp.list_int tptp.int tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_10263 x z) (ho_10263 y z)))) (= x y))))) (let ((_let_1991 (forall ((x |u_(-> tptp.set_Pr9222295170931077689nt_int Bool)|) (y |u_(-> tptp.set_Pr9222295170931077689nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr9222295170931077689nt_int)) (= (ho_7738 x z) (ho_7738 y z)))) (= x y))))) (let ((_let_1992 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_5775 x z) (ho_5775 y z)))) (= x y))))) (let ((_let_1993 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_7747 x z) (ho_7747 y z)))) (= x y))))) (let ((_let_1994 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_5519 x z) (ho_5519 y z)))) (= x y))))) (let ((_let_1995 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.option_num tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.option_num tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_9491 x z) (ho_9491 y z)))) (= x y))))) (let ((_let_1996 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_7758 x z) (ho_7758 y z)))) (= x y))))) (let ((_let_1997 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.option6357759511663192854e_term)|)) (= (ho_7757 x z) (ho_7757 y z)))) (= x y))))) (let ((_let_1998 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat)_ _u_(-> tptp.real tptp.nat)_ tptp.real tptp.nat)|) (y |u_(-> _u_(-> tptp.real tptp.nat)_ _u_(-> tptp.real tptp.nat)_ tptp.real tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat)|)) (= (ho_7997 x z) (ho_7997 y z)))) (= x y))))) (let ((_let_1999 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_8002 x z) (ho_8002 y z)))) (= x y))))) (let ((_let_2000 (forall ((x |u_(-> tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_9161 x z) (ho_9161 y z)))) (= x y))))) (let ((_let_2001 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ tptp.real tptp.real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_4945 x z) (ho_4945 y z)))) (= x y))))) (let ((_let_2002 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.real)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.real)|)) (= (ho_6753 x z) (ho_6753 y z)))) (= x y))))) (let ((_let_2003 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_10136 x z) (ho_10136 y z)))) (= x y))))) (let ((_let_2004 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.set_Pr1261947904930325089at_nat tptp.real)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.real)_ tptp.set_Pr1261947904930325089at_nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.real)|)) (= (ho_9916 x z) (ho_9916 y z)))) (= x y))))) (let ((_let_2005 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ tptp.set_rat)|) (y |u_(-> _u_(-> tptp.rat Bool)_ tptp.set_rat)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_9920 x z) (ho_9920 y z)))) (= x y))))) (let ((_let_2006 (forall ((x |u_(-> _u_(-> tptp.num Bool)_ tptp.set_num)|) (y |u_(-> _u_(-> tptp.num Bool)_ tptp.set_num)|)) (or (not (forall ((z |u_(-> tptp.num Bool)|)) (= (ho_9922 x z) (ho_9922 y z)))) (= x y))))) (let ((_let_2007 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_9926 x z) (ho_9926 y z)))) (= x y))))) (let ((_let_2008 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_9925 x z) (ho_9925 y z)))) (= x y))))) (let ((_let_2009 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9929 x z) (ho_9929 y z)))) (= x y))))) (let ((_let_2010 (forall ((x |u_(-> tptp.set_Pr8056137968301705908nteger tptp.set_Pr8056137968301705908nteger Bool)|) (y |u_(-> tptp.set_Pr8056137968301705908nteger tptp.set_Pr8056137968301705908nteger Bool)|)) (or (not (forall ((z tptp.set_Pr8056137968301705908nteger)) (= (ho_9931 x z) (ho_9931 y z)))) (= x y))))) (let ((_let_2011 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9934 x z) (ho_9934 y z)))) (= x y))))) (let ((_let_2012 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ _u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)_ tptp.produc8923325533196201883nteger Bool)|)) (= (ho_9933 x z) (ho_9933 y z)))) (= x y))))) (let ((_let_2013 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9939 x z) (ho_9939 y z)))) (= x y))))) (let ((_let_2014 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9938 x z) (ho_9938 y z)))) (= x y))))) (let ((_let_2015 (forall ((x |u_(-> tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int Bool)|) (y |u_(-> tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr9222295170931077689nt_int)) (= (ho_9941 x z) (ho_9941 y z)))) (= x y))))) (let ((_let_2016 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.option6357759511663192854e_term)_ tptp.product_prod_int_int Bool)|)) (= (ho_9944 x z) (ho_9944 y z)))) (= x y))))) (let ((_let_2017 (forall ((x |u_(-> tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int Bool)|) (y |u_(-> tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr1872883991513573699nt_int)) (= (ho_9946 x z) (ho_9946 y z)))) (= x y))))) (let ((_let_2018 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_9948 x z) (ho_9948 y z)))) (= x y))))) (let ((_let_2019 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_9952 x z) (ho_9952 y z)))) (= x y))))) (let ((_let_2020 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_9954 x z) (ho_9954 y z)))) (= x y))))) (let ((_let_2021 (forall ((x |u_(-> tptp.product_prod_num_num Bool)|) (y |u_(-> tptp.product_prod_num_num Bool)|)) (or (not (forall ((z tptp.product_prod_num_num)) (= (ho_9992 x z) (ho_9992 y z)))) (= x y))))) (let ((_let_2022 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ tptp.product_prod_num_num Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ tptp.product_prod_num_num Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_9957 x z) (ho_9957 y z)))) (= x y))))) (let ((_let_2023 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num Bool)|)) (= (ho_9960 x z) (ho_9960 y z)))) (= x y))))) (let ((_let_2024 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10313 x z) (ho_10313 y z)))) (= x y))))) (let ((_let_2025 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num Bool)|)) (= (ho_9959 x z) (ho_9959 y z)))) (= x y))))) (let ((_let_2026 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_9963 x z) (ho_9963 y z)))) (= x y))))) (let ((_let_2027 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_10435 x z) (ho_10435 y z)))) (= x y))))) (let ((_let_2028 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_9962 x z) (ho_9962 y z)))) (= x y))))) (let ((_let_2029 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_9965 x z) (ho_9965 y z)))) (= x y))))) (let ((_let_2030 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_9968 x z) (ho_9968 y z)))) (= x y))))) (let ((_let_2031 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|)) (= (ho_10333 x z) (ho_10333 y z)))) (= x y))))) (let ((_let_2032 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_9967 x z) (ho_9967 y z)))) (= x y))))) (let ((_let_2033 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_9970 x z) (ho_9970 y z)))) (= x y))))) (let ((_let_2034 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_9972 x z) (ho_9972 y z)))) (= x y))))) (let ((_let_2035 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_9980 x z) (ho_9980 y z)))) (= x y))))) (let ((_let_2036 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (= (ho_9984 x z) (ho_9984 y z)))) (= x y))))) (let ((_let_2037 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.list_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.list_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (= (ho_9983 x z) (ho_9983 y z)))) (= x y))))) (let ((_let_2038 (forall ((x |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.complex)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.complex)|)) (= (ho_9987 x z) (ho_9987 y z)))) (= x y))))) (let ((_let_2039 (forall ((x |u_(-> _u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)_ tptp.vEBT_VEBT Bool)|) (y |u_(-> _u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)_ tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool)|)) (= (ho_9995 x z) (ho_9995 y z)))) (= x y))))) (let ((_let_2040 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_9999 x z) (ho_9999 y z)))) (= x y))))) (let ((_let_2041 (forall ((x |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z tptp.produc7248412053542808358at_nat)) (= (ho_10003 x z) (ho_10003 y z)))) (= x y))))) (let ((_let_2042 (forall ((x |u_(-> tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z tptp.produc4471711990508489141at_nat)) (= (ho_10008 x z) (ho_10008 y z)))) (= x y))))) (let ((_let_2043 (forall ((x |u_(-> _u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)_ tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)_ tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|)) (= (ho_10007 x z) (ho_10007 y z)))) (= x y))))) (let ((_let_2044 (forall ((x |u_(-> tptp.produc5542196010084753463at_nat Bool)|) (y |u_(-> tptp.produc5542196010084753463at_nat Bool)|)) (or (not (forall ((z tptp.produc5542196010084753463at_nat)) (= (ho_10013 x z) (ho_10013 y z)))) (= x y))))) (let ((_let_2045 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10372 x z) (ho_10372 y z)))) (= x y))))) (let ((_let_2046 (forall ((x |u_(-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool)|) (y |u_(-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool)|)) (or (not (forall ((z tptp.produc5542196010084753463at_nat)) (= (ho_10010 x z) (ho_10010 y z)))) (= x y))))) (let ((_let_2047 (forall ((x |u_(-> _u_(-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool)_ tptp.produc5542196010084753463at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool)_ tptp.produc5542196010084753463at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool)|)) (= (ho_10012 x z) (ho_10012 y z)))) (= x y))))) (let ((_let_2048 (forall ((x |u_(-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool)|) (y |u_(-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool)|)) (or (not (forall ((z tptp.produc1193250871479095198on_num)) (= (ho_10015 x z) (ho_10015 y z)))) (= x y))))) (let ((_let_2049 (forall ((x |u_(-> _u_(-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool)_ tptp.produc1193250871479095198on_num Bool)|) (y |u_(-> _u_(-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool)_ tptp.produc1193250871479095198on_num Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool)|)) (= (ho_10017 x z) (ho_10017 y z)))) (= x y))))) (let ((_let_2050 (forall ((x |u_(-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool)|) (y |u_(-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool)|)) (or (not (forall ((z tptp.produc8306885398267862888on_nat)) (= (ho_10020 x z) (ho_10020 y z)))) (= x y))))) (let ((_let_2051 (forall ((x |u_(-> _u_(-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool)_ tptp.produc8306885398267862888on_nat Bool)|) (y |u_(-> _u_(-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool)_ tptp.produc8306885398267862888on_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool)|)) (= (ho_10022 x z) (ho_10022 y z)))) (= x y))))) (let ((_let_2052 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10025 x z) (ho_10025 y z)))) (= x y))))) (let ((_let_2053 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_10027 x z) (ho_10027 y z)))) (= x y))))) (let ((_let_2054 (forall ((x |u_(-> tptp.set_Pr5488025237498180813et_nat Bool)|) (y |u_(-> tptp.set_Pr5488025237498180813et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr5488025237498180813et_nat)) (= (ho_10033 x z) (ho_10033 y z)))) (= x y))))) (let ((_let_2055 (forall ((x |u_(-> tptp.set_nat tptp.produc7819656566062154093et_nat)|) (y |u_(-> tptp.set_nat tptp.produc7819656566062154093et_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10030 x z) (ho_10030 y z)))) (= x y))))) (let ((_let_2056 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.produc7819656566062154093et_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.produc7819656566062154093et_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10029 x z) (ho_10029 y z)))) (= x y))))) (let ((_let_2057 (forall ((x |u_(-> tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat Bool)|) (y |u_(-> tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat Bool)|)) (or (not (forall ((z tptp.produc7819656566062154093et_nat)) (= (ho_10032 x z) (ho_10032 y z)))) (= x y))))) (let ((_let_2058 (forall ((x |u_(-> tptp.set_int tptp.produc2115011035271226405et_int)|) (y |u_(-> tptp.set_int tptp.produc2115011035271226405et_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_10036 x z) (ho_10036 y z)))) (= x y))))) (let ((_let_2059 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.produc2115011035271226405et_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.produc2115011035271226405et_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_10035 x z) (ho_10035 y z)))) (= x y))))) (let ((_let_2060 (forall ((x |u_(-> tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int Bool)|) (y |u_(-> tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int Bool)|)) (or (not (forall ((z tptp.produc2115011035271226405et_int)) (= (ho_10038 x z) (ho_10038 y z)))) (= x y))))) (let ((_let_2061 (forall ((x |u_(-> tptp.set_Pr6308028481084910985omplex Bool)|) (y |u_(-> tptp.set_Pr6308028481084910985omplex Bool)|)) (or (not (forall ((z tptp.set_Pr6308028481084910985omplex)) (= (ho_10046 x z) (ho_10046 y z)))) (= x y))))) (let ((_let_2062 (forall ((x |u_(-> tptp.set_complex tptp.set_complex tptp.produc8064648209034914857omplex)|) (y |u_(-> tptp.set_complex tptp.set_complex tptp.produc8064648209034914857omplex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_10042 x z) (ho_10042 y z)))) (= x y))))) (let ((_let_2063 (forall ((x |u_(-> tptp.produc8064648209034914857omplex tptp.set_Pr6308028481084910985omplex Bool)|) (y |u_(-> tptp.produc8064648209034914857omplex tptp.set_Pr6308028481084910985omplex Bool)|)) (or (not (forall ((z tptp.produc8064648209034914857omplex)) (= (ho_10045 x z) (ho_10045 y z)))) (= x y))))) (let ((_let_2064 (forall ((x |u_(-> tptp.set_nat tptp.set_complex Bool)|) (y |u_(-> tptp.set_nat tptp.set_complex Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10080 x z) (ho_10080 y z)))) (= x y))))) (let ((_let_2065 (forall ((x |u_(-> tptp.list_o tptp.int)|) (y |u_(-> tptp.list_o tptp.int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_10093 x z) (ho_10093 y z)))) (= x y))))) (let ((_let_2066 (forall ((x |u_(-> tptp.int tptp.list_o tptp.int)|) (y |u_(-> tptp.int tptp.list_o tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_10092 x z) (ho_10092 y z)))) (= x y))))) (let ((_let_2067 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ tptp.int tptp.list_o tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ tptp.int tptp.list_o tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_10091 x z) (ho_10091 y z)))) (= x y))))) (let ((_let_2068 (forall ((x |u_(-> _u_(-> tptp.vEBT_VEBT tptp.nat)_ tptp.list_VEBT_VEBT tptp.nat)|) (y |u_(-> _u_(-> tptp.vEBT_VEBT tptp.nat)_ tptp.list_VEBT_VEBT tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.vEBT_VEBT tptp.nat)|)) (= (ho_10095 x z) (ho_10095 y z)))) (= x y))))) (let ((_let_2069 (forall ((x |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_10100 x z) (ho_10100 y z)))) (= x y))))) (let ((_let_2070 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10111 x z) (ho_10111 y z)))) (= x y))))) (let ((_let_2071 (forall ((x |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.set_complex Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.complex)_ tptp.set_complex tptp.set_complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.complex)|)) (= (ho_10115 x z) (ho_10115 y z)))) (= x y))))) (let ((_let_2072 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_10120 x z) (ho_10120 y z)))) (= x y))))) (let ((_let_2073 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_10119 x z) (ho_10119 y z)))) (= x y))))) (let ((_let_2074 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10124 x z) (ho_10124 y z)))) (= x y))))) (let ((_let_2075 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_10127 x z) (ho_10127 y z)))) (= x y))))) (let ((_let_2076 (forall ((x |u_(-> Bool _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> Bool _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_10126 x z) (ho_10126 y z)))) (= x y))))) (let ((_let_2077 (forall ((x |u_(-> tptp.option_num tptp.int)|) (y |u_(-> tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.option_num)) (= (ho_10132 x z) (ho_10132 y z)))) (= x y))))) (let ((_let_2078 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10165 x z) (ho_10165 y z)))) (= x y))))) (let ((_let_2079 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.filter_real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.real tptp.filter_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10186 x z) (ho_10186 y z)))) (= x y))))) (let ((_let_2080 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_10131 x z) (ho_10131 y z)))) (= x y))))) (let ((_let_2081 (forall ((x |u_(-> tptp.int _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_10130 x z) (ho_10130 y z)))) (= x y))))) (let ((_let_2082 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_10134 x z) (ho_10134 y z)))) (= x y))))) (let ((_let_2083 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10143 x z) (ho_10143 y z)))) (= x y))))) (let ((_let_2084 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10145 x z) (ho_10145 y z)))) (= x y))))) (let ((_let_2085 (forall ((x |u_(-> tptp.set_nat tptp.set_int)|) (y |u_(-> tptp.set_nat tptp.set_int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10149 x z) (ho_10149 y z)))) (= x y))))) (let ((_let_2086 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_10148 x z) (ho_10148 y z)))) (= x y))))) (let ((_let_2087 (forall ((x |u_(-> tptp.set_o tptp.nat)|) (y |u_(-> tptp.set_o tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_10151 x z) (ho_10151 y z)))) (= x y))))) (let ((_let_2088 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real tptp.set_real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10153 x z) (ho_10153 y z)))) (= x y))))) (let ((_let_2089 (forall ((x |u_(-> tptp.real tptp.set_real tptp.set_real)|) (y |u_(-> tptp.real tptp.set_real tptp.set_real)|)) (or (not (forall ((z tptp.real)) (= (ho_10155 x z) (ho_10155 y z)))) (= x y))))) (let ((_let_2090 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_10432 x z) (ho_10432 y z)))) (= x y))))) (let ((_let_2091 (forall ((x |u_(-> tptp.set_nat tptp.set_char)|) (y |u_(-> tptp.set_nat tptp.set_char)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10160 x z) (ho_10160 y z)))) (= x y))))) (let ((_let_2092 (forall ((x |u_(-> tptp.nat tptp.char)|) (y |u_(-> tptp.nat tptp.char)|)) (or (not (forall ((z tptp.nat)) (= (ho_10157 x z) (ho_10157 y z)))) (= x y))))) (let ((_let_2093 (forall ((x |u_(-> _u_(-> tptp.nat tptp.char)_ tptp.set_nat tptp.set_char)|) (y |u_(-> _u_(-> tptp.nat tptp.char)_ tptp.set_nat tptp.set_char)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.char)|)) (= (ho_10159 x z) (ho_10159 y z)))) (= x y))))) (let ((_let_2094 (forall ((x |u_(-> tptp.set_char tptp.nat)|) (y |u_(-> tptp.set_char tptp.nat)|)) (or (not (forall ((z tptp.set_char)) (= (ho_10162 x z) (ho_10162 y z)))) (= x y))))) (let ((_let_2095 (forall ((x |u_(-> Bool tptp.char)|) (y |u_(-> Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10171 x z) (ho_10171 y z)))) (= x y))))) (let ((_let_2096 (forall ((x |u_(-> Bool Bool tptp.char)|) (y |u_(-> Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10170 x z) (ho_10170 y z)))) (= x y))))) (let ((_let_2097 (forall ((x |u_(-> Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10169 x z) (ho_10169 y z)))) (= x y))))) (let ((_let_2098 (forall ((x |u_(-> Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10168 x z) (ho_10168 y z)))) (= x y))))) (let ((_let_2099 (forall ((x |u_(-> Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10167 x z) (ho_10167 y z)))) (= x y))))) (let ((_let_2100 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_10164 x z) (ho_10164 y z)))) (= x y))))) (let ((_let_2101 (forall ((x |u_(-> tptp.set_char tptp.set_nat)|) (y |u_(-> tptp.set_char tptp.set_nat)|)) (or (not (forall ((z tptp.set_char)) (= (ho_10177 x z) (ho_10177 y z)))) (= x y))))) (let ((_let_2102 (forall ((x |u_(-> _u_(-> tptp.char tptp.nat)_ tptp.set_char tptp.set_nat)|) (y |u_(-> _u_(-> tptp.char tptp.nat)_ tptp.set_char tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.char tptp.nat)|)) (= (ho_10176 x z) (ho_10176 y z)))) (= x y))))) (let ((_let_2103 (forall ((x |u_(-> tptp.char tptp.code_integer)|) (y |u_(-> tptp.char tptp.code_integer)|)) (or (not (forall ((z tptp.char)) (= (ho_10179 x z) (ho_10179 y z)))) (= x y))))) (let ((_let_2104 (forall ((x |u_(-> tptp.char tptp.char)|) (y |u_(-> tptp.char tptp.char)|)) (or (not (forall ((z tptp.char)) (= (ho_10181 x z) (ho_10181 y z)))) (= x y))))) (let ((_let_2105 (forall ((x |u_(-> tptp.set_real tptp.filter_real)|) (y |u_(-> tptp.set_real tptp.filter_real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_10184 x z) (ho_10184 y z)))) (= x y))))) (let ((_let_2106 (forall ((x |u_(-> tptp.real tptp.set_real tptp.filter_real)|) (y |u_(-> tptp.real tptp.set_real tptp.filter_real)|)) (or (not (forall ((z tptp.real)) (= (ho_10183 x z) (ho_10183 y z)))) (= x y))))) (let ((_let_2107 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10192 x z) (ho_10192 y z)))) (= x y))))) (let ((_let_2108 (forall ((x |u_(-> tptp.filter_real _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> tptp.filter_real _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_10191 x z) (ho_10191 y z)))) (= x y))))) (let ((_let_2109 (forall ((x |u_(-> tptp.filter_real tptp.filter_real Bool)|) (y |u_(-> tptp.filter_real tptp.filter_real Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_10197 x z) (ho_10197 y z)))) (= x y))))) (let ((_let_2110 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real tptp.filter_real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real tptp.filter_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10196 x z) (ho_10196 y z)))) (= x y))))) (let ((_let_2111 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (= (ho_10380 x z) (ho_10380 y z)))) (= x y))))) (let ((_let_2112 (forall ((x |u_(-> tptp.filter_real tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_real tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_10200 x z) (ho_10200 y z)))) (= x y))))) (let ((_let_2113 (forall ((x |u_(-> tptp.filter_nat tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_10204 x z) (ho_10204 y z)))) (= x y))))) (let ((_let_2114 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.filter_nat tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.filter_nat tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10203 x z) (ho_10203 y z)))) (= x y))))) (let ((_let_2115 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_10210 x z) (ho_10210 y z)))) (= x y))))) (let ((_let_2116 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ tptp.filter_real Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ tptp.filter_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_10213 x z) (ho_10213 y z)))) (= x y))))) (let ((_let_2117 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10218 x z) (ho_10218 y z)))) (= x y))))) (let ((_let_2118 (forall ((x |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> tptp.set_real _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_10220 x z) (ho_10220 y z)))) (= x y))))) (let ((_let_2119 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.set_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10227 x z) (ho_10227 y z)))) (= x y))))) (let ((_let_2120 (forall ((x |u_(-> _u_(-> tptp.nat tptp.char)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.char)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.char)|)) (= (ho_10231 x z) (ho_10231 y z)))) (= x y))))) (let ((_let_2121 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10238 x z) (ho_10238 y z)))) (= x y))))) (let ((_let_2122 (forall ((x |u_(-> tptp.set_nat tptp.list_nat)|) (y |u_(-> tptp.set_nat tptp.list_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_10241 x z) (ho_10241 y z)))) (= x y))))) (let ((_let_2123 (forall ((x |u_(-> tptp.set_list_nat tptp.nat)|) (y |u_(-> tptp.set_list_nat tptp.nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_10243 x z) (ho_10243 y z)))) (= x y))))) (let ((_let_2124 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10245 x z) (ho_10245 y z)))) (= x y))))) (let ((_let_2125 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.list_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.list_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10247 x z) (ho_10247 y z)))) (= x y))))) (let ((_let_2126 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_10250 x z) (ho_10250 y z)))) (= x y))))) (let ((_let_2127 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_10253 x z) (ho_10253 y z)))) (= x y))))) (let ((_let_2128 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_10260 x z) (ho_10260 y z)))) (= x y))))) (let ((_let_2129 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.list_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.list_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_10262 x z) (ho_10262 y z)))) (= x y))))) (let ((_let_2130 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10268 x z) (ho_10268 y z)))) (= x y))))) (let ((_let_2131 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10267 x z) (ho_10267 y z)))) (= x y))))) (let ((_let_2132 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10266 x z) (ho_10266 y z)))) (= x y))))) (let ((_let_2133 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10265 x z) (ho_10265 y z)))) (= x y))))) (let ((_let_2134 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10275 x z) (ho_10275 y z)))) (= x y))))) (let ((_let_2135 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10277 x z) (ho_10277 y z)))) (= x y))))) (let ((_let_2136 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10271 x z) (ho_10271 y z)))) (= x y))))) (let ((_let_2137 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_10278 x z) (ho_10278 y z)))) (= x y))))) (let ((_let_2138 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10281 x z) (ho_10281 y z)))) (= x y))))) (let ((_let_2139 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10283 x z) (ho_10283 y z)))) (= x y))))) (let ((_let_2140 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_10292 x z) (ho_10292 y z)))) (= x y))))) (let ((_let_2141 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_10291 x z) (ho_10291 y z)))) (= x y))))) (let ((_let_2142 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_10301 x z) (ho_10301 y z)))) (= x y))))) (let ((_let_2143 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10287 x z) (ho_10287 y z)))) (= x y))))) (let ((_let_2144 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10286 x z) (ho_10286 y z)))) (= x y))))) (let ((_let_2145 (forall ((x |u_(-> _u_(-> tptp.real tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real tptp.real)|)) (= (ho_10335 x z) (ho_10335 y z)))) (= x y))))) (let ((_let_2146 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (= (ho_10290 x z) (ho_10290 y z)))) (= x y))))) (let ((_let_2147 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10289 x z) (ho_10289 y z)))) (= x y))))) (let ((_let_2148 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_10300 x z) (ho_10300 y z)))) (= x y))))) (let ((_let_2149 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_10299 x z) (ho_10299 y z)))) (= x y))))) (let ((_let_2150 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_10302 x z) (ho_10302 y z)))) (= x y))))) (let ((_let_2151 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10295 x z) (ho_10295 y z)))) (= x y))))) (let ((_let_2152 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (= (ho_10298 x z) (ho_10298 y z)))) (= x y))))) (let ((_let_2153 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10297 x z) (ho_10297 y z)))) (= x y))))) (let ((_let_2154 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_10303 x z) (ho_10303 y z)))) (= x y))))) (let ((_let_2155 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_10311 x z) (ho_10311 y z)))) (= x y))))) (let ((_let_2156 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_10310 x z) (ho_10310 y z)))) (= x y))))) (let ((_let_2157 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_10434 x z) (ho_10434 y z)))) (= x y))))) (let ((_let_2158 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10306 x z) (ho_10306 y z)))) (= x y))))) (let ((_let_2159 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_10305 x z) (ho_10305 y z)))) (= x y))))) (let ((_let_2160 (forall ((x |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (= (ho_10309 x z) (ho_10309 y z)))) (= x y))))) (let ((_let_2161 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_10308 x z) (ho_10308 y z)))) (= x y))))) (let ((_let_2162 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (= (ho_10317 x z) (ho_10317 y z)))) (= x y))))) (let ((_let_2163 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_10321 x z) (ho_10321 y z)))) (= x y))))) (let ((_let_2164 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_10319 x z) (ho_10319 y z)))) (= x y))))) (let ((_let_2165 (forall ((x |u_(-> _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real Bool)|)) (= (ho_10326 x z) (ho_10326 y z)))) (= x y))))) (let ((_let_2166 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_10329 x z) (ho_10329 y z)))) (= x y))))) (let ((_let_2167 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10350 x z) (ho_10350 y z)))) (= x y))))) (let ((_let_2168 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_10328 x z) (ho_10328 y z)))) (= x y))))) (let ((_let_2169 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ _u_(-> tptp.real tptp.real tptp.real)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_10332 x z) (ho_10332 y z)))) (= x y))))) (let ((_let_2170 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10344 x z) (ho_10344 y z)))) (= x y))))) (let ((_let_2171 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10379 x z) (ho_10379 y z)))) (= x y))))) (let ((_let_2172 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_10339 x z) (ho_10339 y z)))) (= x y))))) (let ((_let_2173 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (= (ho_10343 x z) (ho_10343 y z)))) (= x y))))) (let ((_let_2174 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_10342 x z) (ho_10342 y z)))) (= x y))))) (let ((_let_2175 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_10348 x z) (ho_10348 y z)))) (= x y))))) (let ((_let_2176 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_10360 x z) (ho_10360 y z)))) (= x y))))) (let ((_let_2177 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_10357 x z) (ho_10357 y z)))) (= x y))))) (let ((_let_2178 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10369 x z) (ho_10369 y z)))) (= x y))))) (let ((_let_2179 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10374 x z) (ho_10374 y z)))) (= x y))))) (let ((_let_2180 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10365 x z) (ho_10365 y z)))) (= x y))))) (let ((_let_2181 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10364 x z) (ho_10364 y z)))) (= x y))))) (let ((_let_2182 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (= (ho_10368 x z) (ho_10368 y z)))) (= x y))))) (let ((_let_2183 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_10371 x z) (ho_10371 y z)))) (= x y))))) (let ((_let_2184 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10377 x z) (ho_10377 y z)))) (= x y))))) (let ((_let_2185 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real tptp.filter_real)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ tptp.filter_real tptp.filter_real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_10406 x z) (ho_10406 y z)))) (= x y))))) (let ((_let_2186 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_10376 x z) (ho_10376 y z)))) (= x y))))) (let ((_let_2187 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10388 x z) (ho_10388 y z)))) (= x y))))) (let ((_let_2188 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_10390 x z) (ho_10390 y z)))) (= x y))))) (let ((_let_2189 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10392 x z) (ho_10392 y z)))) (= x y))))) (let ((_let_2190 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (= (ho_10396 x z) (ho_10396 y z)))) (= x y))))) (let ((_let_2191 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_10395 x z) (ho_10395 y z)))) (= x y))))) (let ((_let_2192 (forall ((x |u_(-> tptp.filter_nat tptp.filter1242075044329608583at_nat)|) (y |u_(-> tptp.filter_nat tptp.filter1242075044329608583at_nat)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_10401 x z) (ho_10401 y z)))) (= x y))))) (let ((_let_2193 (forall ((x |u_(-> tptp.filter_nat tptp.filter_nat tptp.filter1242075044329608583at_nat)|) (y |u_(-> tptp.filter_nat tptp.filter_nat tptp.filter1242075044329608583at_nat)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_10400 x z) (ho_10400 y z)))) (= x y))))) (let ((_let_2194 (forall ((x |u_(-> tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z tptp.filter1242075044329608583at_nat)) (= (ho_10404 x z) (ho_10404 y z)))) (= x y))))) (let ((_let_2195 (forall ((x |u_(-> tptp.filter_real tptp.filter_real)|) (y |u_(-> tptp.filter_real tptp.filter_real)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_10407 x z) (ho_10407 y z)))) (= x y))))) (let ((_let_2196 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10414 x z) (ho_10414 y z)))) (= x y))))) (let ((_let_2197 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_10423 x z) (ho_10423 y z)))) (= x y))))) (let ((_let_2198 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_10422 x z) (ho_10422 y z)))) (= x y))))) (let ((_let_2199 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10417 x z) (ho_10417 y z)))) (= x y))))) (let ((_let_2200 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_10420 x z) (ho_10420 y z)))) (= x y))))) (let ((_let_2201 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_10425 x z) (ho_10425 y z)))) (= x y))))) (let ((_let_2202 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_10428 x z) (ho_10428 y z)))) (= x y))))) (let ((_let_2203 (forall ((BOUND_VARIABLE_1260451 tptp.num)) (= (ho_4191 k_4190 BOUND_VARIABLE_1260451) (ho_4191 k_4194 (ho_4193 k_4192 BOUND_VARIABLE_1260451)))))) (let ((_let_2204 (forall ((BOUND_VARIABLE_1260405 tptp.nat) (BOUND_VARIABLE_1260406 tptp.num)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) BOUND_VARIABLE_1260405))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1260406)))) (let ((_let_7 (ho_4216 (ho_4215 k_4223 _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 _let_6) _let_4)) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2)))))) (let ((_let_8 (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one))) (= (ho_4191 (ho_4236 k_4235 BOUND_VARIABLE_1260405) BOUND_VARIABLE_1260406) (ho_4231 (ho_4234 (ho_4233 k_4232 _let_8) k_4190) (ho_4231 (ho_4230 (ho_4229 k_4228 (= _let_7 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3))) _let_8) (ho_4191 k_4194 (ho_4225 k_4224 _let_7)))))))))))))))) (let ((_let_2205 (forall ((BOUND_VARIABLE_1260359 tptp.nat) (BOUND_VARIABLE_1260360 tptp.num)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) BOUND_VARIABLE_1260359))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1260360)))) (let ((_let_7 (ho_4216 (ho_4215 k_4223 _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 _let_6) _let_4)) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2)))))) (= (ho_4191 k_4194 (ho_4241 (ho_4240 (ho_4239 k_4238 tptp.one) k_4237) (ho_4231 (ho_4230 (ho_4229 k_4228 (= (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3) _let_7)) (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one)) (ho_4191 k_4194 (ho_4225 k_4224 _let_7))))) (ho_4191 (ho_4236 k_4242 BOUND_VARIABLE_1260359) BOUND_VARIABLE_1260360)))))))))))) (let ((_let_2206 (forall ((BOUND_VARIABLE_1260313 tptp.real) (BOUND_VARIABLE_1260314 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4278 BOUND_VARIABLE_1260313) BOUND_VARIABLE_1260314) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260314 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260314) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260314) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260313) BOUND_VARIABLE_1260314))))))))))))) (let ((_let_2207 (forall ((BOUND_VARIABLE_1260267 tptp.real) (BOUND_VARIABLE_1260268 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4279 BOUND_VARIABLE_1260267) BOUND_VARIABLE_1260268) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260268 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260268) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260268) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260267) BOUND_VARIABLE_1260268))))))))))))) (let ((_let_2208 (forall ((BOUND_VARIABLE_1260221 tptp.real) (BOUND_VARIABLE_1260222 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4280 BOUND_VARIABLE_1260221) BOUND_VARIABLE_1260222) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260222 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260222) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260222) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260221) BOUND_VARIABLE_1260222))))))))))))) (let ((_let_2209 (forall ((BOUND_VARIABLE_1260175 tptp.real) (BOUND_VARIABLE_1260176 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4281 BOUND_VARIABLE_1260175) BOUND_VARIABLE_1260176) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260176 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260176) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260176) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260175) BOUND_VARIABLE_1260176))))))))))))) (let ((_let_2210 (forall ((BOUND_VARIABLE_1260129 tptp.real) (BOUND_VARIABLE_1260130 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4282 BOUND_VARIABLE_1260129) BOUND_VARIABLE_1260130) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260130 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260130) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260130) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260129) BOUND_VARIABLE_1260130))))))))))))) (let ((_let_2211 (forall ((BOUND_VARIABLE_1260083 tptp.real) (BOUND_VARIABLE_1260084 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4283 BOUND_VARIABLE_1260083) BOUND_VARIABLE_1260084) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260084 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1260084) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1260084) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260083) BOUND_VARIABLE_1260084))))))))))))) (let ((_let_2212 (forall ((BOUND_VARIABLE_1260032 tptp.real) (BOUND_VARIABLE_1260033 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4284 BOUND_VARIABLE_1260032) BOUND_VARIABLE_1260033) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1260033 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1260033) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1260033) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1260032) BOUND_VARIABLE_1260033))))))))))))))))) (let ((_let_2213 (forall ((BOUND_VARIABLE_1259986 tptp.real) (BOUND_VARIABLE_1259987 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4285 BOUND_VARIABLE_1259986) BOUND_VARIABLE_1259987) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259987 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259987) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259987) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259986) BOUND_VARIABLE_1259987))))))))))))) (let ((_let_2214 (forall ((BOUND_VARIABLE_1259976 tptp.nat) (BOUND_VARIABLE_1259977 tptp.nat)) (= (ho_4288 (ho_4287 k_4286 BOUND_VARIABLE_1259976) BOUND_VARIABLE_1259977) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1259977)) (ho_4290 k_4289 BOUND_VARIABLE_1259976)))))) (let ((_let_2215 (forall ((BOUND_VARIABLE_1259883 tptp.num) (BOUND_VARIABLE_1259884 tptp.nat)) (= (ho_4191 (ho_4297 (ho_4296 (ho_4295 k_4294 (ho_4191 k_4194 tptp.one)) (ho_4236 k_4235 BOUND_VARIABLE_1259884)) (ho_4236 k_4242 BOUND_VARIABLE_1259884)) BOUND_VARIABLE_1259883) (ho_4300 (ho_4299 k_4298 BOUND_VARIABLE_1259883) BOUND_VARIABLE_1259884))))) (let ((_let_2216 (forall ((BOUND_VARIABLE_1259837 tptp.nat) (BOUND_VARIABLE_1259838 tptp.nat) (BOUND_VARIABLE_1259839 tptp.nat) (BOUND_VARIABLE_1259840 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259837) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259840) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259839) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259838) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4301 BOUND_VARIABLE_1259837) BOUND_VARIABLE_1259838) BOUND_VARIABLE_1259839) BOUND_VARIABLE_1259840)))))))) (let ((_let_2217 (forall ((BOUND_VARIABLE_1259791 tptp.nat) (BOUND_VARIABLE_1259792 tptp.nat) (BOUND_VARIABLE_1259793 tptp.nat) (BOUND_VARIABLE_1259794 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259791) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259794) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259793) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1259792) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4305 BOUND_VARIABLE_1259791) BOUND_VARIABLE_1259792) BOUND_VARIABLE_1259793) BOUND_VARIABLE_1259794)))))))) (let ((_let_2218 (forall ((BOUND_VARIABLE_1259776 tptp.int) (BOUND_VARIABLE_1259777 tptp.int) (BOUND_VARIABLE_1259778 tptp.int) (BOUND_VARIABLE_1259779 tptp.int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1259777) BOUND_VARIABLE_1259778))) (= (ho_4310 (ho_4309 (ho_4308 (ho_4307 k_4306 BOUND_VARIABLE_1259776) BOUND_VARIABLE_1259777) BOUND_VARIABLE_1259778) BOUND_VARIABLE_1259779) (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1259776) BOUND_VARIABLE_1259779)) _let_1))))))) (let ((_let_2219 (forall ((BOUND_VARIABLE_1259759 tptp.int) (BOUND_VARIABLE_1259760 tptp.int) (BOUND_VARIABLE_1259761 tptp.int) (BOUND_VARIABLE_1259762 tptp.int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1259760) BOUND_VARIABLE_1259761))) (= (ho_4310 (ho_4309 (ho_4308 (ho_4307 k_4312 BOUND_VARIABLE_1259759) BOUND_VARIABLE_1259760) BOUND_VARIABLE_1259761) BOUND_VARIABLE_1259762) (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1259759) BOUND_VARIABLE_1259762)) (ho_4196 k_4195 tptp.one))) _let_1))))))) (let ((_let_2220 (forall ((BOUND_VARIABLE_1259713 tptp.real) (BOUND_VARIABLE_1259714 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4313 BOUND_VARIABLE_1259713) BOUND_VARIABLE_1259714) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259714 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259714) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259714) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259713) BOUND_VARIABLE_1259714))))))))))))) (let ((_let_2221 (forall ((BOUND_VARIABLE_1259706 tptp.int) (BOUND_VARIABLE_1259707 tptp.nat)) (= (ho_4316 (ho_4315 k_4314 BOUND_VARIABLE_1259706) BOUND_VARIABLE_1259707) (ho_4318 k_4317 BOUND_VARIABLE_1259706))))) (let ((_let_2222 (forall ((BOUND_VARIABLE_1259697 tptp.int) (BOUND_VARIABLE_1259698 tptp.nat)) (= (ho_4316 (ho_4315 k_4319 BOUND_VARIABLE_1259697) BOUND_VARIABLE_1259698) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259697) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2223 (forall ((BOUND_VARIABLE_1259690 tptp.int) (BOUND_VARIABLE_1259691 tptp.nat)) (= (ho_4316 (ho_4315 k_4320 BOUND_VARIABLE_1259690) BOUND_VARIABLE_1259691) (ho_4318 k_4317 BOUND_VARIABLE_1259690))))) (let ((_let_2224 (forall ((BOUND_VARIABLE_1259681 tptp.int) (BOUND_VARIABLE_1259682 tptp.nat)) (= (ho_4316 (ho_4315 k_4321 BOUND_VARIABLE_1259681) BOUND_VARIABLE_1259682) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259681) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2225 (forall ((BOUND_VARIABLE_1259674 tptp.int) (BOUND_VARIABLE_1259675 tptp.nat)) (= (ho_4316 (ho_4315 k_4322 BOUND_VARIABLE_1259674) BOUND_VARIABLE_1259675) (ho_4318 k_4317 BOUND_VARIABLE_1259674))))) (let ((_let_2226 (forall ((BOUND_VARIABLE_1259665 tptp.int) (BOUND_VARIABLE_1259666 tptp.nat)) (= (ho_4316 (ho_4315 k_4323 BOUND_VARIABLE_1259665) BOUND_VARIABLE_1259666) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259665) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2227 (forall ((BOUND_VARIABLE_1259658 tptp.int) (BOUND_VARIABLE_1259659 tptp.nat)) (= (ho_4316 (ho_4315 k_4324 BOUND_VARIABLE_1259658) BOUND_VARIABLE_1259659) (ho_4318 k_4317 BOUND_VARIABLE_1259658))))) (let ((_let_2228 (forall ((BOUND_VARIABLE_1259649 tptp.int) (BOUND_VARIABLE_1259650 tptp.nat)) (= (ho_4316 (ho_4315 k_4325 BOUND_VARIABLE_1259649) BOUND_VARIABLE_1259650) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259649) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2229 (forall ((BOUND_VARIABLE_1259642 tptp.int) (BOUND_VARIABLE_1259643 tptp.nat)) (= (ho_4316 (ho_4315 k_4326 BOUND_VARIABLE_1259642) BOUND_VARIABLE_1259643) (ho_4318 k_4317 BOUND_VARIABLE_1259642))))) (let ((_let_2230 (forall ((BOUND_VARIABLE_1259633 tptp.int) (BOUND_VARIABLE_1259634 tptp.nat)) (= (ho_4316 (ho_4315 k_4327 BOUND_VARIABLE_1259633) BOUND_VARIABLE_1259634) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259633) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2231 (forall ((BOUND_VARIABLE_1259626 tptp.int) (BOUND_VARIABLE_1259627 tptp.nat)) (= (ho_4316 (ho_4315 k_4328 BOUND_VARIABLE_1259626) BOUND_VARIABLE_1259627) (ho_4318 k_4317 BOUND_VARIABLE_1259626))))) (let ((_let_2232 (forall ((BOUND_VARIABLE_1259617 tptp.int) (BOUND_VARIABLE_1259618 tptp.nat)) (= (ho_4316 (ho_4315 k_4329 BOUND_VARIABLE_1259617) BOUND_VARIABLE_1259618) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1259617) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2233 (forall ((BOUND_VARIABLE_1259571 tptp.real) (BOUND_VARIABLE_1259572 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4330 BOUND_VARIABLE_1259571) BOUND_VARIABLE_1259572) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259572 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259572) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259572) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259571) BOUND_VARIABLE_1259572))))))))))))) (let ((_let_2234 (forall ((BOUND_VARIABLE_1259525 tptp.real) (BOUND_VARIABLE_1259526 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4331 BOUND_VARIABLE_1259525) BOUND_VARIABLE_1259526) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259526 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259526) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259526) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259525) BOUND_VARIABLE_1259526))))))))))))) (let ((_let_2235 (forall ((BOUND_VARIABLE_1259500 tptp.nat) (BOUND_VARIABLE_1259501 tptp.nat) (BOUND_VARIABLE_1259502 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259500) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259500) BOUND_VARIABLE_1259501)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4336 BOUND_VARIABLE_1259500) BOUND_VARIABLE_1259501) BOUND_VARIABLE_1259502))))))) (let ((_let_2236 (forall ((BOUND_VARIABLE_1259475 tptp.nat) (BOUND_VARIABLE_1259476 tptp.nat) (BOUND_VARIABLE_1259477 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259475) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259475) BOUND_VARIABLE_1259476)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4339 BOUND_VARIABLE_1259475) BOUND_VARIABLE_1259476) BOUND_VARIABLE_1259477))))))) (let ((_let_2237 (forall ((BOUND_VARIABLE_1259450 tptp.nat) (BOUND_VARIABLE_1259451 tptp.nat) (BOUND_VARIABLE_1259452 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259450) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259450) BOUND_VARIABLE_1259451)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4340 BOUND_VARIABLE_1259450) BOUND_VARIABLE_1259451) BOUND_VARIABLE_1259452))))))) (let ((_let_2238 (forall ((BOUND_VARIABLE_1259425 tptp.nat) (BOUND_VARIABLE_1259426 tptp.nat) (BOUND_VARIABLE_1259427 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259425) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259425) BOUND_VARIABLE_1259426)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4341 BOUND_VARIABLE_1259425) BOUND_VARIABLE_1259426) BOUND_VARIABLE_1259427))))))) (let ((_let_2239 (forall ((BOUND_VARIABLE_1259400 tptp.nat) (BOUND_VARIABLE_1259401 tptp.nat) (BOUND_VARIABLE_1259402 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259400) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259400) BOUND_VARIABLE_1259401)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4342 BOUND_VARIABLE_1259400) BOUND_VARIABLE_1259401) BOUND_VARIABLE_1259402))))))) (let ((_let_2240 (forall ((BOUND_VARIABLE_1259375 tptp.nat) (BOUND_VARIABLE_1259376 tptp.nat) (BOUND_VARIABLE_1259377 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259375) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1259375) BOUND_VARIABLE_1259376)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2)))) (ho_4316 (ho_4338 (ho_4337 k_4343 BOUND_VARIABLE_1259375) BOUND_VARIABLE_1259376) BOUND_VARIABLE_1259377))))))) (let ((_let_2241 (forall ((BOUND_VARIABLE_1259329 tptp.real) (BOUND_VARIABLE_1259330 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4344 BOUND_VARIABLE_1259329) BOUND_VARIABLE_1259330) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259330 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259330) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259330) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259329) BOUND_VARIABLE_1259330))))))))))))) (let ((_let_2242 (forall ((BOUND_VARIABLE_1259278 tptp.real) (BOUND_VARIABLE_1259279 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4345 BOUND_VARIABLE_1259278) BOUND_VARIABLE_1259279) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259279 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1259279) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1259279) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259278) BOUND_VARIABLE_1259279))))))))))))))))) (let ((_let_2243 (forall ((BOUND_VARIABLE_1259227 tptp.real) (BOUND_VARIABLE_1259228 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4346 BOUND_VARIABLE_1259227) BOUND_VARIABLE_1259228) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259228 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1259228) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1259228) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259227) BOUND_VARIABLE_1259228))))))))))))))))) (let ((_let_2244 (forall ((BOUND_VARIABLE_1259183 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1259183 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1259183 _let_3))) (= (ho_4351 k_4350 BOUND_VARIABLE_1259183) (and (or (and (= BOUND_VARIABLE_1259183 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1259183) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1259183)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4278 BOUND_VARIABLE_1259183)))))))))))))) (let ((_let_2245 (forall ((BOUND_VARIABLE_1259137 tptp.real) (BOUND_VARIABLE_1259138 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4352 BOUND_VARIABLE_1259137) BOUND_VARIABLE_1259138) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259138 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259138) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259138) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259137) BOUND_VARIABLE_1259138))))))))))))) (let ((_let_2246 (forall ((BOUND_VARIABLE_1259093 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1259093 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1259093 _let_3))) (= (ho_4351 k_4353 BOUND_VARIABLE_1259093) (and (or (and (= BOUND_VARIABLE_1259093 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1259093) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1259093)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4279 BOUND_VARIABLE_1259093)))))))))))))) (let ((_let_2247 (forall ((BOUND_VARIABLE_1259047 tptp.real) (BOUND_VARIABLE_1259048 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4354 BOUND_VARIABLE_1259047) BOUND_VARIABLE_1259048) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1259048 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1259048) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1259048) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1259047) BOUND_VARIABLE_1259048))))))))))))) (let ((_let_2248 (forall ((BOUND_VARIABLE_1258996 tptp.real) (BOUND_VARIABLE_1258997 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4355 BOUND_VARIABLE_1258996) BOUND_VARIABLE_1258997) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258997 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258997) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258997) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258996) BOUND_VARIABLE_1258997))))))))))))))))) (let ((_let_2249 (forall ((BOUND_VARIABLE_1258952 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1258952 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1258952 _let_3))) (= (ho_4351 k_4356 BOUND_VARIABLE_1258952) (and (or (and (= BOUND_VARIABLE_1258952 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1258952) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1258952)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4280 BOUND_VARIABLE_1258952)))))))))))))) (let ((_let_2250 (forall ((BOUND_VARIABLE_1258906 tptp.real) (BOUND_VARIABLE_1258907 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4357 BOUND_VARIABLE_1258906) BOUND_VARIABLE_1258907) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258907 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258907) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258907) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258906) BOUND_VARIABLE_1258907))))))))))))) (let ((_let_2251 (forall ((BOUND_VARIABLE_1258860 tptp.real) (BOUND_VARIABLE_1258861 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4358 BOUND_VARIABLE_1258860) BOUND_VARIABLE_1258861) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258861 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258861) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258861) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258860) BOUND_VARIABLE_1258861))))))))))))) (let ((_let_2252 (forall ((BOUND_VARIABLE_1258816 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1258816 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1258816 _let_3))) (= (ho_4351 k_4359 BOUND_VARIABLE_1258816) (and (or (and (= BOUND_VARIABLE_1258816 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1258816) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1258816)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4281 BOUND_VARIABLE_1258816)))))))))))))) (let ((_let_2253 (forall ((BOUND_VARIABLE_1258765 tptp.real) (BOUND_VARIABLE_1258766 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4360 BOUND_VARIABLE_1258765) BOUND_VARIABLE_1258766) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258766 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258766) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258766) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258765) BOUND_VARIABLE_1258766))))))))))))))))) (let ((_let_2254 (forall ((BOUND_VARIABLE_1258714 tptp.real) (BOUND_VARIABLE_1258715 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4361 BOUND_VARIABLE_1258714) BOUND_VARIABLE_1258715) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258715 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258715) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258715) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258714) BOUND_VARIABLE_1258715))))))))))))))))) (let ((_let_2255 (forall ((BOUND_VARIABLE_1258668 tptp.real) (BOUND_VARIABLE_1258669 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4362 BOUND_VARIABLE_1258668) BOUND_VARIABLE_1258669) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258669 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258669) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258669) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258668) BOUND_VARIABLE_1258669))))))))))))) (let ((_let_2256 (forall ((BOUND_VARIABLE_1258617 tptp.real) (BOUND_VARIABLE_1258618 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4363 BOUND_VARIABLE_1258617) BOUND_VARIABLE_1258618) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258618 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258618) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258618) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258617) BOUND_VARIABLE_1258618))))))))))))))))) (let ((_let_2257 (forall ((BOUND_VARIABLE_1258571 tptp.real) (BOUND_VARIABLE_1258572 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4364 BOUND_VARIABLE_1258571) BOUND_VARIABLE_1258572) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258572 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258572) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258572) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258571) BOUND_VARIABLE_1258572))))))))))))) (let ((_let_2258 (forall ((BOUND_VARIABLE_1258520 tptp.real) (BOUND_VARIABLE_1258521 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4365 BOUND_VARIABLE_1258520) BOUND_VARIABLE_1258521) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258521 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258521) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258521) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258520) BOUND_VARIABLE_1258521))))))))))))))))) (let ((_let_2259 (forall ((BOUND_VARIABLE_1258474 tptp.real) (BOUND_VARIABLE_1258475 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4366 BOUND_VARIABLE_1258474) BOUND_VARIABLE_1258475) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258475 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258475) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258475) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258474) BOUND_VARIABLE_1258475))))))))))))) (let ((_let_2260 (forall ((BOUND_VARIABLE_1258423 tptp.real) (BOUND_VARIABLE_1258424 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4367 BOUND_VARIABLE_1258423) BOUND_VARIABLE_1258424) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258424 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258424) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258424) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258423) BOUND_VARIABLE_1258424))))))))))))))))) (let ((_let_2261 (forall ((BOUND_VARIABLE_1258377 tptp.real) (BOUND_VARIABLE_1258378 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4368 BOUND_VARIABLE_1258377) BOUND_VARIABLE_1258378) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258378 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258378) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258378) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258377) BOUND_VARIABLE_1258378))))))))))))) (let ((_let_2262 (forall ((BOUND_VARIABLE_1258333 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1258333 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1258333 _let_3))) (= (ho_4351 k_4369 BOUND_VARIABLE_1258333) (and (or (and (= BOUND_VARIABLE_1258333 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1258333) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1258333)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4282 BOUND_VARIABLE_1258333)))))))))))))) (let ((_let_2263 (forall ((BOUND_VARIABLE_1258287 tptp.real) (BOUND_VARIABLE_1258288 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4370 BOUND_VARIABLE_1258287) BOUND_VARIABLE_1258288) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258288 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258288) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258288) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258287) BOUND_VARIABLE_1258288))))))))))))) (let ((_let_2264 (forall ((BOUND_VARIABLE_1258236 tptp.real) (BOUND_VARIABLE_1258237 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4371 BOUND_VARIABLE_1258236) BOUND_VARIABLE_1258237) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258237 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258237) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258237) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258236) BOUND_VARIABLE_1258237))))))))))))))))) (let ((_let_2265 (forall ((BOUND_VARIABLE_1258190 tptp.real) (BOUND_VARIABLE_1258191 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4372 BOUND_VARIABLE_1258190) BOUND_VARIABLE_1258191) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258191 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258191) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258191) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258190) BOUND_VARIABLE_1258191))))))))))))) (let ((_let_2266 (forall ((BOUND_VARIABLE_1258139 tptp.real) (BOUND_VARIABLE_1258140 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4373 BOUND_VARIABLE_1258139) BOUND_VARIABLE_1258140) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258140 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1258140) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1258140) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258139) BOUND_VARIABLE_1258140))))))))))))))))) (let ((_let_2267 (forall ((BOUND_VARIABLE_1258093 tptp.real) (BOUND_VARIABLE_1258094 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4374 BOUND_VARIABLE_1258093) BOUND_VARIABLE_1258094) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258094 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258094) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258094) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258093) BOUND_VARIABLE_1258094))))))))))))) (let ((_let_2268 (forall ((BOUND_VARIABLE_1258049 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1258049 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1258049 _let_3))) (= (ho_4351 k_4375 BOUND_VARIABLE_1258049) (and (or (and (= BOUND_VARIABLE_1258049 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1258049) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1258049)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4283 BOUND_VARIABLE_1258049)))))))))))))) (let ((_let_2269 (forall ((BOUND_VARIABLE_1258003 tptp.real) (BOUND_VARIABLE_1258004 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4376 BOUND_VARIABLE_1258003) BOUND_VARIABLE_1258004) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1258004 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1258004) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1258004) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1258003) BOUND_VARIABLE_1258004))))))))))))) (let ((_let_2270 (forall ((BOUND_VARIABLE_1257957 tptp.real) (BOUND_VARIABLE_1257958 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4377 BOUND_VARIABLE_1257957) BOUND_VARIABLE_1257958) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257958 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257958) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257958) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257957) BOUND_VARIABLE_1257958))))))))))))) (let ((_let_2271 (forall ((BOUND_VARIABLE_1257911 tptp.real) (BOUND_VARIABLE_1257912 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4378 BOUND_VARIABLE_1257911) BOUND_VARIABLE_1257912) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257912 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257912) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257912) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257911) BOUND_VARIABLE_1257912))))))))))))) (let ((_let_2272 (forall ((BOUND_VARIABLE_1257865 tptp.real) (BOUND_VARIABLE_1257866 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4379 BOUND_VARIABLE_1257865) BOUND_VARIABLE_1257866) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257866 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257866) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257866) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257865) BOUND_VARIABLE_1257866))))))))))))) (let ((_let_2273 (forall ((BOUND_VARIABLE_1257819 tptp.real) (BOUND_VARIABLE_1257820 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4380 BOUND_VARIABLE_1257819) BOUND_VARIABLE_1257820) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257820 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257820) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257820) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257819) BOUND_VARIABLE_1257820))))))))))))) (let ((_let_2274 (forall ((BOUND_VARIABLE_1257773 tptp.real) (BOUND_VARIABLE_1257774 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4381 BOUND_VARIABLE_1257773) BOUND_VARIABLE_1257774) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257774 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257774) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257774) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257773) BOUND_VARIABLE_1257774))))))))))))) (let ((_let_2275 (forall ((BOUND_VARIABLE_1257727 tptp.real) (BOUND_VARIABLE_1257728 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4382 BOUND_VARIABLE_1257727) BOUND_VARIABLE_1257728) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257728 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257728) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257728) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257727) BOUND_VARIABLE_1257728))))))))))))) (let ((_let_2276 (forall ((BOUND_VARIABLE_1257681 tptp.real) (BOUND_VARIABLE_1257682 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4383 BOUND_VARIABLE_1257681) BOUND_VARIABLE_1257682) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257682 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257682) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257682) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257681) BOUND_VARIABLE_1257682))))))))))))) (let ((_let_2277 (forall ((BOUND_VARIABLE_1257635 tptp.real) (BOUND_VARIABLE_1257636 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4384 BOUND_VARIABLE_1257635) BOUND_VARIABLE_1257636) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257636 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257636) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257636) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257635) BOUND_VARIABLE_1257636))))))))))))) (let ((_let_2278 (forall ((BOUND_VARIABLE_1257589 tptp.real) (BOUND_VARIABLE_1257590 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4385 BOUND_VARIABLE_1257589) BOUND_VARIABLE_1257590) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257590 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257590) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257590) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257589) BOUND_VARIABLE_1257590))))))))))))) (let ((_let_2279 (forall ((BOUND_VARIABLE_1257543 tptp.real) (BOUND_VARIABLE_1257544 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4386 BOUND_VARIABLE_1257543) BOUND_VARIABLE_1257544) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257544 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257544) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257544) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257543) BOUND_VARIABLE_1257544))))))))))))) (let ((_let_2280 (forall ((BOUND_VARIABLE_1257497 tptp.real) (BOUND_VARIABLE_1257498 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4387 BOUND_VARIABLE_1257497) BOUND_VARIABLE_1257498) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257498 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257498) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257498) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257497) BOUND_VARIABLE_1257498))))))))))))) (let ((_let_2281 (forall ((BOUND_VARIABLE_1257451 tptp.real) (BOUND_VARIABLE_1257452 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4388 BOUND_VARIABLE_1257451) BOUND_VARIABLE_1257452) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257452 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257452) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257452) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257451) BOUND_VARIABLE_1257452))))))))))))) (let ((_let_2282 (forall ((BOUND_VARIABLE_1257405 tptp.real) (BOUND_VARIABLE_1257406 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4389 BOUND_VARIABLE_1257405) BOUND_VARIABLE_1257406) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257406 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257406) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257406) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257405) BOUND_VARIABLE_1257406))))))))))))) (let ((_let_2283 (forall ((BOUND_VARIABLE_1257359 tptp.real) (BOUND_VARIABLE_1257360 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4390 BOUND_VARIABLE_1257359) BOUND_VARIABLE_1257360) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257360 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257360) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257360) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257359) BOUND_VARIABLE_1257360))))))))))))) (let ((_let_2284 (forall ((BOUND_VARIABLE_1257313 tptp.real) (BOUND_VARIABLE_1257314 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4391 BOUND_VARIABLE_1257313) BOUND_VARIABLE_1257314) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257314 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257314) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257314) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257313) BOUND_VARIABLE_1257314))))))))))))) (let ((_let_2285 (forall ((BOUND_VARIABLE_1257267 tptp.real) (BOUND_VARIABLE_1257268 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4392 BOUND_VARIABLE_1257267) BOUND_VARIABLE_1257268) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257268 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257268) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257268) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257267) BOUND_VARIABLE_1257268))))))))))))) (let ((_let_2286 (forall ((BOUND_VARIABLE_1257221 tptp.real) (BOUND_VARIABLE_1257222 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4393 BOUND_VARIABLE_1257221) BOUND_VARIABLE_1257222) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257222 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257222) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257222) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257221) BOUND_VARIABLE_1257222))))))))))))) (let ((_let_2287 (forall ((BOUND_VARIABLE_1257175 tptp.real) (BOUND_VARIABLE_1257176 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4394 BOUND_VARIABLE_1257175) BOUND_VARIABLE_1257176) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257176 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257176) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257176) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257175) BOUND_VARIABLE_1257176))))))))))))) (let ((_let_2288 (forall ((BOUND_VARIABLE_1257129 tptp.real) (BOUND_VARIABLE_1257130 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4395 BOUND_VARIABLE_1257129) BOUND_VARIABLE_1257130) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257130 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257130) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257130) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257129) BOUND_VARIABLE_1257130))))))))))))) (let ((_let_2289 (forall ((BOUND_VARIABLE_1257083 tptp.real) (BOUND_VARIABLE_1257084 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4396 BOUND_VARIABLE_1257083) BOUND_VARIABLE_1257084) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257084 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257084) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257084) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257083) BOUND_VARIABLE_1257084))))))))))))) (let ((_let_2290 (forall ((BOUND_VARIABLE_1257037 tptp.real) (BOUND_VARIABLE_1257038 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4397 BOUND_VARIABLE_1257037) BOUND_VARIABLE_1257038) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1257038 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1257038) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1257038) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1257037) BOUND_VARIABLE_1257038))))))))))))) (let ((_let_2291 (forall ((BOUND_VARIABLE_1256991 tptp.real) (BOUND_VARIABLE_1256992 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4398 BOUND_VARIABLE_1256991) BOUND_VARIABLE_1256992) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256992 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256992) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256992) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256991) BOUND_VARIABLE_1256992))))))))))))) (let ((_let_2292 (forall ((BOUND_VARIABLE_1256945 tptp.real) (BOUND_VARIABLE_1256946 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4399 BOUND_VARIABLE_1256945) BOUND_VARIABLE_1256946) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256946 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256946) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256946) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256945) BOUND_VARIABLE_1256946))))))))))))) (let ((_let_2293 (forall ((BOUND_VARIABLE_1256899 tptp.real) (BOUND_VARIABLE_1256900 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4400 BOUND_VARIABLE_1256899) BOUND_VARIABLE_1256900) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256900 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256900) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256900) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256899) BOUND_VARIABLE_1256900))))))))))))) (let ((_let_2294 (forall ((BOUND_VARIABLE_1256853 tptp.real) (BOUND_VARIABLE_1256854 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4401 BOUND_VARIABLE_1256853) BOUND_VARIABLE_1256854) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256854 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256854) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256854) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256853) BOUND_VARIABLE_1256854))))))))))))) (let ((_let_2295 (forall ((BOUND_VARIABLE_1256807 tptp.real) (BOUND_VARIABLE_1256808 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4402 BOUND_VARIABLE_1256807) BOUND_VARIABLE_1256808) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256808 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256808) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256808) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256807) BOUND_VARIABLE_1256808))))))))))))) (let ((_let_2296 (forall ((BOUND_VARIABLE_1256761 tptp.real) (BOUND_VARIABLE_1256762 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4403 BOUND_VARIABLE_1256761) BOUND_VARIABLE_1256762) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256762 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256762) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256762) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256761) BOUND_VARIABLE_1256762))))))))))))) (let ((_let_2297 (forall ((BOUND_VARIABLE_1256715 tptp.real) (BOUND_VARIABLE_1256716 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4404 BOUND_VARIABLE_1256715) BOUND_VARIABLE_1256716) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1256716 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1256716) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1256716) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1256715) BOUND_VARIABLE_1256716))))))))))))) (let ((_let_2298 (forall ((BOUND_VARIABLE_1256673 tptp.nat) (BOUND_VARIABLE_1256674 tptp.nat) (BOUND_VARIABLE_1256675 tptp.nat) (BOUND_VARIABLE_1256676 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256673) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256676) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256674) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256675) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4407 BOUND_VARIABLE_1256673) BOUND_VARIABLE_1256674) BOUND_VARIABLE_1256675) BOUND_VARIABLE_1256676)))))))) (let ((_let_2299 (forall ((BOUND_VARIABLE_1256631 tptp.nat) (BOUND_VARIABLE_1256632 tptp.nat) (BOUND_VARIABLE_1256633 tptp.nat) (BOUND_VARIABLE_1256634 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256631) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256634) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256632) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256633) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4410 BOUND_VARIABLE_1256631) BOUND_VARIABLE_1256632) BOUND_VARIABLE_1256633) BOUND_VARIABLE_1256634)))))))) (let ((_let_2300 (forall ((BOUND_VARIABLE_1256589 tptp.nat) (BOUND_VARIABLE_1256590 tptp.nat) (BOUND_VARIABLE_1256591 tptp.nat) (BOUND_VARIABLE_1256592 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256589) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256591) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256590) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256592) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4411 BOUND_VARIABLE_1256589) BOUND_VARIABLE_1256590) BOUND_VARIABLE_1256591) BOUND_VARIABLE_1256592)))))))) (let ((_let_2301 (forall ((BOUND_VARIABLE_1256547 tptp.nat) (BOUND_VARIABLE_1256548 tptp.nat) (BOUND_VARIABLE_1256549 tptp.nat) (BOUND_VARIABLE_1256550 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256547) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256549) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256548) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256550) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4412 BOUND_VARIABLE_1256547) BOUND_VARIABLE_1256548) BOUND_VARIABLE_1256549) BOUND_VARIABLE_1256550)))))))) (let ((_let_2302 (forall ((BOUND_VARIABLE_1256501 tptp.nat) (BOUND_VARIABLE_1256502 tptp.nat) (BOUND_VARIABLE_1256503 tptp.nat) (BOUND_VARIABLE_1256504 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256501) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256504) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256503) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256502) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4413 BOUND_VARIABLE_1256501) BOUND_VARIABLE_1256502) BOUND_VARIABLE_1256503) BOUND_VARIABLE_1256504)))))))) (let ((_let_2303 (forall ((BOUND_VARIABLE_1256455 tptp.nat) (BOUND_VARIABLE_1256456 tptp.nat) (BOUND_VARIABLE_1256457 tptp.nat) (BOUND_VARIABLE_1256458 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256455) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256458) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256457) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256456) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4414 BOUND_VARIABLE_1256455) BOUND_VARIABLE_1256456) BOUND_VARIABLE_1256457) BOUND_VARIABLE_1256458)))))))) (let ((_let_2304 (forall ((BOUND_VARIABLE_1256409 tptp.nat) (BOUND_VARIABLE_1256410 tptp.nat) (BOUND_VARIABLE_1256411 tptp.nat) (BOUND_VARIABLE_1256412 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256409) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256412) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256411) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256410) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4415 BOUND_VARIABLE_1256409) BOUND_VARIABLE_1256410) BOUND_VARIABLE_1256411) BOUND_VARIABLE_1256412)))))))) (let ((_let_2305 (forall ((BOUND_VARIABLE_1256363 tptp.nat) (BOUND_VARIABLE_1256364 tptp.nat) (BOUND_VARIABLE_1256365 tptp.nat) (BOUND_VARIABLE_1256366 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256363) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256366) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256365) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256364) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4416 BOUND_VARIABLE_1256363) BOUND_VARIABLE_1256364) BOUND_VARIABLE_1256365) BOUND_VARIABLE_1256366)))))))) (let ((_let_2306 (forall ((BOUND_VARIABLE_1256323 tptp.nat) (BOUND_VARIABLE_1256324 tptp.nat) (BOUND_VARIABLE_1256325 tptp.nat) (BOUND_VARIABLE_1256326 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4417 BOUND_VARIABLE_1256323) BOUND_VARIABLE_1256324) BOUND_VARIABLE_1256325) BOUND_VARIABLE_1256326) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256323) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256326) _let_2))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256325) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256324) _let_2))))))))))) (let ((_let_2307 (forall ((BOUND_VARIABLE_1256245 tptp.nat) (BOUND_VARIABLE_1256246 tptp.nat) (BOUND_VARIABLE_1256247 tptp.nat) (BOUND_VARIABLE_1256248 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256247) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256246) _let_2)))) (let ((_let_6 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256248) _let_2))) (let ((_let_7 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256245) _let_2)))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_6))) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_6))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4418 BOUND_VARIABLE_1256245) BOUND_VARIABLE_1256246) BOUND_VARIABLE_1256247) BOUND_VARIABLE_1256248)))))))))))) (let ((_let_2308 (forall ((BOUND_VARIABLE_1256167 tptp.nat) (BOUND_VARIABLE_1256168 tptp.nat) (BOUND_VARIABLE_1256169 tptp.nat) (BOUND_VARIABLE_1256170 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256169) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256168) _let_2)))) (let ((_let_6 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256170) _let_2))) (let ((_let_7 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256167) _let_2)))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_6))) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_6))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4419 BOUND_VARIABLE_1256167) BOUND_VARIABLE_1256168) BOUND_VARIABLE_1256169) BOUND_VARIABLE_1256170)))))))))))) (let ((_let_2309 (forall ((BOUND_VARIABLE_1256125 tptp.nat) (BOUND_VARIABLE_1256126 tptp.nat) (BOUND_VARIABLE_1256127 tptp.nat) (BOUND_VARIABLE_1256128 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256125) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256128) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256126) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256127) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4420 BOUND_VARIABLE_1256125) BOUND_VARIABLE_1256126) BOUND_VARIABLE_1256127) BOUND_VARIABLE_1256128)))))))) (let ((_let_2310 (forall ((BOUND_VARIABLE_1256083 tptp.nat) (BOUND_VARIABLE_1256084 tptp.nat) (BOUND_VARIABLE_1256085 tptp.nat) (BOUND_VARIABLE_1256086 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256083) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256085) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256084) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256086) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4421 BOUND_VARIABLE_1256083) BOUND_VARIABLE_1256084) BOUND_VARIABLE_1256085) BOUND_VARIABLE_1256086)))))))) (let ((_let_2311 (forall ((BOUND_VARIABLE_1256037 tptp.nat) (BOUND_VARIABLE_1256038 tptp.nat) (BOUND_VARIABLE_1256039 tptp.nat) (BOUND_VARIABLE_1256040 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256037) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256040) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256039) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1256038) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4422 BOUND_VARIABLE_1256037) BOUND_VARIABLE_1256038) BOUND_VARIABLE_1256039) BOUND_VARIABLE_1256040)))))))) (let ((_let_2312 (forall ((BOUND_VARIABLE_1255991 tptp.nat) (BOUND_VARIABLE_1255992 tptp.nat) (BOUND_VARIABLE_1255993 tptp.nat) (BOUND_VARIABLE_1255994 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255991) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255994) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255993) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255992) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4423 BOUND_VARIABLE_1255991) BOUND_VARIABLE_1255992) BOUND_VARIABLE_1255993) BOUND_VARIABLE_1255994)))))))) (let ((_let_2313 (forall ((BOUND_VARIABLE_1255913 tptp.nat) (BOUND_VARIABLE_1255914 tptp.nat) (BOUND_VARIABLE_1255915 tptp.nat) (BOUND_VARIABLE_1255916 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255915) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255914) _let_2)))) (let ((_let_6 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255916) _let_2))) (let ((_let_7 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255913) _let_2)))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_6))) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_6))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4424 BOUND_VARIABLE_1255913) BOUND_VARIABLE_1255914) BOUND_VARIABLE_1255915) BOUND_VARIABLE_1255916)))))))))))) (let ((_let_2314 (forall ((BOUND_VARIABLE_1255906 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4316 k_4425 BOUND_VARIABLE_1255906) (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))))))))) (let ((_let_2315 (forall ((BOUND_VARIABLE_1279472 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1255896 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1279472 BOUND_VARIABLE_1255896)) (ho_4316 (ho_4249 k_4450 BOUND_VARIABLE_1279472) BOUND_VARIABLE_1255896))))) (let ((_let_2316 (forall ((BOUND_VARIABLE_1255888 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_4451 BOUND_VARIABLE_1255888))))))))) (let ((_let_2317 (forall ((BOUND_VARIABLE_1279490 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1255878 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1279490 BOUND_VARIABLE_1255878)) (ho_4316 (ho_4249 k_4452 BOUND_VARIABLE_1279490) BOUND_VARIABLE_1255878))))) (let ((_let_2318 (forall ((BOUND_VARIABLE_1255870 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_4453 BOUND_VARIABLE_1255870))))))))) (let ((_let_2319 (forall ((BOUND_VARIABLE_1279506 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1255860 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1279506 BOUND_VARIABLE_1255860)) (ho_4316 (ho_4249 k_4454 BOUND_VARIABLE_1279506) BOUND_VARIABLE_1255860))))) (let ((_let_2320 (forall ((BOUND_VARIABLE_1255847 tptp.nat) (BOUND_VARIABLE_1255848 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1255847) (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (ho_4316 (ho_4338 k_4459 BOUND_VARIABLE_1255847) BOUND_VARIABLE_1255848))))))))) (let ((_let_2321 (forall ((BOUND_VARIABLE_1255817 tptp.nat) (BOUND_VARIABLE_1255818 tptp.nat) (BOUND_VARIABLE_1255819 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255819) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255817) _let_2))))) (ho_4290 k_4289 BOUND_VARIABLE_1255818)) (ho_4288 (ho_4287 (ho_4303 k_4460 BOUND_VARIABLE_1255817) BOUND_VARIABLE_1255818) BOUND_VARIABLE_1255819)))))))) (let ((_let_2322 (forall ((BOUND_VARIABLE_1255807 tptp.nat) (BOUND_VARIABLE_1255808 tptp.nat)) (= (ho_4288 (ho_4287 k_4461 BOUND_VARIABLE_1255807) BOUND_VARIABLE_1255808) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1255808)) (ho_4290 k_4289 BOUND_VARIABLE_1255807)))))) (let ((_let_2323 (forall ((BOUND_VARIABLE_1255765 tptp.nat) (BOUND_VARIABLE_1255766 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1255765) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1255766 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_4469 BOUND_VARIABLE_1255765) BOUND_VARIABLE_1255766))))) (let ((_let_2324 (forall ((BOUND_VARIABLE_1255755 tptp.nat) (BOUND_VARIABLE_1255756 tptp.nat)) (= (ho_4288 (ho_4287 k_4470 BOUND_VARIABLE_1255755) BOUND_VARIABLE_1255756) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255756)) (ho_4290 k_4289 BOUND_VARIABLE_1255755)))))) (let ((_let_2325 (forall ((BOUND_VARIABLE_1255737 tptp.nat) (BOUND_VARIABLE_1255738 tptp.nat)) (= (ho_4288 (ho_4287 k_4471 BOUND_VARIABLE_1255737) BOUND_VARIABLE_1255738) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1255737))) (or (not (= BOUND_VARIABLE_1255738 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_2326 (forall ((BOUND_VARIABLE_1279639 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255723 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255723)) (ho_4245 BOUND_VARIABLE_1279639 BOUND_VARIABLE_1255723)) (ho_4245 (ho_4473 k_4472 BOUND_VARIABLE_1279639) BOUND_VARIABLE_1255723)))))) (let ((_let_2327 (forall ((BOUND_VARIABLE_1255690 tptp.nat) (BOUND_VARIABLE_1255691 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255691)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255690) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_4474 BOUND_VARIABLE_1255690) BOUND_VARIABLE_1255691)))))))) (let ((_let_2328 (forall ((BOUND_VARIABLE_1279675 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255676 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255676)) (ho_4245 BOUND_VARIABLE_1279675 BOUND_VARIABLE_1255676)) (ho_4245 (ho_4473 k_4475 BOUND_VARIABLE_1279675) BOUND_VARIABLE_1255676)))))) (let ((_let_2329 (forall ((BOUND_VARIABLE_1255643 tptp.nat) (BOUND_VARIABLE_1255644 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255644)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255643) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_4476 BOUND_VARIABLE_1255643) BOUND_VARIABLE_1255644)))))))) (let ((_let_2330 (forall ((BOUND_VARIABLE_1279708 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255629 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255629)) (ho_4245 BOUND_VARIABLE_1279708 BOUND_VARIABLE_1255629)) (ho_4245 (ho_4473 k_4477 BOUND_VARIABLE_1279708) BOUND_VARIABLE_1255629)))))) (let ((_let_2331 (forall ((BOUND_VARIABLE_1255606 tptp.nat) (BOUND_VARIABLE_1255607 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255607)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255606) _let_2))))) (ho_4288 (ho_4287 k_4478 BOUND_VARIABLE_1255606) BOUND_VARIABLE_1255607)))))))) (let ((_let_2332 (forall ((BOUND_VARIABLE_1279736 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255592 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255592)) (ho_4245 BOUND_VARIABLE_1279736 BOUND_VARIABLE_1255592)) (ho_4245 (ho_4473 k_4479 BOUND_VARIABLE_1279736) BOUND_VARIABLE_1255592)))))) (let ((_let_2333 (forall ((BOUND_VARIABLE_1255559 tptp.nat) (BOUND_VARIABLE_1255560 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255560)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255559) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_4480 BOUND_VARIABLE_1255559) BOUND_VARIABLE_1255560)))))))) (let ((_let_2334 (forall ((BOUND_VARIABLE_1279769 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255545 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255545)) (ho_4245 BOUND_VARIABLE_1279769 BOUND_VARIABLE_1255545)) (ho_4245 (ho_4473 k_4481 BOUND_VARIABLE_1279769) BOUND_VARIABLE_1255545)))))) (let ((_let_2335 (forall ((BOUND_VARIABLE_1255522 tptp.nat) (BOUND_VARIABLE_1255523 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255523)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255522) _let_2))))) (ho_4288 (ho_4287 k_4482 BOUND_VARIABLE_1255522) BOUND_VARIABLE_1255523)))))))) (let ((_let_2336 (forall ((BOUND_VARIABLE_1279797 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255508 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1255508)) (ho_4245 BOUND_VARIABLE_1279797 BOUND_VARIABLE_1255508)) (ho_4245 (ho_4473 k_4483 BOUND_VARIABLE_1279797) BOUND_VARIABLE_1255508)))))) (let ((_let_2337 (forall ((BOUND_VARIABLE_1255485 tptp.nat) (BOUND_VARIABLE_1255486 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1255486)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255485) _let_2))))) (ho_4288 (ho_4287 k_4484 BOUND_VARIABLE_1255485) BOUND_VARIABLE_1255486)))))))) (let ((_let_2338 (forall ((BOUND_VARIABLE_1279825 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255438 tptp.nat) (BOUND_VARIABLE_1255439 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4487 (ho_4486 k_4485 BOUND_VARIABLE_1279825) BOUND_VARIABLE_1255438) BOUND_VARIABLE_1255439) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1255439 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1255439) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1255439) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 (ho_4245 BOUND_VARIABLE_1279825 BOUND_VARIABLE_1255438)) BOUND_VARIABLE_1255439))))))))))))) (let ((_let_2339 (forall ((BOUND_VARIABLE_1279868 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1255429 tptp.nat) (BOUND_VARIABLE_1255430 tptp.nat)) (= (ho_4316 (ho_4338 (ho_4489 k_4488 BOUND_VARIABLE_1279868) BOUND_VARIABLE_1255429) BOUND_VARIABLE_1255430) (ho_4318 k_4317 (ho_4335 BOUND_VARIABLE_1279868 BOUND_VARIABLE_1255429)))))) (let ((_let_2340 (forall ((BOUND_VARIABLE_1279883 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1255372 tptp.nat) (BOUND_VARIABLE_1255373 tptp.real) (BOUND_VARIABLE_1255374 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 _let_2 _let_5))) (let ((_let_7 (ho_4258 (ho_4265 _let_4 _let_5) _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4264 _let_3 k_4275))) (= (ho_4245 (ho_4244 (ho_4492 (ho_4491 k_4490 BOUND_VARIABLE_1279883) BOUND_VARIABLE_1255372) BOUND_VARIABLE_1255373) BOUND_VARIABLE_1255374) (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1255374 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_9 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1255374) _let_8))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1255374) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_7)))) _let_7)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 (ho_4245 BOUND_VARIABLE_1279883 BOUND_VARIABLE_1255372)) (ho_4258 _let_2 BOUND_VARIABLE_1255373))) BOUND_VARIABLE_1255374))))))))))))))) (let ((_let_2341 (forall ((BOUND_VARIABLE_1279930 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1255363 tptp.nat) (BOUND_VARIABLE_1255364 tptp.nat)) (= (ho_4316 (ho_4338 (ho_4489 k_4493 BOUND_VARIABLE_1279930) BOUND_VARIABLE_1255363) BOUND_VARIABLE_1255364) (ho_4318 k_4317 (ho_4335 BOUND_VARIABLE_1279930 BOUND_VARIABLE_1255363)))))) (let ((_let_2342 (forall ((BOUND_VARIABLE_1255309 tptp.nat) (BOUND_VARIABLE_1255310 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1255310 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4494 BOUND_VARIABLE_1255309) BOUND_VARIABLE_1255310) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1255310 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1255310) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1255310)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1255310)) BOUND_VARIABLE_1255310)) BOUND_VARIABLE_1255309)))))))))))))) (let ((_let_2343 (forall ((BOUND_VARIABLE_1255256 tptp.nat) (BOUND_VARIABLE_1255257 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1255257 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4495 BOUND_VARIABLE_1255256) BOUND_VARIABLE_1255257) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1255257 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1255257) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1255257)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1255257)) BOUND_VARIABLE_1255257)) BOUND_VARIABLE_1255256)))))))))))))) (let ((_let_2344 (forall ((BOUND_VARIABLE_1255210 tptp.real) (BOUND_VARIABLE_1255211 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4496 BOUND_VARIABLE_1255210) BOUND_VARIABLE_1255211) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1255211 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1255211) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1255211) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1255210) BOUND_VARIABLE_1255211))))))))))))) (let ((_let_2345 (forall ((BOUND_VARIABLE_1255159 tptp.real) (BOUND_VARIABLE_1255160 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4497 BOUND_VARIABLE_1255159) BOUND_VARIABLE_1255160) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1255160 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1255160) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1255160) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1255159) BOUND_VARIABLE_1255160))))))))))))))))) (let ((_let_2346 (forall ((BOUND_VARIABLE_1255106 tptp.nat) (BOUND_VARIABLE_1255107 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1255107 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4498 BOUND_VARIABLE_1255106) BOUND_VARIABLE_1255107) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1255107 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1255107) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1255107)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1255107)) BOUND_VARIABLE_1255107)) BOUND_VARIABLE_1255106)))))))))))))) (let ((_let_2347 (forall ((BOUND_VARIABLE_1255057 tptp.real) (BOUND_VARIABLE_1255058 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1255058) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4258 (ho_4257 _let_6 k_4248) _let_5))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_9 (ho_4264 _let_8 k_4275))) (= (ho_4258 (ho_4265 _let_9 (ho_4245 (ho_4244 k_4243 _let_7) BOUND_VARIABLE_1255058)) (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 _let_5) (ho_4258 (ho_4257 _let_6 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) _let_4) (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) _let_5) _let_7))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1255057) _let_4))) (ho_4245 (ho_4244 k_4499 BOUND_VARIABLE_1255057) BOUND_VARIABLE_1255058)))))))))))))) (let ((_let_2348 (forall ((BOUND_VARIABLE_1280132 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1255010 tptp.nat) (BOUND_VARIABLE_1255011 tptp.real) (BOUND_VARIABLE_1255012 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4273 BOUND_VARIABLE_1280132 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_7 BOUND_VARIABLE_1255010) _let_6)) (ho_4209 (ho_4220 _let_7 BOUND_VARIABLE_1255012) _let_6)))) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1255012) (ho_4213 k_4212 _let_5))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1255011) BOUND_VARIABLE_1255012)) (ho_4245 (ho_4244 (ho_4492 (ho_4501 k_4500 BOUND_VARIABLE_1280132) BOUND_VARIABLE_1255010) BOUND_VARIABLE_1255011) BOUND_VARIABLE_1255012))))))))))))) (let ((_let_2349 (forall ((BOUND_VARIABLE_1254980 tptp.nat) (BOUND_VARIABLE_1254981 tptp.nat) (BOUND_VARIABLE_1254982 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1254982)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254980) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1254981))) (ho_4288 (ho_4287 (ho_4303 k_4502 BOUND_VARIABLE_1254980) BOUND_VARIABLE_1254981) BOUND_VARIABLE_1254982)))))))) (let ((_let_2350 (forall ((BOUND_VARIABLE_1254927 tptp.nat) (BOUND_VARIABLE_1254928 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1254928 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4503 BOUND_VARIABLE_1254927) BOUND_VARIABLE_1254928) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1254928 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254928) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1254928)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1254928)) BOUND_VARIABLE_1254928)) BOUND_VARIABLE_1254927)))))))))))))) (let ((_let_2351 (forall ((BOUND_VARIABLE_1254876 tptp.real) (BOUND_VARIABLE_1254877 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (let ((_let_5 (= BOUND_VARIABLE_1254877 _let_4))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1254877 _let_6))) (= (ho_4351 (ho_4508 k_4507 BOUND_VARIABLE_1254876) BOUND_VARIABLE_1254877) (and (or (and (= BOUND_VARIABLE_1254877 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254877) _let_6)) (not _let_7)) _let_7) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1254877)) (not _let_5)) _let_5) (= BOUND_VARIABLE_1254876 (ho_4348 k_4347 (ho_4244 k_4284 BOUND_VARIABLE_1254877))))))))))))))) (let ((_let_2352 (forall ((BOUND_VARIABLE_1254825 tptp.real) (BOUND_VARIABLE_1254826 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_4 (= BOUND_VARIABLE_1254826 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1254826 _let_6))) (= (ho_4351 (ho_4508 k_4509 BOUND_VARIABLE_1254825) BOUND_VARIABLE_1254826) (and (or (and (= BOUND_VARIABLE_1254826 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254826) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1254826)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1254825 (ho_4348 k_4347 (ho_4244 k_4285 BOUND_VARIABLE_1254826))))))))))))))) (let ((_let_2353 (forall ((BOUND_VARIABLE_1254772 tptp.nat) (BOUND_VARIABLE_1254773 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1254773 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4510 BOUND_VARIABLE_1254772) BOUND_VARIABLE_1254773) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1254773 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254773) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1254773)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1254773)) BOUND_VARIABLE_1254773)) BOUND_VARIABLE_1254772)))))))))))))) (let ((_let_2354 (forall ((BOUND_VARIABLE_1280308 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1254746 tptp.real) (BOUND_VARIABLE_1254747 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1280308 BOUND_VARIABLE_1254747)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1254746) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254747) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4245 (ho_4244 (ho_4512 k_4511 BOUND_VARIABLE_1280308) BOUND_VARIABLE_1254746) BOUND_VARIABLE_1254747)))))))) (let ((_let_2355 (forall ((BOUND_VARIABLE_1254692 tptp.nat) (BOUND_VARIABLE_1254693 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1254693 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_4513 BOUND_VARIABLE_1254692) BOUND_VARIABLE_1254693) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1254693 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254693) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1254693)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1254693)) BOUND_VARIABLE_1254693)) BOUND_VARIABLE_1254692)))))))))))))) (let ((_let_2356 (forall ((BOUND_VARIABLE_1254631 tptp.nat) (BOUND_VARIABLE_1254632 tptp.real)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4257 _let_4 k_4248))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4258 _let_5 _let_6))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_9 (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) _let_6) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1254632 _let_9))) (let ((_let_11 (not _let_10))) (= (ho_4258 (ho_4273 k_4514 BOUND_VARIABLE_1254631) BOUND_VARIABLE_1254632) (ho_4258 (ho_4265 (ho_4264 _let_8 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_10) _let_9) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1254632 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1254632) _let_9)) _let_11)) _let_6) _let_7))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_9 (ho_4258 (ho_4265 k_4349 _let_9) BOUND_VARIABLE_1254632)) _let_11)) (ho_4258 _let_5 BOUND_VARIABLE_1254632)) BOUND_VARIABLE_1254632)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254631) _let_2)))))))))))))))))))) (let ((_let_2357 (forall ((BOUND_VARIABLE_1280397 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1254609 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 BOUND_VARIABLE_1280397) (ho_4516 k_4515 (ho_4287 k_4286 BOUND_VARIABLE_1254609))) (ho_4245 (ho_4473 k_4520 BOUND_VARIABLE_1280397) BOUND_VARIABLE_1254609))))) (let ((_let_2358 (forall ((BOUND_VARIABLE_1254597 tptp.int) (BOUND_VARIABLE_1254598 tptp.int)) (= (ho_4310 (ho_4309 k_4521 BOUND_VARIABLE_1254597) BOUND_VARIABLE_1254598) (= BOUND_VARIABLE_1254597 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1254598) (ho_4196 k_4195 tptp.one))) BOUND_VARIABLE_1254597)))))) (let ((_let_2359 (forall ((BOUND_VARIABLE_1254590 tptp.int) (BOUND_VARIABLE_1254591 tptp.nat)) (= (ho_4316 (ho_4315 k_4522 BOUND_VARIABLE_1254590) BOUND_VARIABLE_1254591) (ho_4318 k_4317 BOUND_VARIABLE_1254590))))) (let ((_let_2360 (forall ((BOUND_VARIABLE_1254583 tptp.int) (BOUND_VARIABLE_1254584 tptp.nat)) (= (ho_4316 (ho_4315 k_4523 BOUND_VARIABLE_1254583) BOUND_VARIABLE_1254584) (ho_4318 k_4317 BOUND_VARIABLE_1254583))))) (let ((_let_2361 (forall ((BOUND_VARIABLE_1254576 tptp.int) (BOUND_VARIABLE_1254577 tptp.nat)) (= (ho_4316 (ho_4315 k_4524 BOUND_VARIABLE_1254576) BOUND_VARIABLE_1254577) (ho_4318 k_4317 BOUND_VARIABLE_1254576))))) (let ((_let_2362 (forall ((BOUND_VARIABLE_1254556 tptp.nat) (BOUND_VARIABLE_1254557 tptp.num)) (= (ho_4300 (ho_4527 (ho_4526 k_4525 (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one)) (ho_4299 k_4298 BOUND_VARIABLE_1254557)) BOUND_VARIABLE_1254556) (ho_4191 (ho_4236 k_4528 BOUND_VARIABLE_1254556) BOUND_VARIABLE_1254557))))) (let ((_let_2363 (forall ((BOUND_VARIABLE_1254549 tptp.num)) (= (ho_4191 k_4529 BOUND_VARIABLE_1254549) (ho_4191 k_4194 (ho_4193 k_4192 BOUND_VARIABLE_1254549)))))) (let ((_let_2364 (forall ((BOUND_VARIABLE_1254532 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254533 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4530 BOUND_VARIABLE_1254532) BOUND_VARIABLE_1254533) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254533 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254532) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254532))))))))))) (let ((_let_2365 (forall ((BOUND_VARIABLE_1254515 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254516 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4538 BOUND_VARIABLE_1254515) BOUND_VARIABLE_1254516) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254516 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254515) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254515))))))))))) (let ((_let_2366 (forall ((BOUND_VARIABLE_1254498 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254499 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4539 BOUND_VARIABLE_1254498) BOUND_VARIABLE_1254499) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254499 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254498) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254498))))))))))) (let ((_let_2367 (forall ((BOUND_VARIABLE_1254481 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254482 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4540 BOUND_VARIABLE_1254481) BOUND_VARIABLE_1254482) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254482 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254481) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254481))))))))))) (let ((_let_2368 (forall ((BOUND_VARIABLE_1254464 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254465 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4541 BOUND_VARIABLE_1254464) BOUND_VARIABLE_1254465) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254465 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254464) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254464))))))))))) (let ((_let_2369 (forall ((BOUND_VARIABLE_1254447 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254448 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4542 BOUND_VARIABLE_1254447) BOUND_VARIABLE_1254448) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254448 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254447) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254447))))))))))) (let ((_let_2370 (forall ((BOUND_VARIABLE_1254430 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1254431 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_4543 BOUND_VARIABLE_1254430) BOUND_VARIABLE_1254431) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1254431 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1254430) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1254430))))))))))) (let ((_let_2371 (forall ((BOUND_VARIABLE_1254388 tptp.nat) (BOUND_VARIABLE_1254389 tptp.nat) (BOUND_VARIABLE_1254390 tptp.nat) (BOUND_VARIABLE_1254391 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254388) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254390) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254389) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254391) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4544 BOUND_VARIABLE_1254388) BOUND_VARIABLE_1254389) BOUND_VARIABLE_1254390) BOUND_VARIABLE_1254391)))))))) (let ((_let_2372 (forall ((BOUND_VARIABLE_1254346 tptp.nat) (BOUND_VARIABLE_1254347 tptp.nat) (BOUND_VARIABLE_1254348 tptp.nat) (BOUND_VARIABLE_1254349 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254346) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254349) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254347) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254348) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4545 BOUND_VARIABLE_1254346) BOUND_VARIABLE_1254347) BOUND_VARIABLE_1254348) BOUND_VARIABLE_1254349)))))))) (let ((_let_2373 (forall ((BOUND_VARIABLE_1254268 tptp.nat) (BOUND_VARIABLE_1254269 tptp.nat) (BOUND_VARIABLE_1254270 tptp.nat) (BOUND_VARIABLE_1254271 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254270) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254269) _let_2)))) (let ((_let_6 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254271) _let_2))) (let ((_let_7 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254268) _let_2)))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_6))) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_6))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4546 BOUND_VARIABLE_1254268) BOUND_VARIABLE_1254269) BOUND_VARIABLE_1254270) BOUND_VARIABLE_1254271)))))))))))) (let ((_let_2374 (forall ((BOUND_VARIABLE_1254221 tptp.nat) (BOUND_VARIABLE_1254222 tptp.nat) (BOUND_VARIABLE_1254223 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4301 BOUND_VARIABLE_1254221) BOUND_VARIABLE_1254222)) BOUND_VARIABLE_1254223) (ho_4549 (ho_4552 (ho_4551 k_4550 BOUND_VARIABLE_1254221) BOUND_VARIABLE_1254222) BOUND_VARIABLE_1254223))))) (let ((_let_2375 (forall ((BOUND_VARIABLE_1254174 tptp.nat) (BOUND_VARIABLE_1254175 tptp.nat) (BOUND_VARIABLE_1254176 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4305 BOUND_VARIABLE_1254174) BOUND_VARIABLE_1254175)) BOUND_VARIABLE_1254176) (ho_4549 (ho_4552 (ho_4551 k_4553 BOUND_VARIABLE_1254174) BOUND_VARIABLE_1254175) BOUND_VARIABLE_1254176))))) (let ((_let_2376 (forall ((BOUND_VARIABLE_1254132 tptp.nat) (BOUND_VARIABLE_1254133 tptp.nat) (BOUND_VARIABLE_1254134 tptp.nat) (BOUND_VARIABLE_1254135 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254132) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254135) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254133) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254134) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4554 BOUND_VARIABLE_1254132) BOUND_VARIABLE_1254133) BOUND_VARIABLE_1254134) BOUND_VARIABLE_1254135)))))))) (let ((_let_2377 (forall ((BOUND_VARIABLE_1254090 tptp.nat) (BOUND_VARIABLE_1254091 tptp.nat) (BOUND_VARIABLE_1254092 tptp.nat) (BOUND_VARIABLE_1254093 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254090) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254092) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254091) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254093) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4555 BOUND_VARIABLE_1254090) BOUND_VARIABLE_1254091) BOUND_VARIABLE_1254092) BOUND_VARIABLE_1254093)))))))) (let ((_let_2378 (forall ((BOUND_VARIABLE_1254044 tptp.nat) (BOUND_VARIABLE_1254045 tptp.nat) (BOUND_VARIABLE_1254046 tptp.nat) (BOUND_VARIABLE_1254047 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254044) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254047) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254046) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254045) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4556 BOUND_VARIABLE_1254044) BOUND_VARIABLE_1254045) BOUND_VARIABLE_1254046) BOUND_VARIABLE_1254047)))))))) (let ((_let_2379 (forall ((BOUND_VARIABLE_1253998 tptp.nat) (BOUND_VARIABLE_1253999 tptp.nat) (BOUND_VARIABLE_1254000 tptp.nat) (BOUND_VARIABLE_1254001 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253998) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254001) _let_2))))) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1254000) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253999) _let_2))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_4557 BOUND_VARIABLE_1253998) BOUND_VARIABLE_1253999) BOUND_VARIABLE_1254000) BOUND_VARIABLE_1254001)))))))) (let ((_let_2380 (forall ((BOUND_VARIABLE_1253920 tptp.nat) (BOUND_VARIABLE_1253921 tptp.nat) (BOUND_VARIABLE_1253922 tptp.nat) (BOUND_VARIABLE_1253923 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253922) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253921) _let_2)))) (let ((_let_6 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253923) _let_2))) (let ((_let_7 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1253920) _let_2)))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_6))) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_7 _let_6))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) _let_2)))) (ho_4406 (ho_4198 (ho_4409 (ho_4408 k_4558 BOUND_VARIABLE_1253920) BOUND_VARIABLE_1253921) BOUND_VARIABLE_1253922) BOUND_VARIABLE_1253923)))))))))))) (let ((_let_2381 (forall ((BOUND_VARIABLE_1253893 tptp.code_integer) (BOUND_VARIABLE_1253894 tptp.code_integer) (BOUND_VARIABLE_1253895 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4560 k_4559 _let_1))) (let ((_let_3 (ho_4560 (ho_4564 k_4563 _let_1) _let_2))) (let ((_let_4 (ho_4560 k_4559 BOUND_VARIABLE_1253894))) (= (ho_4572 (ho_4571 (ho_4578 k_4577 BOUND_VARIABLE_1253893) BOUND_VARIABLE_1253894) BOUND_VARIABLE_1253895) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1253895 _let_3)) (ho_4572 (ho_4571 k_4570 _let_4) _let_3)) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_4) _let_2)) (ho_4560 (ho_4564 k_4563 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1253893) _let_3)) (ho_4560 k_4559 BOUND_VARIABLE_1253893)) BOUND_VARIABLE_1253893)) (ho_4560 k_4559 BOUND_VARIABLE_1253895)))))))))))) (let ((_let_2382 (forall ((BOUND_VARIABLE_1253857 tptp.rat) (BOUND_VARIABLE_1253858 tptp.int) (BOUND_VARIABLE_1253859 tptp.int)) (= (ho_4582 (ho_4581 k_4580 (ho_4308 (ho_4307 k_4306 BOUND_VARIABLE_1253858) BOUND_VARIABLE_1253859)) (ho_4437 k_4579 BOUND_VARIABLE_1253857)) (ho_4310 (ho_4309 (ho_4584 k_4583 BOUND_VARIABLE_1253857) BOUND_VARIABLE_1253858) BOUND_VARIABLE_1253859))))) (let ((_let_2383 (forall ((BOUND_VARIABLE_1253816 tptp.rat) (BOUND_VARIABLE_1253817 tptp.int) (BOUND_VARIABLE_1253818 tptp.int)) (= (ho_4582 (ho_4581 k_4580 (ho_4308 (ho_4307 k_4312 BOUND_VARIABLE_1253817) BOUND_VARIABLE_1253818)) (ho_4437 k_4579 BOUND_VARIABLE_1253816)) (ho_4310 (ho_4309 (ho_4584 k_4585 BOUND_VARIABLE_1253816) BOUND_VARIABLE_1253817) BOUND_VARIABLE_1253818))))) (let ((_let_2384 (forall ((BOUND_VARIABLE_1253485 tptp.int) (BOUND_VARIABLE_1253486 tptp.int) (BOUND_VARIABLE_1253487 tptp.int) (BOUND_VARIABLE_1253488 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253488)) (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253486)))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253488)))) (let ((_let_6 (ho_4587 k_4586 _let_5))) (let ((_let_7 (ho_4587 k_4588 _let_5))) (let ((_let_8 (ho_4209 (ho_4211 k_4589 _let_7) _let_6))) (let ((_let_9 (ho_4209 _let_2 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_9) _let_1)) _let_3))) (ho_4209 _let_2 _let_9)) _let_9)))) (let ((_let_11 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6))))) (let ((_let_12 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_10)) _let_3))) (let ((_let_13 (ho_4209 k_4594 _let_9))) (let ((_let_14 (ho_4209 k_4594 _let_6))) (let ((_let_15 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_9)) _let_3))) (let ((_let_16 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7))))) (let ((_let_17 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_10)) _let_3))) (let ((_let_18 (ho_4209 k_4594 _let_7))) (let ((_let_19 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_8) _let_1)) _let_3))) _let_9) _let_8)))) (let ((_let_20 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_19)) _let_3))) (let ((_let_21 (ho_4209 k_4594 _let_8))) (let ((_let_22 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_8)) _let_3))) (let ((_let_23 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_19)) _let_3))) (= (ho_4428 (ho_4427 (ho_4597 (ho_4596 k_4595 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253488) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_6 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_3) _let_1)) _let_6))) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_18 _let_21)) _let_23) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_23) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253488)) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253486)))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253488)))) (let ((_let_2 (ho_4587 k_4588 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 _let_2) (ho_4587 k_4586 _let_1))) K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_21)) _let_20) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_20) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253488)) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253486)))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253488)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2)) K3)))))))) _let_3)))) _let_3)))))) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_6)) (ho_4428 (ho_4427 k_4426 _let_3) _let_1)) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_13 _let_18)) _let_17) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_17) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253488)) (ho_4209 _let_1 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253486)))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253488)))) (let ((_let_3 (ho_4587 k_4588 _let_2))) (not (= _let_3 (ho_4209 (ho_4211 k_4222 (ho_4209 _let_1 (ho_4209 (ho_4211 k_4589 _let_3) (ho_4587 k_4586 _let_2)))) K3))))))))) _let_3)))) _let_3))))) (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_13)) _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253485) BOUND_VARIABLE_1253488)) (ho_4209 _let_1 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253487) BOUND_VARIABLE_1253486)))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253486) BOUND_VARIABLE_1253488)))) (let ((_let_3 (ho_4587 k_4586 _let_2))) (not (= _let_3 (ho_4209 (ho_4211 k_4222 (ho_4209 _let_1 (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_2)) _let_3))) K3))))))))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))) (let ((_let_2385 (forall ((BOUND_VARIABLE_1253189 tptp.int) (BOUND_VARIABLE_1253190 tptp.int) (BOUND_VARIABLE_1253191 tptp.int) (BOUND_VARIABLE_1253192 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253192)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253190))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253192)))) (let ((_let_6 (ho_4587 k_4586 _let_5))) (let ((_let_7 (ho_4587 k_4588 _let_5))) (let ((_let_8 (ho_4209 (ho_4211 k_4589 _let_7) _let_6))) (let ((_let_9 (ho_4209 _let_2 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_9) _let_1)) _let_3))) (ho_4209 _let_2 _let_9)) _let_9)))) (let ((_let_11 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6))))) (let ((_let_12 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_10)) _let_3))) (let ((_let_13 (ho_4209 k_4594 _let_6))) (let ((_let_14 (ho_4209 k_4594 _let_9))) (let ((_let_15 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_9)) _let_3))) (let ((_let_16 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7))))) (let ((_let_17 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_10)) _let_3))) (let ((_let_18 (ho_4209 k_4594 _let_7))) (let ((_let_19 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_8) _let_1)) _let_3))) _let_9) _let_8)))) (let ((_let_20 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_19)) _let_3))) (let ((_let_21 (ho_4209 k_4594 _let_8))) (let ((_let_22 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_8)) _let_3))) (let ((_let_23 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_19)) _let_3))) (= (ho_4428 (ho_4427 (ho_4597 (ho_4596 k_4598 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253192) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_6 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_3) _let_1)) _let_6))) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_18 _let_21)) _let_23) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_23) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253192)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253190))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253192)))) (let ((_let_2 (ho_4587 k_4588 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 _let_2) (ho_4587 k_4586 _let_1))) K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_13 _let_21)) _let_20) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_20) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253192)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253190))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253192)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2)) K3)))))))) _let_3)))) _let_3)))))) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_6)) (ho_4428 (ho_4427 k_4426 _let_3) _let_1)) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_18)) _let_17) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_17) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253192)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253190))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253192)))) (let ((_let_2 (ho_4587 k_4588 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4589 _let_2) (ho_4587 k_4586 _let_1)))) K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_13)) _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253189) BOUND_VARIABLE_1253192)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253191) BOUND_VARIABLE_1253190))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1253190) BOUND_VARIABLE_1253192)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2))) K3)))))))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))) (let ((_let_2386 (forall ((BOUND_VARIABLE_1252897 tptp.int) (BOUND_VARIABLE_1252898 tptp.int) (BOUND_VARIABLE_1252899 tptp.int) (BOUND_VARIABLE_1252900 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252897) BOUND_VARIABLE_1252899)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252898) BOUND_VARIABLE_1252900)))) (let ((_let_6 (ho_4587 k_4586 _let_5))) (let ((_let_7 (ho_4587 k_4588 _let_5))) (let ((_let_8 (ho_4209 (ho_4211 k_4589 _let_7) _let_6))) (let ((_let_9 (ho_4209 _let_2 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_9) _let_1)) _let_3))) (ho_4209 _let_2 _let_9)) _let_9)))) (let ((_let_11 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6))))) (let ((_let_12 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_10)) _let_3))) (let ((_let_13 (ho_4209 k_4594 _let_6))) (let ((_let_14 (ho_4209 k_4594 _let_9))) (let ((_let_15 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_9)) _let_3))) (let ((_let_16 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7))))) (let ((_let_17 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_10)) _let_3))) (let ((_let_18 (ho_4209 k_4594 _let_7))) (let ((_let_19 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_8) _let_1)) _let_3))) _let_9) _let_8)))) (let ((_let_20 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_19)) _let_3))) (let ((_let_21 (ho_4209 k_4594 _let_8))) (let ((_let_22 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_8)) _let_3))) (let ((_let_23 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_19)) _let_3))) (= (ho_4428 (ho_4427 (ho_4597 (ho_4596 k_4599 BOUND_VARIABLE_1252897) BOUND_VARIABLE_1252898) BOUND_VARIABLE_1252899) BOUND_VARIABLE_1252900) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_6 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_3) _let_1)) _let_6))) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_18 _let_21)) _let_23) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_23) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252897) BOUND_VARIABLE_1252899)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252898) BOUND_VARIABLE_1252900)))) (let ((_let_2 (ho_4587 k_4588 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 _let_2) (ho_4587 k_4586 _let_1))) K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_22 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_13 _let_21)) _let_20) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_20) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252897) BOUND_VARIABLE_1252899)) (ho_4209 (ho_4211 k_4222 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K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_13)) _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252897) BOUND_VARIABLE_1252899)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252898) BOUND_VARIABLE_1252900)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2))) K3)))))))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))) (let ((_let_2387 (forall ((BOUND_VARIABLE_1252605 tptp.int) (BOUND_VARIABLE_1252606 tptp.int) (BOUND_VARIABLE_1252607 tptp.int) (BOUND_VARIABLE_1252608 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252605) BOUND_VARIABLE_1252608)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252606) BOUND_VARIABLE_1252607)))) (let ((_let_6 (ho_4587 k_4586 _let_5))) (let ((_let_7 (ho_4587 k_4588 _let_5))) (let ((_let_8 (ho_4209 (ho_4211 k_4589 _let_7) _let_6))) (let ((_let_9 (ho_4209 _let_2 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_9) _let_1)) _let_3))) (ho_4209 _let_2 _let_9)) _let_9)))) (let ((_let_11 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6))))) (let ((_let_12 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_10)) _let_3))) (let ((_let_13 (ho_4209 k_4594 _let_6))) (let ((_let_14 (ho_4209 k_4594 _let_9))) (let ((_let_15 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_9)) _let_3))) (let ((_let_16 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7))))) (let ((_let_17 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_10)) _let_3))) (let ((_let_18 (ho_4209 k_4594 _let_7))) (let ((_let_19 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_8) _let_1)) _let_3))) _let_9) _let_8)))) (let ((_let_20 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_11 _let_19)) _let_3))) (let ((_let_21 (ho_4209 k_4594 _let_8))) (let ((_let_22 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_8)) _let_3))) (let ((_let_23 (ho_4209 (ho_4220 _let_4 (ho_4216 _let_16 _let_19)) _let_3))) (= (ho_4428 (ho_4427 (ho_4597 (ho_4596 k_4600 BOUND_VARIABLE_1252605) BOUND_VARIABLE_1252606) 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k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252605) BOUND_VARIABLE_1252608)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252606) BOUND_VARIABLE_1252607)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2)) K3)))))))) _let_3)))) _let_3)))))) (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_6)) (ho_4428 (ho_4427 k_4426 _let_3) _let_1)) (ho_4428 (ho_4427 k_4426 (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_18)) _let_17) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_17) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252605) BOUND_VARIABLE_1252608)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252606) BOUND_VARIABLE_1252607)))) (let ((_let_2 (ho_4587 k_4588 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4589 _let_2) (ho_4587 k_4586 _let_1)))) K3)))))))) _let_3)))) _let_3))))) (ho_4209 _let_15 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_14 _let_13)) _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252605) BOUND_VARIABLE_1252608)) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1252606) BOUND_VARIABLE_1252607)))) (let ((_let_2 (ho_4587 k_4586 _let_1))) (not (= _let_2 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4589 (ho_4587 k_4588 _let_1)) _let_2))) K3)))))))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))) (let ((_let_2388 (forall ((BOUND_VARIABLE_1252584 tptp.code_integer) (BOUND_VARIABLE_1252585 tptp.code_integer) (BOUND_VARIABLE_1252586 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4560 k_4559 _let_1))) (let ((_let_3 (ho_4560 k_4559 BOUND_VARIABLE_1252585))) (let ((_let_4 (ho_4560 (ho_4564 k_4563 _let_1) _let_2))) (= (ho_4572 (ho_4571 (ho_4578 k_4601 BOUND_VARIABLE_1252584) BOUND_VARIABLE_1252585) BOUND_VARIABLE_1252586) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1252586 _let_4)) (ho_4572 (ho_4571 k_4570 _let_3) _let_4)) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_3) _let_2)) (ho_4560 (ho_4564 k_4563 BOUND_VARIABLE_1252584) (ho_4560 k_4559 BOUND_VARIABLE_1252586)))))))))))) (let ((_let_2389 (forall ((BOUND_VARIABLE_1252562 tptp.code_integer) (BOUND_VARIABLE_1252563 tptp.code_integer) (BOUND_VARIABLE_1252564 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4560 k_4559 _let_1))) (let ((_let_3 (ho_4560 k_4559 BOUND_VARIABLE_1252563))) (let ((_let_4 (ho_4560 (ho_4564 k_4563 _let_1) _let_2))) (= (ho_4572 (ho_4571 (ho_4578 k_4602 BOUND_VARIABLE_1252562) BOUND_VARIABLE_1252563) BOUND_VARIABLE_1252564) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1252564 _let_4)) (ho_4572 (ho_4571 k_4570 _let_3) _let_4)) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_3) _let_2)) (ho_4560 (ho_4564 k_4563 (ho_4560 k_4559 BOUND_VARIABLE_1252562)) (ho_4560 k_4559 BOUND_VARIABLE_1252564)))))))))))) (let ((_let_2390 (forall ((BOUND_VARIABLE_1252544 tptp.code_integer) (BOUND_VARIABLE_1252545 tptp.code_integer) (BOUND_VARIABLE_1252546 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (= (ho_4606 (ho_4605 (ho_4604 k_4603 BOUND_VARIABLE_1252544) BOUND_VARIABLE_1252545) BOUND_VARIABLE_1252546) (ho_4609 (ho_4608 k_4607 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4560 k_4559 _let_1))) BOUND_VARIABLE_1252544)) BOUND_VARIABLE_1252545) (ho_4560 (ho_4564 k_4563 (ho_4560 k_4559 BOUND_VARIABLE_1252545)) (ho_4560 k_4559 BOUND_VARIABLE_1252546)))) (= BOUND_VARIABLE_1252546 _let_1))))))) (let ((_let_2391 (forall ((BOUND_VARIABLE_1252509 tptp.code_integer) (BOUND_VARIABLE_1252510 tptp.code_integer)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4611 k_4610 BOUND_VARIABLE_1252509)) _let_2))) (let ((_let_5 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_4) _let_4)))) (let ((_let_6 (ho_4562 k_4561 tptp.one))) (= (ho_4611 (ho_4615 k_4614 BOUND_VARIABLE_1252509) BOUND_VARIABLE_1252510) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1252510 (ho_4560 (ho_4564 k_4563 _let_6) (ho_4560 k_4559 _let_6)))) _let_5) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_5) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))))))))))) (let ((_let_2392 (forall ((BOUND_VARIABLE_1252494 tptp.code_integer) (BOUND_VARIABLE_1252495 tptp.code_integer)) (let ((_let_1 (ho_4617 k_4616 BOUND_VARIABLE_1252494))) (let ((_let_2 (ho_4193 (ho_4619 k_4618 _let_1) _let_1))) (let ((_let_3 (ho_4562 k_4561 tptp.one))) (= (ho_4617 (ho_4623 k_4622 BOUND_VARIABLE_1252494) BOUND_VARIABLE_1252495) (ho_4193 (ho_4619 (ho_4621 k_4620 (= BOUND_VARIABLE_1252495 (ho_4560 (ho_4564 k_4563 _let_3) (ho_4560 k_4559 _let_3)))) _let_2) (ho_4193 (ho_4619 k_4618 _let_2) tptp.one))))))))) (let ((_let_2393 (forall ((BOUND_VARIABLE_1252480 tptp.code_integer) (BOUND_VARIABLE_1252481 tptp.code_integer)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) (ho_4625 k_4624 BOUND_VARIABLE_1252480)))) (let ((_let_2 (ho_4562 k_4561 tptp.one))) (= (ho_4625 (ho_4627 k_4626 BOUND_VARIABLE_1252480) BOUND_VARIABLE_1252481) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1252481 (ho_4560 (ho_4564 k_4563 _let_2) (ho_4560 k_4559 _let_2)))) _let_1) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4196 k_4195 tptp.one))))))))) (let ((_let_2394 (forall ((BOUND_VARIABLE_1252454 tptp.num) (BOUND_VARIABLE_1252455 tptp.code_integer) (BOUND_VARIABLE_1252456 tptp.code_integer)) (let ((_let_1 (ho_4560 (ho_4564 k_4630 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1252455))) (let ((_let_2 (ho_4562 k_4561 BOUND_VARIABLE_1252454))) (let ((_let_3 (ho_4625 k_4624 BOUND_VARIABLE_1252456))) (= (ho_4572 (ho_4571 (ho_4629 k_4628 BOUND_VARIABLE_1252454) BOUND_VARIABLE_1252455) BOUND_VARIABLE_1252456) (ho_4576 (ho_4575 (ho_4574 k_4573 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 _let_2)) _let_3))) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4562 k_4561 tptp.one))) (ho_4560 (ho_4564 k_4563 BOUND_VARIABLE_1252456) (ho_4560 k_4559 _let_2)))) (ho_4572 (ho_4571 k_4570 _let_1) BOUND_VARIABLE_1252456))))))))) (let ((_let_2395 (forall ((BOUND_VARIABLE_1252428 tptp.num) (BOUND_VARIABLE_1252429 tptp.code_integer) (BOUND_VARIABLE_1252430 tptp.code_integer)) (let ((_let_1 (ho_4560 (ho_4564 k_4630 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1252429))) (let ((_let_2 (ho_4562 k_4561 BOUND_VARIABLE_1252428))) (let ((_let_3 (ho_4625 k_4624 BOUND_VARIABLE_1252430))) (= (ho_4572 (ho_4571 (ho_4629 k_4631 BOUND_VARIABLE_1252428) BOUND_VARIABLE_1252429) BOUND_VARIABLE_1252430) (ho_4576 (ho_4575 (ho_4574 k_4573 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 _let_2)) _let_3))) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4562 k_4561 tptp.one))) (ho_4560 (ho_4564 k_4563 BOUND_VARIABLE_1252430) (ho_4560 k_4559 _let_2)))) (ho_4572 (ho_4571 k_4570 _let_1) BOUND_VARIABLE_1252430))))))))) (let ((_let_2396 (forall ((BOUND_VARIABLE_1252384 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1252384 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1252384 _let_3))) (= (ho_4351 k_4632 BOUND_VARIABLE_1252384) (and (or (and (= BOUND_VARIABLE_1252384 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1252384) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1252384)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4313 BOUND_VARIABLE_1252384)))))))))))))) (let ((_let_2397 (forall ((BOUND_VARIABLE_1252364 tptp.int) (BOUND_VARIABLE_1252365 tptp.int) (BOUND_VARIABLE_1252366 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_4633 BOUND_VARIABLE_1252364) BOUND_VARIABLE_1252365) BOUND_VARIABLE_1252366) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1252364) BOUND_VARIABLE_1252365))) (or (not (= BOUND_VARIABLE_1252366 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_2398 (forall ((BOUND_VARIABLE_1252342 tptp.int) (BOUND_VARIABLE_1252343 tptp.int) (BOUND_VARIABLE_1252344 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_4641 BOUND_VARIABLE_1252342) BOUND_VARIABLE_1252343) BOUND_VARIABLE_1252344) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252342) (ho_4196 k_4195 tptp.one))) BOUND_VARIABLE_1252343))) (or (not (= BOUND_VARIABLE_1252344 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_2399 (forall ((BOUND_VARIABLE_1252291 tptp.real) (BOUND_VARIABLE_1252292 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4642 BOUND_VARIABLE_1252291) BOUND_VARIABLE_1252292) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1252292 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1252292) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1252292) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1252291) BOUND_VARIABLE_1252292))))))))))))))))) (let ((_let_2400 (forall ((BOUND_VARIABLE_1252245 tptp.real) (BOUND_VARIABLE_1252246 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4643 BOUND_VARIABLE_1252245) BOUND_VARIABLE_1252246) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1252246 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1252246) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1252246) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1252245) BOUND_VARIABLE_1252246))))))))))))) (let ((_let_2401 (forall ((BOUND_VARIABLE_1252194 tptp.real) (BOUND_VARIABLE_1252195 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4644 BOUND_VARIABLE_1252194) BOUND_VARIABLE_1252195) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1252195 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1252195) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1252195) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1252194) BOUND_VARIABLE_1252195))))))))))))))))) (let ((_let_2402 (forall ((BOUND_VARIABLE_1252148 tptp.real) (BOUND_VARIABLE_1252149 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4645 BOUND_VARIABLE_1252148) BOUND_VARIABLE_1252149) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1252149 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1252149) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1252149) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1252148) BOUND_VARIABLE_1252149))))))))))))) (let ((_let_2403 (forall ((BOUND_VARIABLE_1252141 tptp.int) (BOUND_VARIABLE_1252142 tptp.nat)) (= (ho_4316 (ho_4315 k_4646 BOUND_VARIABLE_1252141) BOUND_VARIABLE_1252142) (ho_4318 k_4317 BOUND_VARIABLE_1252141))))) (let ((_let_2404 (forall ((BOUND_VARIABLE_1252132 tptp.int) (BOUND_VARIABLE_1252133 tptp.nat)) (= (ho_4316 (ho_4315 k_4647 BOUND_VARIABLE_1252132) BOUND_VARIABLE_1252133) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252132) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2405 (forall ((BOUND_VARIABLE_1252125 tptp.int) (BOUND_VARIABLE_1252126 tptp.nat)) (= (ho_4316 (ho_4315 k_4648 BOUND_VARIABLE_1252125) BOUND_VARIABLE_1252126) (ho_4318 k_4317 BOUND_VARIABLE_1252125))))) (let ((_let_2406 (forall ((BOUND_VARIABLE_1252116 tptp.int) (BOUND_VARIABLE_1252117 tptp.nat)) (= (ho_4316 (ho_4315 k_4649 BOUND_VARIABLE_1252116) BOUND_VARIABLE_1252117) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252116) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2407 (forall ((BOUND_VARIABLE_1252109 tptp.int) (BOUND_VARIABLE_1252110 tptp.nat)) (= (ho_4316 (ho_4315 k_4650 BOUND_VARIABLE_1252109) BOUND_VARIABLE_1252110) (ho_4318 k_4317 BOUND_VARIABLE_1252109))))) (let ((_let_2408 (forall ((BOUND_VARIABLE_1252100 tptp.int) (BOUND_VARIABLE_1252101 tptp.nat)) (= (ho_4316 (ho_4315 k_4651 BOUND_VARIABLE_1252100) BOUND_VARIABLE_1252101) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252100) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2409 (forall ((BOUND_VARIABLE_1252093 tptp.int) (BOUND_VARIABLE_1252094 tptp.nat)) (= (ho_4316 (ho_4315 k_4652 BOUND_VARIABLE_1252093) BOUND_VARIABLE_1252094) (ho_4318 k_4317 BOUND_VARIABLE_1252093))))) (let ((_let_2410 (forall ((BOUND_VARIABLE_1252084 tptp.int) (BOUND_VARIABLE_1252085 tptp.nat)) (= (ho_4316 (ho_4315 k_4653 BOUND_VARIABLE_1252084) BOUND_VARIABLE_1252085) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252084) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2411 (forall ((BOUND_VARIABLE_1252077 tptp.int) (BOUND_VARIABLE_1252078 tptp.nat)) (= (ho_4316 (ho_4315 k_4654 BOUND_VARIABLE_1252077) BOUND_VARIABLE_1252078) (ho_4318 k_4317 BOUND_VARIABLE_1252077))))) (let ((_let_2412 (forall ((BOUND_VARIABLE_1252068 tptp.int) (BOUND_VARIABLE_1252069 tptp.nat)) (= (ho_4316 (ho_4315 k_4655 BOUND_VARIABLE_1252068) BOUND_VARIABLE_1252069) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252068) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2413 (forall ((BOUND_VARIABLE_1252061 tptp.int) (BOUND_VARIABLE_1252062 tptp.nat)) (= (ho_4316 (ho_4315 k_4656 BOUND_VARIABLE_1252061) BOUND_VARIABLE_1252062) (ho_4318 k_4317 BOUND_VARIABLE_1252061))))) (let ((_let_2414 (forall ((BOUND_VARIABLE_1252052 tptp.int) (BOUND_VARIABLE_1252053 tptp.nat)) (= (ho_4316 (ho_4315 k_4657 BOUND_VARIABLE_1252052) BOUND_VARIABLE_1252053) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1252052) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2415 (forall ((BOUND_VARIABLE_1252006 tptp.real) (BOUND_VARIABLE_1252007 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4658 BOUND_VARIABLE_1252006) BOUND_VARIABLE_1252007) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1252007 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1252007) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1252007) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1252006) BOUND_VARIABLE_1252007))))))))))))) (let ((_let_2416 (forall ((BOUND_VARIABLE_1251999 tptp.int) (BOUND_VARIABLE_1252000 tptp.nat)) (= (ho_4316 (ho_4315 k_4659 BOUND_VARIABLE_1251999) BOUND_VARIABLE_1252000) (ho_4318 k_4317 BOUND_VARIABLE_1251999))))) (let ((_let_2417 (forall ((BOUND_VARIABLE_1251990 tptp.int) (BOUND_VARIABLE_1251991 tptp.nat)) (= (ho_4316 (ho_4315 k_4660 BOUND_VARIABLE_1251990) BOUND_VARIABLE_1251991) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251990) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2418 (forall ((BOUND_VARIABLE_1251983 tptp.int) (BOUND_VARIABLE_1251984 tptp.nat)) (= (ho_4316 (ho_4315 k_4661 BOUND_VARIABLE_1251983) BOUND_VARIABLE_1251984) (ho_4318 k_4317 BOUND_VARIABLE_1251983))))) (let ((_let_2419 (forall ((BOUND_VARIABLE_1251974 tptp.int) (BOUND_VARIABLE_1251975 tptp.nat)) (= (ho_4316 (ho_4315 k_4662 BOUND_VARIABLE_1251974) BOUND_VARIABLE_1251975) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251974) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2420 (forall ((BOUND_VARIABLE_1251967 tptp.int) (BOUND_VARIABLE_1251968 tptp.nat)) (= (ho_4316 (ho_4315 k_4663 BOUND_VARIABLE_1251967) BOUND_VARIABLE_1251968) (ho_4318 k_4317 BOUND_VARIABLE_1251967))))) (let ((_let_2421 (forall ((BOUND_VARIABLE_1251958 tptp.int) (BOUND_VARIABLE_1251959 tptp.nat)) (= (ho_4316 (ho_4315 k_4664 BOUND_VARIABLE_1251958) BOUND_VARIABLE_1251959) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251958) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2422 (forall ((BOUND_VARIABLE_1251951 tptp.int) (BOUND_VARIABLE_1251952 tptp.nat)) (= (ho_4316 (ho_4315 k_4665 BOUND_VARIABLE_1251951) BOUND_VARIABLE_1251952) (ho_4318 k_4317 BOUND_VARIABLE_1251951))))) (let ((_let_2423 (forall ((BOUND_VARIABLE_1251942 tptp.int) (BOUND_VARIABLE_1251943 tptp.nat)) (= (ho_4316 (ho_4315 k_4666 BOUND_VARIABLE_1251942) BOUND_VARIABLE_1251943) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251942) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2424 (forall ((BOUND_VARIABLE_1251935 tptp.int) (BOUND_VARIABLE_1251936 tptp.nat)) (= (ho_4316 (ho_4315 k_4667 BOUND_VARIABLE_1251935) BOUND_VARIABLE_1251936) (ho_4318 k_4317 BOUND_VARIABLE_1251935))))) (let ((_let_2425 (forall ((BOUND_VARIABLE_1251928 tptp.int) (BOUND_VARIABLE_1251929 tptp.nat)) (= (ho_4316 (ho_4315 k_4668 BOUND_VARIABLE_1251928) BOUND_VARIABLE_1251929) (ho_4318 k_4317 BOUND_VARIABLE_1251928))))) (let ((_let_2426 (forall ((BOUND_VARIABLE_1251919 tptp.int) (BOUND_VARIABLE_1251920 tptp.nat)) (= (ho_4316 (ho_4315 k_4669 BOUND_VARIABLE_1251919) BOUND_VARIABLE_1251920) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251919) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2427 (forall ((BOUND_VARIABLE_1251912 tptp.int) (BOUND_VARIABLE_1251913 tptp.nat)) (= (ho_4316 (ho_4315 k_4670 BOUND_VARIABLE_1251912) BOUND_VARIABLE_1251913) (ho_4318 k_4317 BOUND_VARIABLE_1251912))))) (let ((_let_2428 (forall ((BOUND_VARIABLE_1251903 tptp.int) (BOUND_VARIABLE_1251904 tptp.nat)) (= (ho_4316 (ho_4315 k_4671 BOUND_VARIABLE_1251903) BOUND_VARIABLE_1251904) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251903) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2429 (forall ((BOUND_VARIABLE_1251846 tptp.real) (BOUND_VARIABLE_1251847 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4319 BOUND_VARIABLE_1251847)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4314 BOUND_VARIABLE_1251847)))) (let ((_let_3 (= BOUND_VARIABLE_1251846 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251846 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251846) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251846)) (not (= BOUND_VARIABLE_1251846 _let_1))) (ho_4310 (ho_4673 k_4672 BOUND_VARIABLE_1251846) BOUND_VARIABLE_1251847)))))))) (let ((_let_2430 (forall ((BOUND_VARIABLE_1251789 tptp.real) (BOUND_VARIABLE_1251790 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4321 BOUND_VARIABLE_1251790)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4320 BOUND_VARIABLE_1251790)))) (let ((_let_3 (= BOUND_VARIABLE_1251789 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251789 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251789) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251789)) (not (= BOUND_VARIABLE_1251789 _let_1))) (ho_4310 (ho_4673 k_4674 BOUND_VARIABLE_1251789) BOUND_VARIABLE_1251790)))))))) (let ((_let_2431 (forall ((BOUND_VARIABLE_1251732 tptp.real) (BOUND_VARIABLE_1251733 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4323 BOUND_VARIABLE_1251733)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4322 BOUND_VARIABLE_1251733)))) (let ((_let_3 (= BOUND_VARIABLE_1251732 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251732 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251732) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251732)) (not (= BOUND_VARIABLE_1251732 _let_1))) (ho_4310 (ho_4673 k_4675 BOUND_VARIABLE_1251732) BOUND_VARIABLE_1251733)))))))) (let ((_let_2432 (forall ((BOUND_VARIABLE_1251675 tptp.real) (BOUND_VARIABLE_1251676 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4325 BOUND_VARIABLE_1251676)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4324 BOUND_VARIABLE_1251676)))) (let ((_let_3 (= BOUND_VARIABLE_1251675 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251675 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251675) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251675)) (not (= BOUND_VARIABLE_1251675 _let_1))) (ho_4310 (ho_4673 k_4676 BOUND_VARIABLE_1251675) BOUND_VARIABLE_1251676)))))))) (let ((_let_2433 (forall ((BOUND_VARIABLE_1251618 tptp.real) (BOUND_VARIABLE_1251619 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4327 BOUND_VARIABLE_1251619)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4326 BOUND_VARIABLE_1251619)))) (let ((_let_3 (= BOUND_VARIABLE_1251618 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251618 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251618) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251618)) (not (= BOUND_VARIABLE_1251618 _let_1))) (ho_4310 (ho_4673 k_4677 BOUND_VARIABLE_1251618) BOUND_VARIABLE_1251619)))))))) (let ((_let_2434 (forall ((BOUND_VARIABLE_1251561 tptp.real) (BOUND_VARIABLE_1251562 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4329 BOUND_VARIABLE_1251562)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4328 BOUND_VARIABLE_1251562)))) (let ((_let_3 (= BOUND_VARIABLE_1251561 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1251561 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251561) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1251561)) (not (= BOUND_VARIABLE_1251561 _let_1))) (ho_4310 (ho_4673 k_4678 BOUND_VARIABLE_1251561) BOUND_VARIABLE_1251562)))))))) (let ((_let_2435 (forall ((BOUND_VARIABLE_1251554 tptp.int) (BOUND_VARIABLE_1251555 tptp.nat)) (= (ho_4316 (ho_4315 k_4679 BOUND_VARIABLE_1251554) BOUND_VARIABLE_1251555) (ho_4318 k_4317 BOUND_VARIABLE_1251554))))) (let ((_let_2436 (forall ((BOUND_VARIABLE_1251545 tptp.int) (BOUND_VARIABLE_1251546 tptp.nat)) (= (ho_4316 (ho_4315 k_4680 BOUND_VARIABLE_1251545) BOUND_VARIABLE_1251546) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251545) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2437 (forall ((BOUND_VARIABLE_1251538 tptp.int) (BOUND_VARIABLE_1251539 tptp.nat)) (= (ho_4316 (ho_4315 k_4681 BOUND_VARIABLE_1251538) BOUND_VARIABLE_1251539) (ho_4318 k_4317 BOUND_VARIABLE_1251538))))) (let ((_let_2438 (forall ((BOUND_VARIABLE_1251529 tptp.int) (BOUND_VARIABLE_1251530 tptp.nat)) (= (ho_4316 (ho_4315 k_4682 BOUND_VARIABLE_1251529) BOUND_VARIABLE_1251530) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251529) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2439 (forall ((BOUND_VARIABLE_1251522 tptp.int) (BOUND_VARIABLE_1251523 tptp.nat)) (= (ho_4316 (ho_4315 k_4683 BOUND_VARIABLE_1251522) BOUND_VARIABLE_1251523) (ho_4318 k_4317 BOUND_VARIABLE_1251522))))) (let ((_let_2440 (forall ((BOUND_VARIABLE_1251513 tptp.int) (BOUND_VARIABLE_1251514 tptp.nat)) (= (ho_4316 (ho_4315 k_4684 BOUND_VARIABLE_1251513) BOUND_VARIABLE_1251514) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251513) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2441 (forall ((BOUND_VARIABLE_1251506 tptp.int) (BOUND_VARIABLE_1251507 tptp.nat)) (= (ho_4316 (ho_4315 k_4685 BOUND_VARIABLE_1251506) BOUND_VARIABLE_1251507) (ho_4318 k_4317 BOUND_VARIABLE_1251506))))) (let ((_let_2442 (forall ((BOUND_VARIABLE_1251497 tptp.int) (BOUND_VARIABLE_1251498 tptp.nat)) (= (ho_4316 (ho_4315 k_4686 BOUND_VARIABLE_1251497) BOUND_VARIABLE_1251498) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251497) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2443 (forall ((BOUND_VARIABLE_1251490 tptp.int) (BOUND_VARIABLE_1251491 tptp.nat)) (= (ho_4316 (ho_4315 k_4687 BOUND_VARIABLE_1251490) BOUND_VARIABLE_1251491) (ho_4318 k_4317 BOUND_VARIABLE_1251490))))) (let ((_let_2444 (forall ((BOUND_VARIABLE_1251481 tptp.int) (BOUND_VARIABLE_1251482 tptp.nat)) (= (ho_4316 (ho_4315 k_4688 BOUND_VARIABLE_1251481) BOUND_VARIABLE_1251482) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251481) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2445 (forall ((BOUND_VARIABLE_1251474 tptp.int) (BOUND_VARIABLE_1251475 tptp.nat)) (= (ho_4316 (ho_4315 k_4689 BOUND_VARIABLE_1251474) BOUND_VARIABLE_1251475) (ho_4318 k_4317 BOUND_VARIABLE_1251474))))) (let ((_let_2446 (forall ((BOUND_VARIABLE_1251465 tptp.int) (BOUND_VARIABLE_1251466 tptp.nat)) (= (ho_4316 (ho_4315 k_4690 BOUND_VARIABLE_1251465) BOUND_VARIABLE_1251466) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251465) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2447 (forall ((BOUND_VARIABLE_1251458 tptp.int) (BOUND_VARIABLE_1251459 tptp.nat)) (= (ho_4316 (ho_4315 k_4691 BOUND_VARIABLE_1251458) BOUND_VARIABLE_1251459) (ho_4318 k_4317 BOUND_VARIABLE_1251458))))) (let ((_let_2448 (forall ((BOUND_VARIABLE_1251449 tptp.int) (BOUND_VARIABLE_1251450 tptp.nat)) (= (ho_4316 (ho_4315 k_4692 BOUND_VARIABLE_1251449) BOUND_VARIABLE_1251450) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251449) (ho_4196 k_4195 tptp.one))))))) (let ((_let_2449 (forall ((BOUND_VARIABLE_1251405 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1251405 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1251405 _let_3))) (= (ho_4351 k_4693 BOUND_VARIABLE_1251405) (and (or (and (= BOUND_VARIABLE_1251405 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251405) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1251405)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4330 BOUND_VARIABLE_1251405)))))))))))))) (let ((_let_2450 (forall ((BOUND_VARIABLE_1251361 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1251361 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1251361 _let_3))) (= (ho_4351 k_4694 BOUND_VARIABLE_1251361) (and (or (and (= BOUND_VARIABLE_1251361 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1251361) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1251361)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4331 BOUND_VARIABLE_1251361)))))))))))))) (let ((_let_2451 (forall ((BOUND_VARIABLE_1251338 tptp.real) (BOUND_VARIABLE_1251339 tptp.nat) (BOUND_VARIABLE_1251340 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1251338)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1251339) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1251340) (ho_4258 (ho_4273 (ho_4696 k_4695 BOUND_VARIABLE_1251338) BOUND_VARIABLE_1251339) BOUND_VARIABLE_1251340)))))))))) (let ((_let_2452 (forall ((BOUND_VARIABLE_1251315 tptp.rat) (BOUND_VARIABLE_1251316 tptp.nat) (BOUND_VARIABLE_1251317 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1251315)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1251316) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1251317) (ho_4442 (ho_4458 (ho_4699 k_4698 BOUND_VARIABLE_1251315) BOUND_VARIABLE_1251316) BOUND_VARIABLE_1251317)))))))))))) (let ((_let_2453 (forall ((BOUND_VARIABLE_1251294 tptp.complex) (BOUND_VARIABLE_1251295 tptp.nat) (BOUND_VARIABLE_1251296 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1251294)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1251295) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1251296) (ho_4703 (ho_4709 (ho_4712 k_4711 BOUND_VARIABLE_1251294) BOUND_VARIABLE_1251295) BOUND_VARIABLE_1251296)))))) (let ((_let_2454 (forall ((BOUND_VARIABLE_1251258 tptp.real) (BOUND_VARIABLE_1251259 tptp.nat) (BOUND_VARIABLE_1251260 tptp.nat) (BOUND_VARIABLE_1251261 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1251258) (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1251259) _let_6)))) _let_1)) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1251260) _let_6))) BOUND_VARIABLE_1251261) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_4713 BOUND_VARIABLE_1251258) BOUND_VARIABLE_1251259) BOUND_VARIABLE_1251260) BOUND_VARIABLE_1251261)))))))))))) (let ((_let_2455 (forall ((BOUND_VARIABLE_1251222 tptp.rat) (BOUND_VARIABLE_1251223 tptp.nat) (BOUND_VARIABLE_1251224 tptp.nat) (BOUND_VARIABLE_1251225 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1251222) (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1251223) _let_8)))) _let_3)) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1251224) _let_8))) BOUND_VARIABLE_1251225) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_4716 BOUND_VARIABLE_1251222) BOUND_VARIABLE_1251223) BOUND_VARIABLE_1251224) BOUND_VARIABLE_1251225)))))))))))))) (let ((_let_2456 (forall ((BOUND_VARIABLE_1251187 tptp.complex) (BOUND_VARIABLE_1251188 tptp.nat) (BOUND_VARIABLE_1251189 tptp.nat) (BOUND_VARIABLE_1251190 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (let ((_let_3 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1251187) (ho_4703 k_4702 (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1251188) _let_2)))) _let_1)) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1251189) _let_2))) BOUND_VARIABLE_1251190) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_4719 BOUND_VARIABLE_1251187) BOUND_VARIABLE_1251188) BOUND_VARIABLE_1251189) BOUND_VARIABLE_1251190)))))))) (let ((_let_2457 (forall ((BOUND_VARIABLE_1251167 tptp.int) (BOUND_VARIABLE_1251168 tptp.nat) (BOUND_VARIABLE_1251169 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251167) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1251168) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) BOUND_VARIABLE_1251169) (ho_4209 (ho_4220 (ho_4723 k_4722 BOUND_VARIABLE_1251167) BOUND_VARIABLE_1251168) BOUND_VARIABLE_1251169)))))) (let ((_let_2458 (forall ((BOUND_VARIABLE_1251149 tptp.int) (BOUND_VARIABLE_1251150 tptp.nat) (BOUND_VARIABLE_1251151 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1251149) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1251150) BOUND_VARIABLE_1251151)) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (ho_4335 (ho_4726 (ho_4725 k_4724 BOUND_VARIABLE_1251149) BOUND_VARIABLE_1251150) BOUND_VARIABLE_1251151)))))) (let ((_let_2459 (forall ((BOUND_VARIABLE_1251107 tptp.nat) (BOUND_VARIABLE_1251108 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1251107) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1251108 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_4727 BOUND_VARIABLE_1251107) BOUND_VARIABLE_1251108))))) (let ((_let_2460 (forall ((BOUND_VARIABLE_1251066 tptp.nat) (BOUND_VARIABLE_1251067 tptp.nat) (BOUND_VARIABLE_1251068 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1251066) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1251067) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1251068) _let_2))) (ho_4216 (ho_4215 (ho_4269 k_4731 BOUND_VARIABLE_1251066) BOUND_VARIABLE_1251067) BOUND_VARIABLE_1251068)))))))) (let ((_let_2461 (forall ((BOUND_VARIABLE_1251037 tptp.nat) (BOUND_VARIABLE_1251038 tptp.nat) (BOUND_VARIABLE_1251039 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1251037) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1251038) BOUND_VARIABLE_1251039)) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2))) (ho_4216 (ho_4215 (ho_4269 k_4732 BOUND_VARIABLE_1251037) BOUND_VARIABLE_1251038) BOUND_VARIABLE_1251039)))))))) (let ((_let_2462 (forall ((BOUND_VARIABLE_1250995 tptp.nat) (BOUND_VARIABLE_1250996 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1250995) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1250996 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_4733 BOUND_VARIABLE_1250995) BOUND_VARIABLE_1250996))))) (let ((_let_2463 (forall ((BOUND_VARIABLE_1250974 tptp.rat) (BOUND_VARIABLE_1250975 tptp.nat) (BOUND_VARIABLE_1250976 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1250974) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1250975) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1250976) (ho_4442 (ho_4458 (ho_4699 k_4734 BOUND_VARIABLE_1250974) BOUND_VARIABLE_1250975) BOUND_VARIABLE_1250976))))))))))) (let ((_let_2464 (forall ((BOUND_VARIABLE_1250955 tptp.rat) (BOUND_VARIABLE_1250956 tptp.nat) (BOUND_VARIABLE_1250957 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443))) (= (ho_4442 (ho_4448 _let_5 BOUND_VARIABLE_1250955) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1250956) BOUND_VARIABLE_1250957)) (ho_4442 (ho_4448 _let_5 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (ho_4316 (ho_4338 (ho_4736 k_4735 BOUND_VARIABLE_1250955) BOUND_VARIABLE_1250956) BOUND_VARIABLE_1250957)))))))))) (let ((_let_2465 (forall ((BOUND_VARIABLE_1250913 tptp.nat) (BOUND_VARIABLE_1250914 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1250913) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1250914 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_4737 BOUND_VARIABLE_1250913) BOUND_VARIABLE_1250914))))) (let ((_let_2466 (forall ((BOUND_VARIABLE_1250892 tptp.real) (BOUND_VARIABLE_1250893 tptp.nat) (BOUND_VARIABLE_1250894 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1250892) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1250893) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1250894) (ho_4258 (ho_4273 (ho_4696 k_4738 BOUND_VARIABLE_1250892) BOUND_VARIABLE_1250893) BOUND_VARIABLE_1250894))))))))) (let ((_let_2467 (forall ((BOUND_VARIABLE_1250873 tptp.real) (BOUND_VARIABLE_1250874 tptp.nat) (BOUND_VARIABLE_1250875 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (= (ho_4258 (ho_4265 _let_3 BOUND_VARIABLE_1250873) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1250874) BOUND_VARIABLE_1250875)) (ho_4258 (ho_4265 _let_3 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (ho_4245 (ho_4487 (ho_4740 k_4739 BOUND_VARIABLE_1250873) BOUND_VARIABLE_1250874) BOUND_VARIABLE_1250875)))))))) (let ((_let_2468 (forall ((BOUND_VARIABLE_1250831 tptp.nat) (BOUND_VARIABLE_1250832 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1250831) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1250832 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_4741 BOUND_VARIABLE_1250831) BOUND_VARIABLE_1250832))))) (let ((_let_2469 (forall ((BOUND_VARIABLE_1250808 tptp.rat) (BOUND_VARIABLE_1250809 tptp.nat) (BOUND_VARIABLE_1250810 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1250808)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1250809) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1250810) (ho_4442 (ho_4458 (ho_4699 k_4742 BOUND_VARIABLE_1250808) BOUND_VARIABLE_1250809) BOUND_VARIABLE_1250810)))))))))))) (let ((_let_2470 (forall ((BOUND_VARIABLE_1250770 tptp.nat) (BOUND_VARIABLE_1250771 tptp.rat) (BOUND_VARIABLE_1250772 tptp.nat) (BOUND_VARIABLE_1250773 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (let ((_let_9 (ho_4442 (ho_4448 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 (ho_4442 (ho_4448 _let_8 (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1250770) _let_9)) (ho_4442 _let_5 BOUND_VARIABLE_1250771))) _let_6))) (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1250772) _let_9))) BOUND_VARIABLE_1250773) (ho_4442 (ho_4458 (ho_4699 (ho_4744 k_4743 BOUND_VARIABLE_1250770) BOUND_VARIABLE_1250771) BOUND_VARIABLE_1250772) BOUND_VARIABLE_1250773))))))))))))))) (let ((_let_2471 (forall ((BOUND_VARIABLE_1250747 tptp.real) (BOUND_VARIABLE_1250748 tptp.nat) (BOUND_VARIABLE_1250749 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1250747)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1250748) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1250749) (ho_4258 (ho_4273 (ho_4696 k_4745 BOUND_VARIABLE_1250747) BOUND_VARIABLE_1250748) BOUND_VARIABLE_1250749)))))))))) (let ((_let_2472 (forall ((BOUND_VARIABLE_1250709 tptp.nat) (BOUND_VARIABLE_1250710 tptp.real) (BOUND_VARIABLE_1250711 tptp.nat) (BOUND_VARIABLE_1250712 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 _let_1) _let_4))) (let ((_let_8 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1250709) _let_7)) (ho_4258 _let_3 BOUND_VARIABLE_1250710))) _let_4))) (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1250711) _let_7))) BOUND_VARIABLE_1250712) (ho_4258 (ho_4273 (ho_4696 (ho_4747 k_4746 BOUND_VARIABLE_1250709) BOUND_VARIABLE_1250710) BOUND_VARIABLE_1250711) BOUND_VARIABLE_1250712))))))))))))) (let ((_let_2473 (forall ((BOUND_VARIABLE_1250688 tptp.complex) (BOUND_VARIABLE_1250689 tptp.nat) (BOUND_VARIABLE_1250690 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1250688)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1250689) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1250690) (ho_4703 (ho_4709 (ho_4712 k_4748 BOUND_VARIABLE_1250688) BOUND_VARIABLE_1250689) BOUND_VARIABLE_1250690)))))) (let ((_let_2474 (forall ((BOUND_VARIABLE_1250651 tptp.nat) (BOUND_VARIABLE_1250652 tptp.complex) (BOUND_VARIABLE_1250653 tptp.nat) (BOUND_VARIABLE_1250654 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (let ((_let_4 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1250651) _let_3)) (ho_4703 k_4702 BOUND_VARIABLE_1250652))) _let_2))) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1250653) _let_3))) BOUND_VARIABLE_1250654) (ho_4703 (ho_4709 (ho_4712 (ho_4750 k_4749 BOUND_VARIABLE_1250651) BOUND_VARIABLE_1250652) BOUND_VARIABLE_1250653) BOUND_VARIABLE_1250654))))))))) (let ((_let_2475 (forall ((BOUND_VARIABLE_1250619 tptp.real) (BOUND_VARIABLE_1250620 tptp.nat) (BOUND_VARIABLE_1250621 tptp.nat) (BOUND_VARIABLE_1250622 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1250619) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1250620) _let_6)))) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1250621) _let_6))) BOUND_VARIABLE_1250622) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_4751 BOUND_VARIABLE_1250619) BOUND_VARIABLE_1250620) BOUND_VARIABLE_1250621) BOUND_VARIABLE_1250622)))))))))))) (let ((_let_2476 (forall ((BOUND_VARIABLE_1250587 tptp.rat) (BOUND_VARIABLE_1250588 tptp.nat) (BOUND_VARIABLE_1250589 tptp.nat) (BOUND_VARIABLE_1250590 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1250587) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1250588) _let_8)))) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1250589) _let_8))) BOUND_VARIABLE_1250590) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_4752 BOUND_VARIABLE_1250587) BOUND_VARIABLE_1250588) BOUND_VARIABLE_1250589) BOUND_VARIABLE_1250590)))))))))))))) (let ((_let_2477 (forall ((BOUND_VARIABLE_1250556 tptp.complex) (BOUND_VARIABLE_1250557 tptp.nat) (BOUND_VARIABLE_1250558 tptp.nat) (BOUND_VARIABLE_1250559 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (let ((_let_3 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1250556) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1250557) _let_2)))) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1250558) _let_2))) BOUND_VARIABLE_1250559) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_4753 BOUND_VARIABLE_1250556) BOUND_VARIABLE_1250557) BOUND_VARIABLE_1250558) BOUND_VARIABLE_1250559)))))))) (let ((_let_2478 (forall ((BOUND_VARIABLE_1250546 tptp.nat) (BOUND_VARIABLE_1250547 tptp.nat)) (= (ho_4288 (ho_4287 k_4754 BOUND_VARIABLE_1250546) BOUND_VARIABLE_1250547) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1250547)) (ho_4290 k_4289 BOUND_VARIABLE_1250546)))))) (let ((_let_2479 (forall ((BOUND_VARIABLE_1283393 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1250538 tptp.nat) (BOUND_VARIABLE_1250539 tptp.nat)) (= (ho_4335 (ho_4726 (ho_4756 k_4755 BOUND_VARIABLE_1283393) BOUND_VARIABLE_1250538) BOUND_VARIABLE_1250539) (ho_4335 (ho_4726 BOUND_VARIABLE_1283393 BOUND_VARIABLE_1250539) BOUND_VARIABLE_1250538))))) (let ((_let_2480 (forall ((BOUND_VARIABLE_1250482 tptp.nat) (BOUND_VARIABLE_1250483 tptp.nat) (BOUND_VARIABLE_1250484 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1250482) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1250483) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1250484 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4757 BOUND_VARIABLE_1250482) BOUND_VARIABLE_1250483) BOUND_VARIABLE_1250484))))) (let ((_let_2481 (forall ((BOUND_VARIABLE_1250472 tptp.nat) (BOUND_VARIABLE_1250473 tptp.nat)) (= (ho_4288 (ho_4287 k_4758 BOUND_VARIABLE_1250472) BOUND_VARIABLE_1250473) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1250473)) (ho_4290 k_4289 BOUND_VARIABLE_1250472)))))) (let ((_let_2482 (forall ((BOUND_VARIABLE_1283453 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1250464 tptp.nat) (BOUND_VARIABLE_1250465 tptp.nat)) (= (ho_4216 (ho_4215 (ho_4760 k_4759 BOUND_VARIABLE_1283453) BOUND_VARIABLE_1250464) BOUND_VARIABLE_1250465) (ho_4216 (ho_4215 BOUND_VARIABLE_1283453 BOUND_VARIABLE_1250465) BOUND_VARIABLE_1250464))))) (let ((_let_2483 (forall ((BOUND_VARIABLE_1250408 tptp.nat) (BOUND_VARIABLE_1250409 tptp.nat) (BOUND_VARIABLE_1250410 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1250408) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1250409) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1250410 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4761 BOUND_VARIABLE_1250408) BOUND_VARIABLE_1250409) BOUND_VARIABLE_1250410))))) (let ((_let_2484 (forall ((BOUND_VARIABLE_1250385 tptp.real) (BOUND_VARIABLE_1250386 tptp.nat) (BOUND_VARIABLE_1250387 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1250385)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1250386) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1250387) (ho_4258 (ho_4273 (ho_4696 k_4762 BOUND_VARIABLE_1250385) BOUND_VARIABLE_1250386) BOUND_VARIABLE_1250387)))))))))) (let ((_let_2485 (forall ((BOUND_VARIABLE_1250362 tptp.rat) (BOUND_VARIABLE_1250363 tptp.nat) (BOUND_VARIABLE_1250364 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1250362)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1250363) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1250364) (ho_4442 (ho_4458 (ho_4699 k_4763 BOUND_VARIABLE_1250362) BOUND_VARIABLE_1250363) BOUND_VARIABLE_1250364)))))))))))) (let ((_let_2486 (forall ((BOUND_VARIABLE_1250341 tptp.complex) (BOUND_VARIABLE_1250342 tptp.nat) (BOUND_VARIABLE_1250343 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1250341)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1250342) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1250343) (ho_4703 (ho_4709 (ho_4712 k_4764 BOUND_VARIABLE_1250341) BOUND_VARIABLE_1250342) BOUND_VARIABLE_1250343)))))) (let ((_let_2487 (forall ((BOUND_VARIABLE_1250235 tptp.complex) (BOUND_VARIABLE_1250236 tptp.complex) (BOUND_VARIABLE_1250237 tptp.nat) (BOUND_VARIABLE_1250238 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1250235) BOUND_VARIABLE_1250238))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_6 (ho_4193 k_4192 tptp.one))) (let ((_let_7 (ho_4257 _let_4 k_4274))) (let ((_let_8 (ho_4264 _let_5 k_4275))) (let ((_let_9 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4336 BOUND_VARIABLE_1250237) BOUND_VARIABLE_1250238))) (ho_4258 _let_7 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 _let_6))) BOUND_VARIABLE_1250237) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) (ho_4258 (ho_4257 _let_4 k_4248) _let_3)))))))) (let ((_let_10 (ho_4247 k_4246 _let_6))) (= (ho_4767 (ho_4779 (ho_4778 (ho_4777 k_4776 BOUND_VARIABLE_1250235) BOUND_VARIABLE_1250236) BOUND_VARIABLE_1250237) BOUND_VARIABLE_1250238) (ho_4703 (ho_4705 (ho_4775 k_4774 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1250237 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1250238 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))))) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_9 (ho_4769 k_4773 _let_2)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 _let_10) (ho_4506 k_4505 k_4504))) (ho_4258 _let_7 _let_10)))) (ho_4771 k_4770 (ho_4258 _let_9 (ho_4769 k_4768 _let_2)))))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1250236) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1250237) BOUND_VARIABLE_1250238)))) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))))))))))))))) (let ((_let_2488 (forall ((BOUND_VARIABLE_1250225 tptp.nat) (BOUND_VARIABLE_1250226 tptp.nat)) (= (ho_4288 (ho_4287 k_4780 BOUND_VARIABLE_1250225) BOUND_VARIABLE_1250226) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1250226)) (ho_4290 k_4289 BOUND_VARIABLE_1250225)))))) (let ((_let_2489 (forall ((BOUND_VARIABLE_1250133 tptp.real) (BOUND_VARIABLE_1250134 tptp.real) (BOUND_VARIABLE_1250135 tptp.nat) (BOUND_VARIABLE_1250136 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4245 (ho_4487 (ho_4740 (ho_4782 k_4781 BOUND_VARIABLE_1250133) BOUND_VARIABLE_1250134) BOUND_VARIABLE_1250135) BOUND_VARIABLE_1250136) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1250135 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1250136 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))))) (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4339 BOUND_VARIABLE_1250135) BOUND_VARIABLE_1250136))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1250135) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1250133) BOUND_VARIABLE_1250136))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1250134) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1250135) BOUND_VARIABLE_1250136)))) _let_4)))))))))) (let ((_let_2490 (forall ((BOUND_VARIABLE_1250123 tptp.nat) (BOUND_VARIABLE_1250124 tptp.nat)) (= (ho_4288 (ho_4287 k_4783 BOUND_VARIABLE_1250123) BOUND_VARIABLE_1250124) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1250124)) (ho_4290 k_4289 BOUND_VARIABLE_1250123)))))) (let ((_let_2491 (forall ((BOUND_VARIABLE_1250027 tptp.complex) (BOUND_VARIABLE_1250028 tptp.complex) (BOUND_VARIABLE_1250029 tptp.nat) (BOUND_VARIABLE_1250030 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1250027) BOUND_VARIABLE_1250030))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_6 (ho_4193 k_4192 tptp.one))) (let ((_let_7 (ho_4257 _let_4 k_4274))) (let ((_let_8 (ho_4264 _let_5 k_4275))) (let ((_let_9 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4340 BOUND_VARIABLE_1250029) BOUND_VARIABLE_1250030))) (ho_4258 _let_7 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 _let_6))) BOUND_VARIABLE_1250029) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) (ho_4258 (ho_4257 _let_4 k_4248) _let_3)))))))) (let ((_let_10 (ho_4247 k_4246 _let_6))) (= (ho_4767 (ho_4779 (ho_4778 (ho_4777 k_4784 BOUND_VARIABLE_1250027) BOUND_VARIABLE_1250028) BOUND_VARIABLE_1250029) BOUND_VARIABLE_1250030) (ho_4703 (ho_4705 (ho_4775 k_4774 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1250029 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_9 (ho_4769 k_4773 _let_2)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 _let_10) (ho_4506 k_4505 k_4504))) (ho_4258 _let_7 _let_10)))) (ho_4771 k_4770 (ho_4258 _let_9 (ho_4769 k_4768 _let_2)))))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1250028) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1250029) BOUND_VARIABLE_1250030)))) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))))))))))))))) (let ((_let_2492 (forall ((BOUND_VARIABLE_1250017 tptp.nat) (BOUND_VARIABLE_1250018 tptp.nat)) (= (ho_4288 (ho_4287 k_4785 BOUND_VARIABLE_1250017) BOUND_VARIABLE_1250018) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1250018)) (ho_4290 k_4289 BOUND_VARIABLE_1250017)))))) (let ((_let_2493 (forall ((BOUND_VARIABLE_1249935 tptp.real) (BOUND_VARIABLE_1249936 tptp.real) (BOUND_VARIABLE_1249937 tptp.nat) (BOUND_VARIABLE_1249938 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4245 (ho_4487 (ho_4740 (ho_4782 k_4786 BOUND_VARIABLE_1249935) BOUND_VARIABLE_1249936) BOUND_VARIABLE_1249937) BOUND_VARIABLE_1249938) (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1249937 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4341 BOUND_VARIABLE_1249937) BOUND_VARIABLE_1249938))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1249937) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249935) BOUND_VARIABLE_1249938))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249936) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249937) BOUND_VARIABLE_1249938)))) _let_4)))))))))) (let ((_let_2494 (forall ((BOUND_VARIABLE_1249925 tptp.nat) (BOUND_VARIABLE_1249926 tptp.nat)) (= (ho_4288 (ho_4287 k_4787 BOUND_VARIABLE_1249925) BOUND_VARIABLE_1249926) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249926)) (ho_4290 k_4289 BOUND_VARIABLE_1249925)))))) (let ((_let_2495 (forall ((BOUND_VARIABLE_1249819 tptp.complex) (BOUND_VARIABLE_1249820 tptp.complex) (BOUND_VARIABLE_1249821 tptp.nat) (BOUND_VARIABLE_1249822 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1249819) BOUND_VARIABLE_1249822))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4257 _let_4 k_4248))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4257 _let_4 k_4274))) (let ((_let_9 (ho_4264 _let_6 k_4275))) (let ((_let_10 (ho_4265 _let_9 (ho_4258 _let_5 (ho_4258 (ho_4265 _let_9 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4342 BOUND_VARIABLE_1249821) BOUND_VARIABLE_1249822))) (ho_4258 _let_8 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 _let_7))) BOUND_VARIABLE_1249821) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 (ho_4264 _let_6 k_4259) _let_3) (ho_4258 _let_5 _let_3))))))))) (let ((_let_11 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4779 (ho_4778 (ho_4777 k_4788 BOUND_VARIABLE_1249819) BOUND_VARIABLE_1249820) BOUND_VARIABLE_1249821) BOUND_VARIABLE_1249822) (ho_4703 (ho_4705 (ho_4775 k_4774 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1249821 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1249822 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_10 (ho_4769 k_4773 _let_2)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 _let_10 (ho_4769 k_4768 _let_2)))))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1249820) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249821) BOUND_VARIABLE_1249822)))) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))))))))))))))))) (let ((_let_2496 (forall ((BOUND_VARIABLE_1249809 tptp.nat) (BOUND_VARIABLE_1249810 tptp.nat)) (= (ho_4288 (ho_4287 k_4789 BOUND_VARIABLE_1249809) BOUND_VARIABLE_1249810) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249810)) (ho_4290 k_4289 BOUND_VARIABLE_1249809)))))) (let ((_let_2497 (forall ((BOUND_VARIABLE_1249716 tptp.real) (BOUND_VARIABLE_1249717 tptp.real) (BOUND_VARIABLE_1249718 tptp.nat) (BOUND_VARIABLE_1249719 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4487 (ho_4740 (ho_4782 k_4790 BOUND_VARIABLE_1249716) BOUND_VARIABLE_1249717) BOUND_VARIABLE_1249718) BOUND_VARIABLE_1249719) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1249718 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1249719 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 (ho_4251 k_4250 (ho_4338 (ho_4337 k_4343 BOUND_VARIABLE_1249718) BOUND_VARIABLE_1249719))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1249718) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249716) BOUND_VARIABLE_1249719))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249717) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249718) BOUND_VARIABLE_1249719)))) _let_5))))))))))) (let ((_let_2498 (forall ((BOUND_VARIABLE_1249706 tptp.nat) (BOUND_VARIABLE_1249707 tptp.nat)) (= (ho_4288 (ho_4287 k_4791 BOUND_VARIABLE_1249706) BOUND_VARIABLE_1249707) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249707)) (ho_4290 k_4289 BOUND_VARIABLE_1249706)))))) (let ((_let_2499 (forall ((BOUND_VARIABLE_1283926 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1249686 tptp.real) (BOUND_VARIABLE_1249687 tptp.nat) (BOUND_VARIABLE_1249688 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1283926 BOUND_VARIABLE_1249688)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249686) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249688) BOUND_VARIABLE_1249687)) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))) (ho_4245 (ho_4487 (ho_4740 (ho_4793 k_4792 BOUND_VARIABLE_1283926) BOUND_VARIABLE_1249686) BOUND_VARIABLE_1249687) BOUND_VARIABLE_1249688))))) (let ((_let_2500 (forall ((BOUND_VARIABLE_1249630 tptp.nat) (BOUND_VARIABLE_1249631 tptp.nat) (BOUND_VARIABLE_1249632 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249630) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249631) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1249632 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4794 BOUND_VARIABLE_1249630) BOUND_VARIABLE_1249631) BOUND_VARIABLE_1249632))))) (let ((_let_2501 (forall ((BOUND_VARIABLE_1283982 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1249614 tptp.int) (BOUND_VARIABLE_1249615 tptp.nat) (BOUND_VARIABLE_1249616 tptp.nat)) (= (ho_4335 (ho_4726 (ho_4725 (ho_4796 k_4795 BOUND_VARIABLE_1283982) BOUND_VARIABLE_1249614) BOUND_VARIABLE_1249615) BOUND_VARIABLE_1249616) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1283982 BOUND_VARIABLE_1249616)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1249614) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249616) BOUND_VARIABLE_1249615)) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))))))) (let ((_let_2502 (forall ((BOUND_VARIABLE_1249558 tptp.nat) (BOUND_VARIABLE_1249559 tptp.nat) (BOUND_VARIABLE_1249560 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249558) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249559) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1249560 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4797 BOUND_VARIABLE_1249558) BOUND_VARIABLE_1249559) BOUND_VARIABLE_1249560))))) (let ((_let_2503 (forall ((BOUND_VARIABLE_1284046 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1249538 tptp.rat) (BOUND_VARIABLE_1249539 tptp.nat) (BOUND_VARIABLE_1249540 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1284046 BOUND_VARIABLE_1249540)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1249538) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249540) BOUND_VARIABLE_1249539)) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))) (ho_4316 (ho_4338 (ho_4736 (ho_4801 k_4800 BOUND_VARIABLE_1284046) BOUND_VARIABLE_1249538) BOUND_VARIABLE_1249539) BOUND_VARIABLE_1249540))))) (let ((_let_2504 (forall ((BOUND_VARIABLE_1249482 tptp.nat) (BOUND_VARIABLE_1249483 tptp.nat) (BOUND_VARIABLE_1249484 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249482) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249483) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1249484 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4802 BOUND_VARIABLE_1249482) BOUND_VARIABLE_1249483) BOUND_VARIABLE_1249484))))) (let ((_let_2505 (forall ((BOUND_VARIABLE_1284102 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1249466 tptp.complex) (BOUND_VARIABLE_1249467 tptp.nat) (BOUND_VARIABLE_1249468 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4778 (ho_4804 k_4803 BOUND_VARIABLE_1284102) BOUND_VARIABLE_1249466) BOUND_VARIABLE_1249467) BOUND_VARIABLE_1249468) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284102 BOUND_VARIABLE_1249468)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1249466) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249468) BOUND_VARIABLE_1249467)) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))))))) (let ((_let_2506 (forall ((BOUND_VARIABLE_1249410 tptp.nat) (BOUND_VARIABLE_1249411 tptp.nat) (BOUND_VARIABLE_1249412 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249410) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249411) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1249412 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4805 BOUND_VARIABLE_1249410) BOUND_VARIABLE_1249411) BOUND_VARIABLE_1249412))))) (let ((_let_2507 (forall ((BOUND_VARIABLE_1284172 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1249362 tptp.real) (BOUND_VARIABLE_1249363 tptp.real) (BOUND_VARIABLE_1249364 tptp.nat) (BOUND_VARIABLE_1249365 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275))) (= (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 (ho_4245 BOUND_VARIABLE_1284172 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249364) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249365) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249362) BOUND_VARIABLE_1249365))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1249363) BOUND_VARIABLE_1249364)) (ho_4245 (ho_4487 (ho_4740 (ho_4782 (ho_4807 k_4806 BOUND_VARIABLE_1284172) BOUND_VARIABLE_1249362) BOUND_VARIABLE_1249363) BOUND_VARIABLE_1249364) BOUND_VARIABLE_1249365))))))))) (let ((_let_2508 (forall ((BOUND_VARIABLE_1249348 tptp.nat) (BOUND_VARIABLE_1249349 tptp.nat) (BOUND_VARIABLE_1249350 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_4808 BOUND_VARIABLE_1249348) BOUND_VARIABLE_1249349) BOUND_VARIABLE_1249350) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1249350)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249348) BOUND_VARIABLE_1249349))))))) (let ((_let_2509 (forall ((BOUND_VARIABLE_1284227 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1249300 tptp.int) (BOUND_VARIABLE_1249301 tptp.int) (BOUND_VARIABLE_1249302 tptp.nat) (BOUND_VARIABLE_1249303 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1284227 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249302) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249303) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1249300) BOUND_VARIABLE_1249303))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1249301) BOUND_VARIABLE_1249302)) (ho_4335 (ho_4726 (ho_4725 (ho_4811 (ho_4810 k_4809 BOUND_VARIABLE_1284227) BOUND_VARIABLE_1249300) BOUND_VARIABLE_1249301) BOUND_VARIABLE_1249302) BOUND_VARIABLE_1249303)))))))) (let ((_let_2510 (forall ((BOUND_VARIABLE_1249286 tptp.nat) (BOUND_VARIABLE_1249287 tptp.nat) (BOUND_VARIABLE_1249288 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_4812 BOUND_VARIABLE_1249286) BOUND_VARIABLE_1249287) BOUND_VARIABLE_1249288) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1249288)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249286) BOUND_VARIABLE_1249287))))))) (let ((_let_2511 (forall ((BOUND_VARIABLE_1284285 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1249238 tptp.rat) (BOUND_VARIABLE_1249239 tptp.rat) (BOUND_VARIABLE_1249240 tptp.nat) (BOUND_VARIABLE_1249241 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697))) (= (ho_4442 (ho_4448 _let_4 (ho_4442 (ho_4448 _let_4 (ho_4316 BOUND_VARIABLE_1284285 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249240) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249241) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1249238) BOUND_VARIABLE_1249241))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1249239) BOUND_VARIABLE_1249240)) (ho_4316 (ho_4338 (ho_4736 (ho_4815 (ho_4814 k_4813 BOUND_VARIABLE_1284285) BOUND_VARIABLE_1249238) BOUND_VARIABLE_1249239) BOUND_VARIABLE_1249240) BOUND_VARIABLE_1249241))))))))) (let ((_let_2512 (forall ((BOUND_VARIABLE_1249224 tptp.nat) (BOUND_VARIABLE_1249225 tptp.nat) (BOUND_VARIABLE_1249226 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_4816 BOUND_VARIABLE_1249224) BOUND_VARIABLE_1249225) BOUND_VARIABLE_1249226) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1249226)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249224) BOUND_VARIABLE_1249225))))))) (let ((_let_2513 (forall ((BOUND_VARIABLE_1284343 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1249176 tptp.complex) (BOUND_VARIABLE_1249177 tptp.complex) (BOUND_VARIABLE_1249178 tptp.nat) (BOUND_VARIABLE_1249179 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284343 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249178) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1249179) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1249176) BOUND_VARIABLE_1249179))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1249177) BOUND_VARIABLE_1249178)) (ho_4767 (ho_4779 (ho_4778 (ho_4777 (ho_4818 k_4817 BOUND_VARIABLE_1284343) BOUND_VARIABLE_1249176) BOUND_VARIABLE_1249177) BOUND_VARIABLE_1249178) BOUND_VARIABLE_1249179)))))))) (let ((_let_2514 (forall ((BOUND_VARIABLE_1249162 tptp.nat) (BOUND_VARIABLE_1249163 tptp.nat) (BOUND_VARIABLE_1249164 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_4819 BOUND_VARIABLE_1249162) BOUND_VARIABLE_1249163) BOUND_VARIABLE_1249164) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1249164)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249162) BOUND_VARIABLE_1249163))))))) (let ((_let_2515 (forall ((BOUND_VARIABLE_1284386 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1284384 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1249146 tptp.nat) (BOUND_VARIABLE_1249147 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284386 BOUND_VARIABLE_1249147)) (ho_4245 BOUND_VARIABLE_1284384 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249146) BOUND_VARIABLE_1249147))) (ho_4245 (ho_4487 (ho_4486 (ho_4821 k_4820 BOUND_VARIABLE_1284386) BOUND_VARIABLE_1284384) BOUND_VARIABLE_1249146) BOUND_VARIABLE_1249147))))) (let ((_let_2516 (forall ((BOUND_VARIABLE_1249134 tptp.nat) (BOUND_VARIABLE_1249135 tptp.nat)) (= (ho_4288 (ho_4287 k_4822 BOUND_VARIABLE_1249134) BOUND_VARIABLE_1249135) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249135)) (ho_4290 k_4289 BOUND_VARIABLE_1249134)))))) (let ((_let_2517 (forall ((BOUND_VARIABLE_1284422 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1284421 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1249122 tptp.nat) (BOUND_VARIABLE_1249123 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4825 (ho_4824 k_4823 BOUND_VARIABLE_1284422) BOUND_VARIABLE_1284421) BOUND_VARIABLE_1249122) BOUND_VARIABLE_1249123) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284422 BOUND_VARIABLE_1249123)) (ho_4767 BOUND_VARIABLE_1284421 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249122) BOUND_VARIABLE_1249123))))))) (let ((_let_2518 (forall ((BOUND_VARIABLE_1249110 tptp.nat) (BOUND_VARIABLE_1249111 tptp.nat)) (= (ho_4288 (ho_4287 k_4826 BOUND_VARIABLE_1249110) BOUND_VARIABLE_1249111) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249111)) (ho_4290 k_4289 BOUND_VARIABLE_1249110)))))) (let ((_let_2519 (forall ((BOUND_VARIABLE_1284462 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1284458 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1249084 tptp.nat) (BOUND_VARIABLE_1249085 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1284462 BOUND_VARIABLE_1249085)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1284458 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249084) BOUND_VARIABLE_1249085))) _let_2))) (ho_4216 (ho_4215 (ho_4730 (ho_4828 k_4827 BOUND_VARIABLE_1284462) BOUND_VARIABLE_1284458) BOUND_VARIABLE_1249084) BOUND_VARIABLE_1249085)))))))) (let ((_let_2520 (forall ((BOUND_VARIABLE_1249072 tptp.nat) (BOUND_VARIABLE_1249073 tptp.nat)) (= (ho_4288 (ho_4287 k_4829 BOUND_VARIABLE_1249072) BOUND_VARIABLE_1249073) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249073)) (ho_4290 k_4289 BOUND_VARIABLE_1249072)))))) (let ((_let_2521 (forall ((BOUND_VARIABLE_1284500 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1284498 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1249056 tptp.nat) (BOUND_VARIABLE_1249057 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284500 BOUND_VARIABLE_1249057)) (ho_4245 BOUND_VARIABLE_1284498 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249056) BOUND_VARIABLE_1249057))) (ho_4245 (ho_4487 (ho_4486 (ho_4821 k_4830 BOUND_VARIABLE_1284500) BOUND_VARIABLE_1284498) BOUND_VARIABLE_1249056) BOUND_VARIABLE_1249057))))) (let ((_let_2522 (forall ((BOUND_VARIABLE_1249044 tptp.nat) (BOUND_VARIABLE_1249045 tptp.nat)) (= (ho_4288 (ho_4287 k_4831 BOUND_VARIABLE_1249044) BOUND_VARIABLE_1249045) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249045)) (ho_4290 k_4289 BOUND_VARIABLE_1249044)))))) (let ((_let_2523 (forall ((BOUND_VARIABLE_1284532 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1284531 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1249032 tptp.nat) (BOUND_VARIABLE_1249033 tptp.nat)) (= (ho_4335 (ho_4726 (ho_4834 (ho_4833 k_4832 BOUND_VARIABLE_1284532) BOUND_VARIABLE_1284531) BOUND_VARIABLE_1249032) BOUND_VARIABLE_1249033) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1284532 BOUND_VARIABLE_1249033)) (ho_4335 BOUND_VARIABLE_1284531 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249032) BOUND_VARIABLE_1249033))))))) (let ((_let_2524 (forall ((BOUND_VARIABLE_1249020 tptp.nat) (BOUND_VARIABLE_1249021 tptp.nat)) (= (ho_4288 (ho_4287 k_4835 BOUND_VARIABLE_1249020) BOUND_VARIABLE_1249021) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1249021)) (ho_4290 k_4289 BOUND_VARIABLE_1249020)))))) (let ((_let_2525 (forall ((BOUND_VARIABLE_1284570 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1284568 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1249004 tptp.nat) (BOUND_VARIABLE_1249005 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1284570 BOUND_VARIABLE_1249005)) (ho_4316 BOUND_VARIABLE_1284568 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1249004) BOUND_VARIABLE_1249005))) (ho_4316 (ho_4338 (ho_4838 (ho_4837 k_4836 BOUND_VARIABLE_1284570) BOUND_VARIABLE_1284568) BOUND_VARIABLE_1249004) BOUND_VARIABLE_1249005))))) (let ((_let_2526 (forall ((BOUND_VARIABLE_1248992 tptp.nat) (BOUND_VARIABLE_1248993 tptp.nat)) (= (ho_4288 (ho_4287 k_4839 BOUND_VARIABLE_1248992) BOUND_VARIABLE_1248993) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248993)) (ho_4290 k_4289 BOUND_VARIABLE_1248992)))))) (let ((_let_2527 (forall ((BOUND_VARIABLE_1284610 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1284609 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1248980 tptp.nat) (BOUND_VARIABLE_1248981 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4825 (ho_4824 k_4840 BOUND_VARIABLE_1284610) BOUND_VARIABLE_1284609) BOUND_VARIABLE_1248980) BOUND_VARIABLE_1248981) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284610 BOUND_VARIABLE_1248981)) (ho_4767 BOUND_VARIABLE_1284609 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248980) BOUND_VARIABLE_1248981))))))) (let ((_let_2528 (forall ((BOUND_VARIABLE_1248968 tptp.nat) (BOUND_VARIABLE_1248969 tptp.nat)) (= (ho_4288 (ho_4287 k_4841 BOUND_VARIABLE_1248968) BOUND_VARIABLE_1248969) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248969)) (ho_4290 k_4289 BOUND_VARIABLE_1248968)))))) (let ((_let_2529 (forall ((BOUND_VARIABLE_1284640 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1284638 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1248952 tptp.nat) (BOUND_VARIABLE_1248953 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284640 BOUND_VARIABLE_1248953)) (ho_4245 BOUND_VARIABLE_1284638 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248952) BOUND_VARIABLE_1248953))) (ho_4245 (ho_4487 (ho_4486 (ho_4821 k_4842 BOUND_VARIABLE_1284640) BOUND_VARIABLE_1284638) BOUND_VARIABLE_1248952) BOUND_VARIABLE_1248953))))) (let ((_let_2530 (forall ((BOUND_VARIABLE_1248940 tptp.nat) (BOUND_VARIABLE_1248941 tptp.nat)) (= (ho_4288 (ho_4287 k_4843 BOUND_VARIABLE_1248940) BOUND_VARIABLE_1248941) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248941)) (ho_4290 k_4289 BOUND_VARIABLE_1248940)))))) (let ((_let_2531 (forall ((BOUND_VARIABLE_1284672 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1284671 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1248928 tptp.nat) (BOUND_VARIABLE_1248929 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4825 (ho_4824 k_4844 BOUND_VARIABLE_1284672) BOUND_VARIABLE_1284671) BOUND_VARIABLE_1248928) BOUND_VARIABLE_1248929) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284672 BOUND_VARIABLE_1248929)) (ho_4767 BOUND_VARIABLE_1284671 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248928) BOUND_VARIABLE_1248929))))))) (let ((_let_2532 (forall ((BOUND_VARIABLE_1248916 tptp.nat) (BOUND_VARIABLE_1248917 tptp.nat)) (= (ho_4288 (ho_4287 k_4845 BOUND_VARIABLE_1248916) BOUND_VARIABLE_1248917) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248917)) (ho_4290 k_4289 BOUND_VARIABLE_1248916)))))) (let ((_let_2533 (forall ((BOUND_VARIABLE_1284702 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1284700 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1248900 tptp.nat) (BOUND_VARIABLE_1248901 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284702 BOUND_VARIABLE_1248901)) (ho_4245 BOUND_VARIABLE_1284700 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248900) BOUND_VARIABLE_1248901))) (ho_4245 (ho_4487 (ho_4486 (ho_4821 k_4846 BOUND_VARIABLE_1284702) BOUND_VARIABLE_1284700) BOUND_VARIABLE_1248900) BOUND_VARIABLE_1248901))))) (let ((_let_2534 (forall ((BOUND_VARIABLE_1248888 tptp.nat) (BOUND_VARIABLE_1248889 tptp.nat)) (= (ho_4288 (ho_4287 k_4847 BOUND_VARIABLE_1248888) BOUND_VARIABLE_1248889) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248889)) (ho_4290 k_4289 BOUND_VARIABLE_1248888)))))) (let ((_let_2535 (forall ((BOUND_VARIABLE_1284734 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1284733 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1248876 tptp.nat) (BOUND_VARIABLE_1248877 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4825 (ho_4824 k_4848 BOUND_VARIABLE_1284734) BOUND_VARIABLE_1284733) BOUND_VARIABLE_1248876) BOUND_VARIABLE_1248877) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284734 BOUND_VARIABLE_1248877)) (ho_4767 BOUND_VARIABLE_1284733 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248876) BOUND_VARIABLE_1248877))))))) (let ((_let_2536 (forall ((BOUND_VARIABLE_1248864 tptp.nat) (BOUND_VARIABLE_1248865 tptp.nat)) (= (ho_4288 (ho_4287 k_4849 BOUND_VARIABLE_1248864) BOUND_VARIABLE_1248865) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248865)) (ho_4290 k_4289 BOUND_VARIABLE_1248864)))))) (let ((_let_2537 (forall ((BOUND_VARIABLE_1284763 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1248854 tptp.nat) (BOUND_VARIABLE_1248855 tptp.nat)) (= (ho_4245 (ho_4487 (ho_4851 k_4850 BOUND_VARIABLE_1284763) BOUND_VARIABLE_1248854) BOUND_VARIABLE_1248855) (ho_4245 (ho_4487 BOUND_VARIABLE_1284763 BOUND_VARIABLE_1248855) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248854) BOUND_VARIABLE_1248855)))))) (let ((_let_2538 (forall ((BOUND_VARIABLE_1248843 tptp.nat) (BOUND_VARIABLE_1248844 tptp.nat)) (= (ho_4288 (ho_4287 k_4852 BOUND_VARIABLE_1248843) BOUND_VARIABLE_1248844) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248844)) (ho_4290 k_4289 BOUND_VARIABLE_1248843)))))) (let ((_let_2539 (forall ((BOUND_VARIABLE_1284793 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1248833 tptp.nat) (BOUND_VARIABLE_1248834 tptp.nat)) (= (ho_4216 (ho_4215 (ho_4760 k_4853 BOUND_VARIABLE_1284793) BOUND_VARIABLE_1248833) BOUND_VARIABLE_1248834) (ho_4216 (ho_4215 BOUND_VARIABLE_1284793 BOUND_VARIABLE_1248834) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248833) BOUND_VARIABLE_1248834)))))) (let ((_let_2540 (forall ((BOUND_VARIABLE_1248822 tptp.nat) (BOUND_VARIABLE_1248823 tptp.nat)) (= (ho_4288 (ho_4287 k_4854 BOUND_VARIABLE_1248822) BOUND_VARIABLE_1248823) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248823)) (ho_4290 k_4289 BOUND_VARIABLE_1248822)))))) (let ((_let_2541 (forall ((BOUND_VARIABLE_1284818 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1248807 tptp.real) (BOUND_VARIABLE_1248808 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284818 BOUND_VARIABLE_1248808)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248807) BOUND_VARIABLE_1248808)) (ho_4245 (ho_4244 (ho_4512 k_4855 BOUND_VARIABLE_1284818) BOUND_VARIABLE_1248807) BOUND_VARIABLE_1248808))))) (let ((_let_2542 (forall ((BOUND_VARIABLE_1248796 tptp.nat) (BOUND_VARIABLE_1248797 tptp.nat)) (= (ho_4288 (ho_4287 k_4856 BOUND_VARIABLE_1248796) BOUND_VARIABLE_1248797) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248797)) (ho_4290 k_4289 BOUND_VARIABLE_1248796)))))) (let ((_let_2543 (forall ((BOUND_VARIABLE_1284846 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1248785 tptp.complex) (BOUND_VARIABLE_1248786 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_4857 BOUND_VARIABLE_1284846) BOUND_VARIABLE_1248785) BOUND_VARIABLE_1248786) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284846 BOUND_VARIABLE_1248786)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1248785) BOUND_VARIABLE_1248786)))))) (let ((_let_2544 (forall ((BOUND_VARIABLE_1248774 tptp.nat) (BOUND_VARIABLE_1248775 tptp.nat)) (= (ho_4288 (ho_4287 k_4859 BOUND_VARIABLE_1248774) BOUND_VARIABLE_1248775) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248775)) (ho_4290 k_4289 BOUND_VARIABLE_1248774)))))) (let ((_let_2545 (forall ((BOUND_VARIABLE_1284876 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1248759 tptp.real) (BOUND_VARIABLE_1248760 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1284876 BOUND_VARIABLE_1248760)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248759) BOUND_VARIABLE_1248760)) (ho_4245 (ho_4244 (ho_4512 k_4860 BOUND_VARIABLE_1284876) BOUND_VARIABLE_1248759) BOUND_VARIABLE_1248760))))) (let ((_let_2546 (forall ((BOUND_VARIABLE_1248748 tptp.nat) (BOUND_VARIABLE_1248749 tptp.nat)) (= (ho_4288 (ho_4287 k_4861 BOUND_VARIABLE_1248748) BOUND_VARIABLE_1248749) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248749)) (ho_4290 k_4289 BOUND_VARIABLE_1248748)))))) (let ((_let_2547 (forall ((BOUND_VARIABLE_1284904 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1248737 tptp.complex) (BOUND_VARIABLE_1248738 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_4862 BOUND_VARIABLE_1284904) BOUND_VARIABLE_1248737) BOUND_VARIABLE_1248738) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1284904 BOUND_VARIABLE_1248738)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1248737) BOUND_VARIABLE_1248738)))))) (let ((_let_2548 (forall ((BOUND_VARIABLE_1248726 tptp.nat) (BOUND_VARIABLE_1248727 tptp.nat)) (= (ho_4288 (ho_4287 k_4863 BOUND_VARIABLE_1248726) BOUND_VARIABLE_1248727) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248727)) (ho_4290 k_4289 BOUND_VARIABLE_1248726)))))) (let ((_let_2549 (forall ((BOUND_VARIABLE_1284931 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1248716 tptp.nat) (BOUND_VARIABLE_1248717 tptp.nat)) (= (ho_4245 (ho_4487 (ho_4851 k_4864 BOUND_VARIABLE_1284931) BOUND_VARIABLE_1248716) BOUND_VARIABLE_1248717) (ho_4245 (ho_4487 BOUND_VARIABLE_1284931 BOUND_VARIABLE_1248717) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248716) BOUND_VARIABLE_1248717)))))) (let ((_let_2550 (forall ((BOUND_VARIABLE_1248705 tptp.nat) (BOUND_VARIABLE_1248706 tptp.nat)) (= (ho_4288 (ho_4287 k_4865 BOUND_VARIABLE_1248705) BOUND_VARIABLE_1248706) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248706)) (ho_4290 k_4289 BOUND_VARIABLE_1248705)))))) (let ((_let_2551 (forall ((BOUND_VARIABLE_1284957 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1248695 tptp.nat) (BOUND_VARIABLE_1248696 tptp.nat)) (= (ho_4216 (ho_4215 (ho_4760 k_4866 BOUND_VARIABLE_1284957) BOUND_VARIABLE_1248695) BOUND_VARIABLE_1248696) (ho_4216 (ho_4215 BOUND_VARIABLE_1284957 BOUND_VARIABLE_1248696) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248695) BOUND_VARIABLE_1248696)))))) (let ((_let_2552 (forall ((BOUND_VARIABLE_1248684 tptp.nat) (BOUND_VARIABLE_1248685 tptp.nat)) (= (ho_4288 (ho_4287 k_4867 BOUND_VARIABLE_1248684) BOUND_VARIABLE_1248685) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248685)) (ho_4290 k_4289 BOUND_VARIABLE_1248684)))))) (let ((_let_2553 (forall ((BOUND_VARIABLE_1248674 tptp.nat) (BOUND_VARIABLE_1248675 tptp.nat)) (= (ho_4288 (ho_4287 k_4868 BOUND_VARIABLE_1248674) BOUND_VARIABLE_1248675) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1248675)) (ho_4290 k_4289 BOUND_VARIABLE_1248674)))))) (let ((_let_2554 (forall ((BOUND_VARIABLE_1284994 |u_(-> tptp.nat tptp.nat tptp.real)|) (BOUND_VARIABLE_1248666 tptp.nat) (BOUND_VARIABLE_1248667 tptp.nat)) (= (ho_4245 (ho_4487 (ho_4851 k_4869 BOUND_VARIABLE_1284994) BOUND_VARIABLE_1248666) BOUND_VARIABLE_1248667) (ho_4245 (ho_4487 BOUND_VARIABLE_1284994 BOUND_VARIABLE_1248667) BOUND_VARIABLE_1248666))))) (let ((_let_2555 (forall ((BOUND_VARIABLE_1248610 tptp.nat) (BOUND_VARIABLE_1248611 tptp.nat) (BOUND_VARIABLE_1248612 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1248610) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1248611) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1248612 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4870 BOUND_VARIABLE_1248610) BOUND_VARIABLE_1248611) BOUND_VARIABLE_1248612))))) (let ((_let_2556 (forall ((BOUND_VARIABLE_1248600 tptp.nat) (BOUND_VARIABLE_1248601 tptp.nat)) (= (ho_4288 (ho_4287 k_4871 BOUND_VARIABLE_1248600) BOUND_VARIABLE_1248601) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1248601)) (ho_4290 k_4289 BOUND_VARIABLE_1248600)))))) (let ((_let_2557 (forall ((BOUND_VARIABLE_1285050 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1248592 tptp.nat) (BOUND_VARIABLE_1248593 tptp.nat)) (= (ho_4216 (ho_4215 (ho_4760 k_4872 BOUND_VARIABLE_1285050) BOUND_VARIABLE_1248592) BOUND_VARIABLE_1248593) (ho_4216 (ho_4215 BOUND_VARIABLE_1285050 BOUND_VARIABLE_1248593) BOUND_VARIABLE_1248592))))) (let ((_let_2558 (forall ((BOUND_VARIABLE_1248536 tptp.nat) (BOUND_VARIABLE_1248537 tptp.nat) (BOUND_VARIABLE_1248538 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1248536) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1248537) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1248538 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_4873 BOUND_VARIABLE_1248536) BOUND_VARIABLE_1248537) BOUND_VARIABLE_1248538))))) (let ((_let_2559 (forall ((BOUND_VARIABLE_1248515 tptp.real) (BOUND_VARIABLE_1248516 tptp.nat) (BOUND_VARIABLE_1248517 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1248515) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1248516) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1248517) (ho_4258 (ho_4273 (ho_4696 k_4874 BOUND_VARIABLE_1248515) BOUND_VARIABLE_1248516) BOUND_VARIABLE_1248517))))))))) (let ((_let_2560 (forall ((BOUND_VARIABLE_1248494 tptp.real) (BOUND_VARIABLE_1248495 tptp.nat) (BOUND_VARIABLE_1248496 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1248494) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1248495) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1248496) (ho_4258 (ho_4273 (ho_4696 k_4875 BOUND_VARIABLE_1248494) BOUND_VARIABLE_1248495) BOUND_VARIABLE_1248496))))))))) (let ((_let_2561 (forall ((BOUND_VARIABLE_1248473 tptp.rat) (BOUND_VARIABLE_1248474 tptp.nat) (BOUND_VARIABLE_1248475 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1248473) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1248474) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1248475) (ho_4442 (ho_4458 (ho_4699 k_4876 BOUND_VARIABLE_1248473) BOUND_VARIABLE_1248474) BOUND_VARIABLE_1248475))))))))))) (let ((_let_2562 (forall ((BOUND_VARIABLE_1248452 tptp.rat) (BOUND_VARIABLE_1248453 tptp.nat) (BOUND_VARIABLE_1248454 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1248452) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1248453) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1248454) (ho_4442 (ho_4458 (ho_4699 k_4877 BOUND_VARIABLE_1248452) BOUND_VARIABLE_1248453) BOUND_VARIABLE_1248454))))))))))) (let ((_let_2563 (forall ((BOUND_VARIABLE_1248432 tptp.int) (BOUND_VARIABLE_1248433 tptp.nat) (BOUND_VARIABLE_1248434 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1248432) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1248433) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) BOUND_VARIABLE_1248434) (ho_4209 (ho_4220 (ho_4723 k_4878 BOUND_VARIABLE_1248432) BOUND_VARIABLE_1248433) BOUND_VARIABLE_1248434)))))) (let ((_let_2564 (forall ((BOUND_VARIABLE_1248412 tptp.int) (BOUND_VARIABLE_1248413 tptp.nat) (BOUND_VARIABLE_1248414 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1248412) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1248413) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) BOUND_VARIABLE_1248414) (ho_4209 (ho_4220 (ho_4723 k_4879 BOUND_VARIABLE_1248412) BOUND_VARIABLE_1248413) BOUND_VARIABLE_1248414)))))) (let ((_let_2565 (forall ((BOUND_VARIABLE_1248402 tptp.nat) (BOUND_VARIABLE_1248403 tptp.nat)) (= (ho_4288 (ho_4287 k_4880 BOUND_VARIABLE_1248402) BOUND_VARIABLE_1248403) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1248403)) (ho_4290 k_4289 BOUND_VARIABLE_1248402)))))) (let ((_let_2566 (forall ((BOUND_VARIABLE_1248351 tptp.real) (BOUND_VARIABLE_1248352 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_4 (= BOUND_VARIABLE_1248352 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1248352 _let_6))) (= (ho_4351 (ho_4508 k_4881 BOUND_VARIABLE_1248351) BOUND_VARIABLE_1248352) (and (or (and (= BOUND_VARIABLE_1248352 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1248352) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1248352)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1248351 (ho_4348 k_4347 (ho_4244 k_4344 BOUND_VARIABLE_1248352))))))))))))))) (let ((_let_2567 (forall ((BOUND_VARIABLE_1248305 tptp.real) (BOUND_VARIABLE_1248306 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4882 BOUND_VARIABLE_1248305) BOUND_VARIABLE_1248306) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1248306 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1248306) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1248306) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248305) BOUND_VARIABLE_1248306))))))))))))) (let ((_let_2568 (forall ((BOUND_VARIABLE_1248259 tptp.real) (BOUND_VARIABLE_1248260 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4883 BOUND_VARIABLE_1248259) BOUND_VARIABLE_1248260) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1248260 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1248260) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1248260) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248259) BOUND_VARIABLE_1248260))))))))))))) (let ((_let_2569 (forall ((BOUND_VARIABLE_1248208 tptp.real) (BOUND_VARIABLE_1248209 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4884 BOUND_VARIABLE_1248208) BOUND_VARIABLE_1248209) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1248209 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248209) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1248209) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248208) BOUND_VARIABLE_1248209))))))))))))))))) (let ((_let_2570 (forall ((BOUND_VARIABLE_1248157 tptp.real) (BOUND_VARIABLE_1248158 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4885 BOUND_VARIABLE_1248157) BOUND_VARIABLE_1248158) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1248158 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248158) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1248158) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248157) BOUND_VARIABLE_1248158))))))))))))))))) (let ((_let_2571 (forall ((BOUND_VARIABLE_1248106 tptp.real) (BOUND_VARIABLE_1248107 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4886 BOUND_VARIABLE_1248106) BOUND_VARIABLE_1248107) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1248107 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1248107) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1248107) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1248106) BOUND_VARIABLE_1248107))))))))))))))))) (let ((_let_2572 (forall ((BOUND_VARIABLE_1248055 tptp.real) (BOUND_VARIABLE_1248056 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (let ((_let_5 (= BOUND_VARIABLE_1248056 _let_4))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1248056 _let_6))) (= (ho_4351 (ho_4508 k_4887 BOUND_VARIABLE_1248055) BOUND_VARIABLE_1248056) (and (or (and (= BOUND_VARIABLE_1248056 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1248056) _let_6)) (not _let_7)) _let_7) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1248056)) (not _let_5)) _let_5) (= BOUND_VARIABLE_1248055 (ho_4348 k_4347 (ho_4244 k_4345 BOUND_VARIABLE_1248056))))))))))))))) (let ((_let_2573 (forall ((BOUND_VARIABLE_1248004 tptp.real) (BOUND_VARIABLE_1248005 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 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BOUND_VARIABLE_1247954 _let_4))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1247954 _let_6))) (= (ho_4351 (ho_4508 k_4889 BOUND_VARIABLE_1247953) BOUND_VARIABLE_1247954) (and (or (and (= BOUND_VARIABLE_1247954 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1247954) _let_6)) (not _let_7)) _let_7) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1247954)) (not _let_5)) _let_5) (= BOUND_VARIABLE_1247953 (ho_4348 k_4347 (ho_4244 k_4346 BOUND_VARIABLE_1247954))))))))))))))) (let ((_let_2575 (forall ((BOUND_VARIABLE_1247902 tptp.real) (BOUND_VARIABLE_1247903 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4890 BOUND_VARIABLE_1247902) BOUND_VARIABLE_1247903) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247903 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 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(ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4891 BOUND_VARIABLE_1247851) BOUND_VARIABLE_1247852) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247852 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1247852) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1247852) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247851) BOUND_VARIABLE_1247852))))))))))))))))) (let ((_let_2577 (forall ((BOUND_VARIABLE_1247800 tptp.real) (BOUND_VARIABLE_1247801 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4892 BOUND_VARIABLE_1247800) BOUND_VARIABLE_1247801) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247801 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1247801) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1247801) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247800) BOUND_VARIABLE_1247801))))))))))))))))) (let ((_let_2578 (forall ((BOUND_VARIABLE_1247749 tptp.real) (BOUND_VARIABLE_1247750 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4893 BOUND_VARIABLE_1247749) BOUND_VARIABLE_1247750) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247750 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1247750) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1247750) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247749) BOUND_VARIABLE_1247750))))))))))))))))) (let ((_let_2579 (forall ((BOUND_VARIABLE_1247698 tptp.real) (BOUND_VARIABLE_1247699 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4894 BOUND_VARIABLE_1247698) BOUND_VARIABLE_1247699) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247699 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1247699) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1247699) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247698) BOUND_VARIABLE_1247699))))))))))))))))) (let ((_let_2580 (forall ((BOUND_VARIABLE_1247647 tptp.real) (BOUND_VARIABLE_1247648 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4895 BOUND_VARIABLE_1247647) BOUND_VARIABLE_1247648) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247648 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1247648) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1247648) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247647) BOUND_VARIABLE_1247648))))))))))))))))) (let ((_let_2581 (forall ((BOUND_VARIABLE_1247601 tptp.real) (BOUND_VARIABLE_1247602 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4896 BOUND_VARIABLE_1247601) BOUND_VARIABLE_1247602) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247602 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247602) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247602) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247601) BOUND_VARIABLE_1247602))))))))))))) (let ((_let_2582 (forall ((BOUND_VARIABLE_1247555 tptp.real) (BOUND_VARIABLE_1247556 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4897 BOUND_VARIABLE_1247555) BOUND_VARIABLE_1247556) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247556 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247556) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247556) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247555) BOUND_VARIABLE_1247556))))))))))))) (let ((_let_2583 (forall ((BOUND_VARIABLE_1247509 tptp.real) (BOUND_VARIABLE_1247510 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4898 BOUND_VARIABLE_1247509) BOUND_VARIABLE_1247510) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247510 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247510) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247510) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247509) BOUND_VARIABLE_1247510))))))))))))) (let ((_let_2584 (forall ((BOUND_VARIABLE_1247463 tptp.real) (BOUND_VARIABLE_1247464 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4899 BOUND_VARIABLE_1247463) BOUND_VARIABLE_1247464) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247464 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247464) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247464) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247463) BOUND_VARIABLE_1247464))))))))))))) (let ((_let_2585 (forall ((BOUND_VARIABLE_1247408 tptp.real) (BOUND_VARIABLE_1247409 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4350)))) (let ((_let_4 (= BOUND_VARIABLE_1247409 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1247409 _let_6))) (= (ho_4351 (ho_4508 k_4900 BOUND_VARIABLE_1247408) BOUND_VARIABLE_1247409) (and (or (and (= BOUND_VARIABLE_1247409 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1247409) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1247409)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1247408 (ho_4348 k_4347 (ho_4244 k_4352 BOUND_VARIABLE_1247409))))))))))))))) (let ((_let_2586 (forall ((BOUND_VARIABLE_1247362 tptp.real) (BOUND_VARIABLE_1247363 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4901 BOUND_VARIABLE_1247362) BOUND_VARIABLE_1247363) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247363 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247363) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247363) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247362) BOUND_VARIABLE_1247363))))))))))))) (let ((_let_2587 (forall ((BOUND_VARIABLE_1247316 tptp.real) (BOUND_VARIABLE_1247317 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4902 BOUND_VARIABLE_1247316) BOUND_VARIABLE_1247317) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247317 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247317) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247317) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247316) BOUND_VARIABLE_1247317))))))))))))) (let ((_let_2588 (forall ((BOUND_VARIABLE_1247270 tptp.real) (BOUND_VARIABLE_1247271 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4903 BOUND_VARIABLE_1247270) BOUND_VARIABLE_1247271) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247271 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247271) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247271) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247270) BOUND_VARIABLE_1247271))))))))))))) (let ((_let_2589 (forall ((BOUND_VARIABLE_1247224 tptp.real) (BOUND_VARIABLE_1247225 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4904 BOUND_VARIABLE_1247224) BOUND_VARIABLE_1247225) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247225 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247225) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247225) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247224) BOUND_VARIABLE_1247225))))))))))))) (let ((_let_2590 (forall ((BOUND_VARIABLE_1247178 tptp.real) (BOUND_VARIABLE_1247179 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4905 BOUND_VARIABLE_1247178) BOUND_VARIABLE_1247179) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247179 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247179) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247179) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247178) BOUND_VARIABLE_1247179))))))))))))) (let ((_let_2591 (forall ((BOUND_VARIABLE_1247132 tptp.real) (BOUND_VARIABLE_1247133 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4906 BOUND_VARIABLE_1247132) BOUND_VARIABLE_1247133) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247133 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247133) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247133) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247132) BOUND_VARIABLE_1247133))))))))))))) (let ((_let_2592 (forall ((BOUND_VARIABLE_1247086 tptp.real) (BOUND_VARIABLE_1247087 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4907 BOUND_VARIABLE_1247086) BOUND_VARIABLE_1247087) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1247087 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1247087) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1247087) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1247086) BOUND_VARIABLE_1247087))))))))))))) (let ((_let_2593 (forall ((BOUND_VARIABLE_1247031 tptp.real) (BOUND_VARIABLE_1247032 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4353)))) (let ((_let_4 (= BOUND_VARIABLE_1247032 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1247032 _let_6))) (= (ho_4351 (ho_4508 k_4908 BOUND_VARIABLE_1247031) BOUND_VARIABLE_1247032) (and (or (and (= BOUND_VARIABLE_1247032 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1247032) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1247032)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1247031 (ho_4348 k_4347 (ho_4244 k_4354 BOUND_VARIABLE_1247032))))))))))))))) (let ((_let_2594 (forall ((BOUND_VARIABLE_1246980 tptp.real) (BOUND_VARIABLE_1246981 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4909 BOUND_VARIABLE_1246980) BOUND_VARIABLE_1246981) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246981 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246981) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246981) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246980) BOUND_VARIABLE_1246981))))))))))))))))) (let ((_let_2595 (forall ((BOUND_VARIABLE_1246929 tptp.real) (BOUND_VARIABLE_1246930 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4910 BOUND_VARIABLE_1246929) BOUND_VARIABLE_1246930) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246930 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246930) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246930) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246929) BOUND_VARIABLE_1246930))))))))))))))))) (let ((_let_2596 (forall ((BOUND_VARIABLE_1246878 tptp.real) (BOUND_VARIABLE_1246879 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4911 BOUND_VARIABLE_1246878) BOUND_VARIABLE_1246879) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246879 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246879) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246879) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246878) BOUND_VARIABLE_1246879))))))))))))))))) (let ((_let_2597 (forall ((BOUND_VARIABLE_1246827 tptp.real) (BOUND_VARIABLE_1246828 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4912 BOUND_VARIABLE_1246827) BOUND_VARIABLE_1246828) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246828 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246828) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246828) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246827) BOUND_VARIABLE_1246828))))))))))))))))) (let ((_let_2598 (forall ((BOUND_VARIABLE_1246781 tptp.real) (BOUND_VARIABLE_1246782 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4913 BOUND_VARIABLE_1246781) BOUND_VARIABLE_1246782) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246782 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246782) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246782) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246781) BOUND_VARIABLE_1246782))))))))))))) (let ((_let_2599 (forall ((BOUND_VARIABLE_1246735 tptp.real) (BOUND_VARIABLE_1246736 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4914 BOUND_VARIABLE_1246735) BOUND_VARIABLE_1246736) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246736 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246736) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246736) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246735) BOUND_VARIABLE_1246736))))))))))))) (let ((_let_2600 (forall ((BOUND_VARIABLE_1246689 tptp.real) (BOUND_VARIABLE_1246690 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4915 BOUND_VARIABLE_1246689) BOUND_VARIABLE_1246690) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246690 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246690) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246690) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246689) BOUND_VARIABLE_1246690))))))))))))) (let ((_let_2601 (forall ((BOUND_VARIABLE_1246643 tptp.real) (BOUND_VARIABLE_1246644 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4916 BOUND_VARIABLE_1246643) BOUND_VARIABLE_1246644) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246644 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246644) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246644) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246643) BOUND_VARIABLE_1246644))))))))))))) (let ((_let_2602 (forall ((BOUND_VARIABLE_1246597 tptp.real) (BOUND_VARIABLE_1246598 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4917 BOUND_VARIABLE_1246597) BOUND_VARIABLE_1246598) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246598 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246598) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246598) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246597) BOUND_VARIABLE_1246598))))))))))))) (let ((_let_2603 (forall ((BOUND_VARIABLE_1246551 tptp.real) (BOUND_VARIABLE_1246552 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4918 BOUND_VARIABLE_1246551) BOUND_VARIABLE_1246552) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246552 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246552) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246552) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246551) BOUND_VARIABLE_1246552))))))))))))) (let ((_let_2604 (forall ((BOUND_VARIABLE_1246505 tptp.real) (BOUND_VARIABLE_1246506 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4919 BOUND_VARIABLE_1246505) BOUND_VARIABLE_1246506) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246506 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246506) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246506) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246505) BOUND_VARIABLE_1246506))))))))))))) (let ((_let_2605 (forall ((BOUND_VARIABLE_1246459 tptp.real) (BOUND_VARIABLE_1246460 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4920 BOUND_VARIABLE_1246459) BOUND_VARIABLE_1246460) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246460 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246460) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246460) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246459) BOUND_VARIABLE_1246460))))))))))))) (let ((_let_2606 (forall ((BOUND_VARIABLE_1246408 tptp.real) (BOUND_VARIABLE_1246409 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4921 BOUND_VARIABLE_1246408) BOUND_VARIABLE_1246409) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246409 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246409) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246409) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246408) BOUND_VARIABLE_1246409))))))))))))))))) (let ((_let_2607 (forall ((BOUND_VARIABLE_1246357 tptp.real) (BOUND_VARIABLE_1246358 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4922 BOUND_VARIABLE_1246357) BOUND_VARIABLE_1246358) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246358 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246358) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246358) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246357) BOUND_VARIABLE_1246358))))))))))))))))) (let ((_let_2608 (forall ((BOUND_VARIABLE_1246306 tptp.real) (BOUND_VARIABLE_1246307 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4923 BOUND_VARIABLE_1246306) BOUND_VARIABLE_1246307) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246307 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246307) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246307) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246306) BOUND_VARIABLE_1246307))))))))))))))))) (let ((_let_2609 (forall ((BOUND_VARIABLE_1246255 tptp.real) (BOUND_VARIABLE_1246256 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4924 BOUND_VARIABLE_1246255) BOUND_VARIABLE_1246256) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246256 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246256) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246256) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246255) BOUND_VARIABLE_1246256))))))))))))))))) (let ((_let_2610 (forall ((BOUND_VARIABLE_1246204 tptp.real) (BOUND_VARIABLE_1246205 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4925 BOUND_VARIABLE_1246204) BOUND_VARIABLE_1246205) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246205 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246205) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246205) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246204) BOUND_VARIABLE_1246205))))))))))))))))) (let ((_let_2611 (forall ((BOUND_VARIABLE_1246153 tptp.real) (BOUND_VARIABLE_1246154 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4926 BOUND_VARIABLE_1246153) BOUND_VARIABLE_1246154) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246154 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246154) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246154) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246153) BOUND_VARIABLE_1246154))))))))))))))))) (let ((_let_2612 (forall ((BOUND_VARIABLE_1246102 tptp.real) (BOUND_VARIABLE_1246103 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4927 BOUND_VARIABLE_1246102) BOUND_VARIABLE_1246103) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246103 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246103) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246103) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246102) BOUND_VARIABLE_1246103))))))))))))))))) (let ((_let_2613 (forall ((BOUND_VARIABLE_1246051 tptp.real) (BOUND_VARIABLE_1246052 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4928 BOUND_VARIABLE_1246051) BOUND_VARIABLE_1246052) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246052 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1246052) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1246052) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246051) BOUND_VARIABLE_1246052))))))))))))))))) (let ((_let_2614 (forall ((BOUND_VARIABLE_1246005 tptp.real) (BOUND_VARIABLE_1246006 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4929 BOUND_VARIABLE_1246005) BOUND_VARIABLE_1246006) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1246006 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1246006) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1246006) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1246005) BOUND_VARIABLE_1246006))))))))))))) (let ((_let_2615 (forall ((BOUND_VARIABLE_1245959 tptp.real) (BOUND_VARIABLE_1245960 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4930 BOUND_VARIABLE_1245959) BOUND_VARIABLE_1245960) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245960 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245960) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245960) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245959) BOUND_VARIABLE_1245960))))))))))))) (let ((_let_2616 (forall ((BOUND_VARIABLE_1245913 tptp.real) (BOUND_VARIABLE_1245914 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4931 BOUND_VARIABLE_1245913) BOUND_VARIABLE_1245914) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245914 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245914) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245914) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245913) BOUND_VARIABLE_1245914))))))))))))) (let ((_let_2617 (forall ((BOUND_VARIABLE_1245867 tptp.real) (BOUND_VARIABLE_1245868 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4932 BOUND_VARIABLE_1245867) BOUND_VARIABLE_1245868) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245868 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245868) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245868) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245867) BOUND_VARIABLE_1245868))))))))))))) (let ((_let_2618 (forall ((BOUND_VARIABLE_1245821 tptp.real) (BOUND_VARIABLE_1245822 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4933 BOUND_VARIABLE_1245821) BOUND_VARIABLE_1245822) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245822 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245822) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245822) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245821) BOUND_VARIABLE_1245822))))))))))))) (let ((_let_2619 (forall ((BOUND_VARIABLE_1245775 tptp.real) (BOUND_VARIABLE_1245776 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4934 BOUND_VARIABLE_1245775) BOUND_VARIABLE_1245776) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245776 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245776) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245776) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245775) BOUND_VARIABLE_1245776))))))))))))) (let ((_let_2620 (forall ((BOUND_VARIABLE_1245724 tptp.real) (BOUND_VARIABLE_1245725 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4935 BOUND_VARIABLE_1245724) BOUND_VARIABLE_1245725) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245725 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1245725) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1245725) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245724) BOUND_VARIABLE_1245725))))))))))))))))) (let ((_let_2621 (forall ((BOUND_VARIABLE_1245673 tptp.real) (BOUND_VARIABLE_1245674 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4936 BOUND_VARIABLE_1245673) BOUND_VARIABLE_1245674) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245674 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1245674) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1245674) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245673) BOUND_VARIABLE_1245674))))))))))))))))) (let ((_let_2622 (forall ((BOUND_VARIABLE_1245627 tptp.real) (BOUND_VARIABLE_1245628 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4937 BOUND_VARIABLE_1245627) BOUND_VARIABLE_1245628) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245628 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245628) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245628) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245627) BOUND_VARIABLE_1245628))))))))))))) (let ((_let_2623 (forall ((BOUND_VARIABLE_1245576 tptp.real) (BOUND_VARIABLE_1245577 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (let ((_let_5 (= BOUND_VARIABLE_1245577 _let_4))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1245577 _let_6))) (= (ho_4351 (ho_4508 k_4938 BOUND_VARIABLE_1245576) BOUND_VARIABLE_1245577) (and (or (and (= BOUND_VARIABLE_1245577 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245577) _let_6)) (not _let_7)) _let_7) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1245577)) (not _let_5)) _let_5) (= BOUND_VARIABLE_1245576 (ho_4348 k_4347 (ho_4244 k_4355 BOUND_VARIABLE_1245577))))))))))))))) (let ((_let_2624 (forall ((BOUND_VARIABLE_1245521 tptp.real) (BOUND_VARIABLE_1245522 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4356)))) (let ((_let_4 (= BOUND_VARIABLE_1245522 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1245522 _let_6))) (= (ho_4351 (ho_4508 k_4939 BOUND_VARIABLE_1245521) BOUND_VARIABLE_1245522) (and (or (and (= BOUND_VARIABLE_1245522 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245522) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1245522)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1245521 (ho_4348 k_4347 (ho_4244 k_4357 BOUND_VARIABLE_1245522))))))))))))))) (let ((_let_2625 (forall ((BOUND_VARIABLE_1245470 tptp.real) (BOUND_VARIABLE_1245471 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_4 (= BOUND_VARIABLE_1245471 _let_3))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) _let_5) (ho_4258 (ho_4257 _let_1 k_4248) _let_5)))) (let ((_let_7 (= BOUND_VARIABLE_1245471 _let_6))) (= (ho_4351 (ho_4508 k_4940 BOUND_VARIABLE_1245470) BOUND_VARIABLE_1245471) (and (or (and (= BOUND_VARIABLE_1245471 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245471) _let_6)) (not _let_7)) _let_7) (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) BOUND_VARIABLE_1245471)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1245470 (ho_4348 k_4347 (ho_4244 k_4358 BOUND_VARIABLE_1245471))))))))))))))) (let ((_let_2626 (forall ((BOUND_VARIABLE_1245412 tptp.real) (BOUND_VARIABLE_1245413 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4359))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (let ((_let_5 (= BOUND_VARIABLE_1245413 _let_4))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1245413 _let_6))) (= (and (or (and (= BOUND_VARIABLE_1245413 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245413) _let_6)) (not _let_7)) _let_7) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1245413)) (not _let_5)) _let_5) (= BOUND_VARIABLE_1245412 (ho_4348 k_4347 (ho_4244 k_4360 BOUND_VARIABLE_1245413)))) (ho_4351 (ho_4508 k_4941 BOUND_VARIABLE_1245412) BOUND_VARIABLE_1245413)))))))))))) (let ((_let_2627 (forall ((BOUND_VARIABLE_1245350 tptp.real) (BOUND_VARIABLE_1245351 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (ho_4351 (ho_4508 k_4942 BOUND_VARIABLE_1245350) BOUND_VARIABLE_1245351) (and (= BOUND_VARIABLE_1245350 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4361 BOUND_VARIABLE_1245351))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4362 BOUND_VARIABLE_1245351))))) (= BOUND_VARIABLE_1245351 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245351) _let_6)) (not (= BOUND_VARIABLE_1245351 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1245351)) (not (= BOUND_VARIABLE_1245351 _let_5))))))))))))) (let ((_let_2628 (forall ((BOUND_VARIABLE_1245272 tptp.real) (BOUND_VARIABLE_1245273 tptp.real)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4247 k_4246 _let_1))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4257 _let_3 k_4274))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4264 _let_5 k_4275))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 _let_2) (ho_4506 k_4505 k_4504))) (ho_4258 _let_4 _let_2)))) (let ((_let_8 (ho_4257 _let_3 k_4248))) (let ((_let_9 (ho_4258 _let_8 _let_7))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_11 (ho_4247 k_4246 tptp.one))) (let ((_let_12 (ho_4265 (ho_4264 _let_5 k_4259) _let_11))) (= (ho_4351 (ho_4508 k_4947 BOUND_VARIABLE_1245272) BOUND_VARIABLE_1245273) (and (= (ho_4258 (ho_4265 _let_6 (ho_4348 k_4347 (ho_4244 k_4363 BOUND_VARIABLE_1245273))) (ho_4258 _let_4 (ho_4348 k_4347 (ho_4244 k_4364 BOUND_VARIABLE_1245273)))) (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1245272) (ho_4258 _let_4 (ho_4258 _let_12 (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_10 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_10))) (ho_4258 _let_12 (ho_4258 _let_8 _let_11))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 _let_12 (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245272) _let_10)))))))) (= BOUND_VARIABLE_1245273 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245273) _let_9)) (not (= BOUND_VARIABLE_1245273 _let_9)) (= _let_7 (ho_4258 (ho_4265 k_4349 _let_7) BOUND_VARIABLE_1245273)) (not (= BOUND_VARIABLE_1245273 _let_7))))))))))))))))))) (let ((_let_2629 (forall ((BOUND_VARIABLE_1245210 tptp.real) (BOUND_VARIABLE_1245211 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (ho_4351 (ho_4508 k_4948 BOUND_VARIABLE_1245210) BOUND_VARIABLE_1245211) (and (= BOUND_VARIABLE_1245210 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4365 BOUND_VARIABLE_1245211))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4366 BOUND_VARIABLE_1245211))))) (= BOUND_VARIABLE_1245211 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245211) _let_6)) (not (= BOUND_VARIABLE_1245211 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1245211)) (not (= BOUND_VARIABLE_1245211 _let_5))))))))))))) (let ((_let_2630 (forall ((BOUND_VARIABLE_1245141 tptp.real) (BOUND_VARIABLE_1245142 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4369))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (and (= BOUND_VARIABLE_1245141 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4367 BOUND_VARIABLE_1245142))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4368 BOUND_VARIABLE_1245142))))) (= BOUND_VARIABLE_1245142 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245142) _let_6)) (not (= BOUND_VARIABLE_1245142 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1245142)) (not (= BOUND_VARIABLE_1245142 _let_5))) (ho_4351 (ho_4508 k_4949 BOUND_VARIABLE_1245141) BOUND_VARIABLE_1245142))))))))))) (let ((_let_2631 (forall ((BOUND_VARIABLE_1245097 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1245097 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1245097 _let_3))) (= (ho_4351 k_4950 BOUND_VARIABLE_1245097) (and (or (and (= BOUND_VARIABLE_1245097 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1245097) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1245097)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4370 BOUND_VARIABLE_1245097)))))))))))))) (let ((_let_2632 (forall ((BOUND_VARIABLE_1245046 tptp.real) (BOUND_VARIABLE_1245047 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4951 BOUND_VARIABLE_1245046) BOUND_VARIABLE_1245047) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245047 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1245047) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1245047) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245046) BOUND_VARIABLE_1245047))))))))))))))))) (let ((_let_2633 (forall ((BOUND_VARIABLE_1245000 tptp.real) (BOUND_VARIABLE_1245001 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4952 BOUND_VARIABLE_1245000) BOUND_VARIABLE_1245001) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1245001 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1245001) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1245001) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1245000) BOUND_VARIABLE_1245001))))))))))))) (let ((_let_2634 (forall ((BOUND_VARIABLE_1244945 tptp.real) (BOUND_VARIABLE_1244946 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (let ((_let_7 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_5) _let_6))) (let ((_let_8 (ho_4196 k_4195 tptp.one))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_11 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_8)))) (let ((_let_12 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_4953 BOUND_VARIABLE_1244945) BOUND_VARIABLE_1244946) (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244946 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_7) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244946) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_12 (ho_4216 (ho_4215 k_4221 _let_9) _let_10)) _let_11)) (ho_4209 (ho_4220 _let_12 _let_9) _let_11))))) _let_10))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1244946) _let_9)) _let_7))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 (ho_4247 k_4246 _let_1)) BOUND_VARIABLE_1244945)) BOUND_VARIABLE_1244946)))))))))))))))))) (let ((_let_2635 (forall ((BOUND_VARIABLE_1244895 tptp.real) (BOUND_VARIABLE_1244896 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (let ((_let_7 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_5) _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (= (ho_4245 (ho_4244 k_4954 BOUND_VARIABLE_1244895) BOUND_VARIABLE_1244896) (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244896 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244896) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244896) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_7)))) _let_7)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 (ho_4247 k_4246 _let_1)) BOUND_VARIABLE_1244895)) BOUND_VARIABLE_1244896)))))))))))))) (let ((_let_2636 (forall ((BOUND_VARIABLE_1244830 tptp.complex) (BOUND_VARIABLE_1244831 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1244830) BOUND_VARIABLE_1244831))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244831 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244831) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1244831) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_4955 BOUND_VARIABLE_1244830) BOUND_VARIABLE_1244831) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_2637 (forall ((BOUND_VARIABLE_1244770 tptp.complex) (BOUND_VARIABLE_1244771 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1244770) BOUND_VARIABLE_1244771))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244771 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244771) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244771) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_4956 BOUND_VARIABLE_1244770) BOUND_VARIABLE_1244771) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_2638 (forall ((BOUND_VARIABLE_1244704 tptp.complex) (BOUND_VARIABLE_1244705 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 (ho_4703 (ho_4705 k_4710 (ho_4701 k_4700 _let_1)) BOUND_VARIABLE_1244704)) BOUND_VARIABLE_1244705))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4258 (ho_4257 _let_4 k_4248) _let_3))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_7 (ho_4258 (ho_4265 (ho_4264 _let_6 k_4259) _let_3) _let_5))) (let ((_let_8 (ho_4196 k_4195 tptp.one))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_11 (ho_4257 _let_4 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_8)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_6 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244705 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_7) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_5) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244705) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_9) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_9) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1244705) _let_9)) _let_7))))))) (let ((_let_16 (ho_4247 k_4246 _let_1))) (= (ho_4767 (ho_4766 k_4957 BOUND_VARIABLE_1244704) BOUND_VARIABLE_1244705) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_2)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_2))))))))))))))))))))))))) (let ((_let_2639 (forall ((BOUND_VARIABLE_1244643 tptp.complex) (BOUND_VARIABLE_1244644 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 (ho_4703 (ho_4705 k_4710 (ho_4701 k_4700 _let_1)) BOUND_VARIABLE_1244643)) BOUND_VARIABLE_1244644))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4258 (ho_4257 _let_4 k_4248) _let_3))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_7 (ho_4258 (ho_4265 (ho_4264 _let_6 k_4259) _let_3) _let_5))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_9 (ho_4257 _let_4 k_4274))) (let ((_let_10 (ho_4264 _let_6 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244644 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_5) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244644) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244644) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_7)))) _let_7)))) (let ((_let_12 (ho_4247 k_4246 _let_1))) (= (ho_4767 (ho_4766 k_4958 BOUND_VARIABLE_1244643) BOUND_VARIABLE_1244644) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_2)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_2))))))))))))))))))))) (let ((_let_2640 (forall ((BOUND_VARIABLE_1244581 tptp.real) (BOUND_VARIABLE_1244582 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (ho_4351 (ho_4508 k_4959 BOUND_VARIABLE_1244581) BOUND_VARIABLE_1244582) (and (= BOUND_VARIABLE_1244581 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4371 BOUND_VARIABLE_1244582))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4372 BOUND_VARIABLE_1244582))))) (= BOUND_VARIABLE_1244582 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1244582) _let_6)) (not (= BOUND_VARIABLE_1244582 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1244582)) (not (= BOUND_VARIABLE_1244582 _let_5))))))))))))) (let ((_let_2641 (forall ((BOUND_VARIABLE_1244512 tptp.real) (BOUND_VARIABLE_1244513 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4375))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (and (= BOUND_VARIABLE_1244512 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4373 BOUND_VARIABLE_1244513))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4374 BOUND_VARIABLE_1244513))))) (= BOUND_VARIABLE_1244513 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1244513) _let_6)) (not (= BOUND_VARIABLE_1244513 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1244513)) (not (= BOUND_VARIABLE_1244513 _let_5))) (ho_4351 (ho_4508 k_4960 BOUND_VARIABLE_1244512) BOUND_VARIABLE_1244513))))))))))) (let ((_let_2642 (forall ((BOUND_VARIABLE_1244461 tptp.real) (BOUND_VARIABLE_1244462 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4961 BOUND_VARIABLE_1244461) BOUND_VARIABLE_1244462) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244462) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244462) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244461) BOUND_VARIABLE_1244462))))))))))))))))) (let ((_let_2643 (forall ((BOUND_VARIABLE_1244415 tptp.real) (BOUND_VARIABLE_1244416 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4962 BOUND_VARIABLE_1244415) BOUND_VARIABLE_1244416) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244416 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244416) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1244416) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244415) BOUND_VARIABLE_1244416))))))))))))) (let ((_let_2644 (forall ((BOUND_VARIABLE_1244364 tptp.real) (BOUND_VARIABLE_1244365 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4963 BOUND_VARIABLE_1244364) BOUND_VARIABLE_1244365) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244365 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244365) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244365) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244364) BOUND_VARIABLE_1244365))))))))))))))))) (let ((_let_2645 (forall ((BOUND_VARIABLE_1244318 tptp.real) (BOUND_VARIABLE_1244319 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4964 BOUND_VARIABLE_1244318) BOUND_VARIABLE_1244319) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244319 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244319) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1244319) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244318) BOUND_VARIABLE_1244319))))))))))))) (let ((_let_2646 (forall ((BOUND_VARIABLE_1244267 tptp.real) (BOUND_VARIABLE_1244268 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4965 BOUND_VARIABLE_1244267) BOUND_VARIABLE_1244268) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244268 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244268) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244268) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244267) BOUND_VARIABLE_1244268))))))))))))))))) (let ((_let_2647 (forall ((BOUND_VARIABLE_1244221 tptp.real) (BOUND_VARIABLE_1244222 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4966 BOUND_VARIABLE_1244221) BOUND_VARIABLE_1244222) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244222 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244222) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1244222) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244221) BOUND_VARIABLE_1244222))))))))))))) (let ((_let_2648 (forall ((BOUND_VARIABLE_1244170 tptp.real) (BOUND_VARIABLE_1244171 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4967 BOUND_VARIABLE_1244170) BOUND_VARIABLE_1244171) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244171 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244171) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244171) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244170) BOUND_VARIABLE_1244171))))))))))))))))) (let ((_let_2649 (forall ((BOUND_VARIABLE_1244124 tptp.real) (BOUND_VARIABLE_1244125 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4968 BOUND_VARIABLE_1244124) BOUND_VARIABLE_1244125) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244125 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244125) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1244125) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244124) BOUND_VARIABLE_1244125))))))))))))) (let ((_let_2650 (forall ((BOUND_VARIABLE_1244073 tptp.real) (BOUND_VARIABLE_1244074 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4969 BOUND_VARIABLE_1244073) BOUND_VARIABLE_1244074) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244074 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1244074) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1244074) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244073) BOUND_VARIABLE_1244074))))))))))))))))) (let ((_let_2651 (forall ((BOUND_VARIABLE_1244027 tptp.real) (BOUND_VARIABLE_1244028 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4970 BOUND_VARIABLE_1244027) BOUND_VARIABLE_1244028) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1244028 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1244028) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1244028) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1244027) BOUND_VARIABLE_1244028))))))))))))) (let ((_let_2652 (forall ((BOUND_VARIABLE_1243976 tptp.real) (BOUND_VARIABLE_1243977 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4971 BOUND_VARIABLE_1243976) BOUND_VARIABLE_1243977) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1243977 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1243977) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1243977) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1243976) BOUND_VARIABLE_1243977))))))))))))))))) (let ((_let_2653 (forall ((BOUND_VARIABLE_1243930 tptp.real) (BOUND_VARIABLE_1243931 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4972 BOUND_VARIABLE_1243930) BOUND_VARIABLE_1243931) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1243931 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1243931) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1243931) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1243930) BOUND_VARIABLE_1243931))))))))))))) (let ((_let_2654 (forall ((BOUND_VARIABLE_1243879 tptp.real) (BOUND_VARIABLE_1243880 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4973 BOUND_VARIABLE_1243879) BOUND_VARIABLE_1243880) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 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((_let_2655 (forall ((BOUND_VARIABLE_1243833 tptp.real) (BOUND_VARIABLE_1243834 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4974 BOUND_VARIABLE_1243833) BOUND_VARIABLE_1243834) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1243834 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1243834) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1243834) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1243833) BOUND_VARIABLE_1243834))))))))))))) (let ((_let_2656 (forall ((BOUND_VARIABLE_1243782 tptp.real) (BOUND_VARIABLE_1243783 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4975 BOUND_VARIABLE_1243782) BOUND_VARIABLE_1243783) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1243783 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1243783) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1243783) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1243782) BOUND_VARIABLE_1243783))))))))))))))))) (let ((_let_2657 (forall ((BOUND_VARIABLE_1243736 tptp.real) (BOUND_VARIABLE_1243737 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_4976 BOUND_VARIABLE_1243736) BOUND_VARIABLE_1243737) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1243737 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1243737) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1243737) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1243736) BOUND_VARIABLE_1243737))))))))))))) (let ((_let_2658 (forall ((BOUND_VARIABLE_1243692 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243692 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243692 _let_3))) (= (ho_4351 k_4977 BOUND_VARIABLE_1243692) (and (or (and (= BOUND_VARIABLE_1243692 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243692) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243692)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4376 BOUND_VARIABLE_1243692)))))))))))))) (let ((_let_2659 (forall ((BOUND_VARIABLE_1243648 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243648 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243648 _let_3))) (= (ho_4351 k_4978 BOUND_VARIABLE_1243648) (and (or (and (= BOUND_VARIABLE_1243648 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243648) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243648)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4377 BOUND_VARIABLE_1243648)))))))))))))) (let ((_let_2660 (forall ((BOUND_VARIABLE_1243604 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243604 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243604 _let_3))) (= (ho_4351 k_4979 BOUND_VARIABLE_1243604) (and (or (and (= BOUND_VARIABLE_1243604 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243604) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243604)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4378 BOUND_VARIABLE_1243604)))))))))))))) (let ((_let_2661 (forall ((BOUND_VARIABLE_1243560 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243560 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243560 _let_3))) (= (ho_4351 k_4980 BOUND_VARIABLE_1243560) (and (or (and (= BOUND_VARIABLE_1243560 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243560) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243560)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4379 BOUND_VARIABLE_1243560)))))))))))))) (let ((_let_2662 (forall ((BOUND_VARIABLE_1243553 tptp.int) (BOUND_VARIABLE_1243554 tptp.nat)) (= (ho_4316 (ho_4315 k_4981 BOUND_VARIABLE_1243553) BOUND_VARIABLE_1243554) (ho_4318 k_4317 BOUND_VARIABLE_1243553))))) (let ((_let_2663 (forall ((BOUND_VARIABLE_1243546 tptp.int) (BOUND_VARIABLE_1243547 tptp.nat)) (= (ho_4316 (ho_4315 k_4982 BOUND_VARIABLE_1243546) BOUND_VARIABLE_1243547) (ho_4318 k_4317 BOUND_VARIABLE_1243546))))) (let ((_let_2664 (forall ((BOUND_VARIABLE_1243502 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243502 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243502 _let_3))) (= (ho_4351 k_4983 BOUND_VARIABLE_1243502) (and (or (and (= BOUND_VARIABLE_1243502 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243502) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243502)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4380 BOUND_VARIABLE_1243502)))))))))))))) (let ((_let_2665 (forall ((BOUND_VARIABLE_1243458 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243458 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243458 _let_3))) (= (ho_4351 k_4984 BOUND_VARIABLE_1243458) (and (or (and (= BOUND_VARIABLE_1243458 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243458) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243458)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4381 BOUND_VARIABLE_1243458)))))))))))))) (let ((_let_2666 (forall ((BOUND_VARIABLE_1243414 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243414 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243414 _let_3))) (= (ho_4351 k_4985 BOUND_VARIABLE_1243414) (and (or (and (= BOUND_VARIABLE_1243414 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243414) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243414)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4382 BOUND_VARIABLE_1243414)))))))))))))) (let ((_let_2667 (forall ((BOUND_VARIABLE_1243370 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243370 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243370 _let_3))) (= (ho_4351 k_4986 BOUND_VARIABLE_1243370) (and (or (and (= BOUND_VARIABLE_1243370 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243370) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243370)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4383 BOUND_VARIABLE_1243370)))))))))))))) (let ((_let_2668 (forall ((BOUND_VARIABLE_1243326 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243326 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243326 _let_3))) (= (ho_4351 k_4987 BOUND_VARIABLE_1243326) (and (or (and (= BOUND_VARIABLE_1243326 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243326) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243326)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4384 BOUND_VARIABLE_1243326)))))))))))))) (let ((_let_2669 (forall ((BOUND_VARIABLE_1243282 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243282 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243282 _let_3))) (= (ho_4351 k_4988 BOUND_VARIABLE_1243282) (and (or (and (= BOUND_VARIABLE_1243282 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243282) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243282)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4385 BOUND_VARIABLE_1243282)))))))))))))) (let ((_let_2670 (forall ((BOUND_VARIABLE_1243238 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243238 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243238 _let_3))) (= (ho_4351 k_4989 BOUND_VARIABLE_1243238) (and (or (and (= BOUND_VARIABLE_1243238 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243238) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243238)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4386 BOUND_VARIABLE_1243238)))))))))))))) (let ((_let_2671 (forall ((BOUND_VARIABLE_1243194 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243194 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243194 _let_3))) (= (ho_4351 k_4990 BOUND_VARIABLE_1243194) (and (or (and (= BOUND_VARIABLE_1243194 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243194) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243194)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4387 BOUND_VARIABLE_1243194)))))))))))))) (let ((_let_2672 (forall ((BOUND_VARIABLE_1243150 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243150 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243150 _let_3))) (= (ho_4351 k_4991 BOUND_VARIABLE_1243150) (and (or (and (= BOUND_VARIABLE_1243150 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243150) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243150)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4388 BOUND_VARIABLE_1243150)))))))))))))) (let ((_let_2673 (forall ((BOUND_VARIABLE_1243106 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243106 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243106 _let_3))) (= (ho_4351 k_4992 BOUND_VARIABLE_1243106) (and (or (and (= BOUND_VARIABLE_1243106 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243106) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243106)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4389 BOUND_VARIABLE_1243106)))))))))))))) (let ((_let_2674 (forall ((BOUND_VARIABLE_1243062 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243062 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243062 _let_3))) (= (ho_4351 k_4993 BOUND_VARIABLE_1243062) (and (or (and (= BOUND_VARIABLE_1243062 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243062) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243062)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4390 BOUND_VARIABLE_1243062)))))))))))))) (let ((_let_2675 (forall ((BOUND_VARIABLE_1243018 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1243018 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1243018 _let_3))) (= (ho_4351 k_4994 BOUND_VARIABLE_1243018) (and (or (and (= BOUND_VARIABLE_1243018 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1243018) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1243018)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4391 BOUND_VARIABLE_1243018)))))))))))))) (let ((_let_2676 (forall ((BOUND_VARIABLE_1243010 tptp.int) (BOUND_VARIABLE_1243011 tptp.nat)) (= (ho_4316 (ho_4315 k_4995 BOUND_VARIABLE_1243010) BOUND_VARIABLE_1243011) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1243010)))))) (let ((_let_2677 (forall ((BOUND_VARIABLE_1242966 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242966 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242966 _let_3))) (= (ho_4351 k_4996 BOUND_VARIABLE_1242966) (and (or (and (= BOUND_VARIABLE_1242966 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242966) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242966)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4392 BOUND_VARIABLE_1242966)))))))))))))) (let ((_let_2678 (forall ((BOUND_VARIABLE_1242959 tptp.int) (BOUND_VARIABLE_1242960 tptp.nat)) (= (ho_4316 (ho_4315 k_4997 BOUND_VARIABLE_1242959) BOUND_VARIABLE_1242960) (ho_4318 k_4317 BOUND_VARIABLE_1242959))))) (let ((_let_2679 (forall ((BOUND_VARIABLE_1242915 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242915 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242915 _let_3))) (= (ho_4351 k_4998 BOUND_VARIABLE_1242915) (and (or (and (= BOUND_VARIABLE_1242915 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242915) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242915)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4393 BOUND_VARIABLE_1242915)))))))))))))) (let ((_let_2680 (forall ((BOUND_VARIABLE_1242871 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242871 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242871 _let_3))) (= (ho_4351 k_4999 BOUND_VARIABLE_1242871) (and (or (and (= BOUND_VARIABLE_1242871 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242871) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242871)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4394 BOUND_VARIABLE_1242871)))))))))))))) (let ((_let_2681 (forall ((BOUND_VARIABLE_1242864 tptp.int) (BOUND_VARIABLE_1242865 tptp.nat)) (= (ho_4316 (ho_4315 k_5000 BOUND_VARIABLE_1242864) BOUND_VARIABLE_1242865) (ho_4318 k_4317 BOUND_VARIABLE_1242864))))) (let ((_let_2682 (forall ((BOUND_VARIABLE_1242857 tptp.int) (BOUND_VARIABLE_1242858 tptp.nat)) (= (ho_4316 (ho_4315 k_5001 BOUND_VARIABLE_1242857) BOUND_VARIABLE_1242858) (ho_4318 k_4317 BOUND_VARIABLE_1242857))))) (let ((_let_2683 (forall ((BOUND_VARIABLE_1242813 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242813 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242813 _let_3))) (= (ho_4351 k_5002 BOUND_VARIABLE_1242813) (and (or (and (= BOUND_VARIABLE_1242813 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242813) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242813)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4395 BOUND_VARIABLE_1242813)))))))))))))) (let ((_let_2684 (forall ((BOUND_VARIABLE_1242769 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242769 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242769 _let_3))) (= (ho_4351 k_5003 BOUND_VARIABLE_1242769) (and (or (and (= BOUND_VARIABLE_1242769 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242769) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242769)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4396 BOUND_VARIABLE_1242769)))))))))))))) (let ((_let_2685 (forall ((BOUND_VARIABLE_1242725 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242725 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242725 _let_3))) (= (ho_4351 k_5004 BOUND_VARIABLE_1242725) (and (or (and (= BOUND_VARIABLE_1242725 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242725) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242725)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4397 BOUND_VARIABLE_1242725)))))))))))))) (let ((_let_2686 (forall ((BOUND_VARIABLE_1242681 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242681 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242681 _let_3))) (= (ho_4351 k_5005 BOUND_VARIABLE_1242681) (and (or (and (= BOUND_VARIABLE_1242681 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242681) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242681)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4398 BOUND_VARIABLE_1242681)))))))))))))) (let ((_let_2687 (forall ((BOUND_VARIABLE_1242637 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242637 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242637 _let_3))) (= (ho_4351 k_5006 BOUND_VARIABLE_1242637) (and (or (and (= BOUND_VARIABLE_1242637 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242637) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242637)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4399 BOUND_VARIABLE_1242637)))))))))))))) (let ((_let_2688 (forall ((BOUND_VARIABLE_1242593 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242593 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242593 _let_3))) (= (ho_4351 k_5007 BOUND_VARIABLE_1242593) (and (or (and (= BOUND_VARIABLE_1242593 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242593) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242593)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4400 BOUND_VARIABLE_1242593)))))))))))))) (let ((_let_2689 (forall ((BOUND_VARIABLE_1242549 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242549 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242549 _let_3))) (= (ho_4351 k_5008 BOUND_VARIABLE_1242549) (and (or (and (= BOUND_VARIABLE_1242549 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242549) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242549)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4401 BOUND_VARIABLE_1242549)))))))))))))) (let ((_let_2690 (forall ((BOUND_VARIABLE_1242542 tptp.int) (BOUND_VARIABLE_1242543 tptp.nat)) (= (ho_4316 (ho_4315 k_5009 BOUND_VARIABLE_1242542) BOUND_VARIABLE_1242543) (ho_4318 k_4317 BOUND_VARIABLE_1242542))))) (let ((_let_2691 (forall ((BOUND_VARIABLE_1242498 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242498 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242498 _let_3))) (= (ho_4351 k_5010 BOUND_VARIABLE_1242498) (and (or (and (= BOUND_VARIABLE_1242498 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242498) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242498)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4402 BOUND_VARIABLE_1242498)))))))))))))) (let ((_let_2692 (forall ((BOUND_VARIABLE_1242454 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242454 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242454 _let_3))) (= (ho_4351 k_5011 BOUND_VARIABLE_1242454) (and (or (and (= BOUND_VARIABLE_1242454 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242454) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242454)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4403 BOUND_VARIABLE_1242454)))))))))))))) (let ((_let_2693 (forall ((BOUND_VARIABLE_1242410 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1242410 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1242410 _let_3))) (= (ho_4351 k_5012 BOUND_VARIABLE_1242410) (and (or (and (= BOUND_VARIABLE_1242410 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1242410) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1242410)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4404 BOUND_VARIABLE_1242410)))))))))))))) (let ((_let_2694 (forall ((BOUND_VARIABLE_1242359 tptp.real) (BOUND_VARIABLE_1242360 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5013 BOUND_VARIABLE_1242359) BOUND_VARIABLE_1242360) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242360 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1242360) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1242360) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242359) BOUND_VARIABLE_1242360))))))))))))))))) (let ((_let_2695 (forall ((BOUND_VARIABLE_1242313 tptp.real) (BOUND_VARIABLE_1242314 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5014 BOUND_VARIABLE_1242313) BOUND_VARIABLE_1242314) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242314 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1242314) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1242314) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242313) BOUND_VARIABLE_1242314))))))))))))) (let ((_let_2696 (forall ((BOUND_VARIABLE_1242262 tptp.real) (BOUND_VARIABLE_1242263 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5015 BOUND_VARIABLE_1242262) BOUND_VARIABLE_1242263) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242263 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1242263) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1242263) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242262) BOUND_VARIABLE_1242263))))))))))))))))) (let ((_let_2697 (forall ((BOUND_VARIABLE_1242216 tptp.real) (BOUND_VARIABLE_1242217 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5016 BOUND_VARIABLE_1242216) BOUND_VARIABLE_1242217) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242217 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1242217) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1242217) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242216) BOUND_VARIABLE_1242217))))))))))))) (let ((_let_2698 (forall ((BOUND_VARIABLE_1242165 tptp.real) (BOUND_VARIABLE_1242166 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5017 BOUND_VARIABLE_1242165) BOUND_VARIABLE_1242166) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242166 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1242166) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1242166) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242165) BOUND_VARIABLE_1242166))))))))))))))))) (let ((_let_2699 (forall ((BOUND_VARIABLE_1242119 tptp.real) (BOUND_VARIABLE_1242120 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5018 BOUND_VARIABLE_1242119) BOUND_VARIABLE_1242120) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242120 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1242120) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1242120) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242119) BOUND_VARIABLE_1242120))))))))))))) (let ((_let_2700 (forall ((BOUND_VARIABLE_1242068 tptp.real) (BOUND_VARIABLE_1242069 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5019 BOUND_VARIABLE_1242068) BOUND_VARIABLE_1242069) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242069 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1242069) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1242069) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242068) BOUND_VARIABLE_1242069))))))))))))))))) (let ((_let_2701 (forall ((BOUND_VARIABLE_1242022 tptp.real) (BOUND_VARIABLE_1242023 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5020 BOUND_VARIABLE_1242022) BOUND_VARIABLE_1242023) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1242023 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1242023) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1242023) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1242022) BOUND_VARIABLE_1242023))))))))))))) (let ((_let_2702 (forall ((BOUND_VARIABLE_1241971 tptp.real) (BOUND_VARIABLE_1241972 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5021 BOUND_VARIABLE_1241971) BOUND_VARIABLE_1241972) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241972 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241972) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241972) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241971) BOUND_VARIABLE_1241972))))))))))))))))) (let ((_let_2703 (forall ((BOUND_VARIABLE_1241925 tptp.real) (BOUND_VARIABLE_1241926 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5022 BOUND_VARIABLE_1241925) BOUND_VARIABLE_1241926) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241926 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241926) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241926) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241925) BOUND_VARIABLE_1241926))))))))))))) (let ((_let_2704 (forall ((BOUND_VARIABLE_1241874 tptp.real) (BOUND_VARIABLE_1241875 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5023 BOUND_VARIABLE_1241874) BOUND_VARIABLE_1241875) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241875 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241875) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241875) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241874) BOUND_VARIABLE_1241875))))))))))))))))) (let ((_let_2705 (forall ((BOUND_VARIABLE_1241828 tptp.real) (BOUND_VARIABLE_1241829 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5024 BOUND_VARIABLE_1241828) BOUND_VARIABLE_1241829) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241829 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241829) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241829) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241828) BOUND_VARIABLE_1241829))))))))))))) (let ((_let_2706 (forall ((BOUND_VARIABLE_1241777 tptp.real) (BOUND_VARIABLE_1241778 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5025 BOUND_VARIABLE_1241777) BOUND_VARIABLE_1241778) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241778 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241778) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241778) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241777) BOUND_VARIABLE_1241778))))))))))))))))) (let ((_let_2707 (forall ((BOUND_VARIABLE_1241731 tptp.real) (BOUND_VARIABLE_1241732 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5026 BOUND_VARIABLE_1241731) BOUND_VARIABLE_1241732) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241732 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241732) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241732) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241731) BOUND_VARIABLE_1241732))))))))))))) (let ((_let_2708 (forall ((BOUND_VARIABLE_1241680 tptp.real) (BOUND_VARIABLE_1241681 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5027 BOUND_VARIABLE_1241680) BOUND_VARIABLE_1241681) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241681 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241681) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241681) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241680) BOUND_VARIABLE_1241681))))))))))))))))) (let ((_let_2709 (forall ((BOUND_VARIABLE_1241634 tptp.real) (BOUND_VARIABLE_1241635 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5028 BOUND_VARIABLE_1241634) BOUND_VARIABLE_1241635) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241635 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241635) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241635) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241634) BOUND_VARIABLE_1241635))))))))))))) (let ((_let_2710 (forall ((BOUND_VARIABLE_1241583 tptp.real) (BOUND_VARIABLE_1241584 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5029 BOUND_VARIABLE_1241583) BOUND_VARIABLE_1241584) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241584 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241584) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241584) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241583) BOUND_VARIABLE_1241584))))))))))))))))) (let ((_let_2711 (forall ((BOUND_VARIABLE_1241537 tptp.real) (BOUND_VARIABLE_1241538 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5030 BOUND_VARIABLE_1241537) BOUND_VARIABLE_1241538) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241538 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241538) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241538) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241537) BOUND_VARIABLE_1241538))))))))))))) (let ((_let_2712 (forall ((BOUND_VARIABLE_1241486 tptp.real) (BOUND_VARIABLE_1241487 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5031 BOUND_VARIABLE_1241486) BOUND_VARIABLE_1241487) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241487 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241487) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241487) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241486) BOUND_VARIABLE_1241487))))))))))))))))) (let ((_let_2713 (forall ((BOUND_VARIABLE_1241440 tptp.real) (BOUND_VARIABLE_1241441 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5032 BOUND_VARIABLE_1241440) BOUND_VARIABLE_1241441) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241441 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241441) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241441) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241440) BOUND_VARIABLE_1241441))))))))))))) (let ((_let_2714 (forall ((BOUND_VARIABLE_1241389 tptp.real) (BOUND_VARIABLE_1241390 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5033 BOUND_VARIABLE_1241389) BOUND_VARIABLE_1241390) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241390 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241390) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241390) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241389) BOUND_VARIABLE_1241390))))))))))))))))) (let ((_let_2715 (forall ((BOUND_VARIABLE_1241343 tptp.real) (BOUND_VARIABLE_1241344 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5034 BOUND_VARIABLE_1241343) BOUND_VARIABLE_1241344) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241344 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241344) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241344) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241343) BOUND_VARIABLE_1241344))))))))))))) (let ((_let_2716 (forall ((BOUND_VARIABLE_1241292 tptp.real) (BOUND_VARIABLE_1241293 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5035 BOUND_VARIABLE_1241292) BOUND_VARIABLE_1241293) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241293 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241293) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241293) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241292) BOUND_VARIABLE_1241293))))))))))))))))) (let ((_let_2717 (forall ((BOUND_VARIABLE_1241246 tptp.real) (BOUND_VARIABLE_1241247 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5036 BOUND_VARIABLE_1241246) BOUND_VARIABLE_1241247) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241247 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241247) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241247) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241246) BOUND_VARIABLE_1241247))))))))))))) (let ((_let_2718 (forall ((BOUND_VARIABLE_1241195 tptp.real) (BOUND_VARIABLE_1241196 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5037 BOUND_VARIABLE_1241195) BOUND_VARIABLE_1241196) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241196 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241196) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1241196) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241195) BOUND_VARIABLE_1241196))))))))))))))))) (let ((_let_2719 (forall ((BOUND_VARIABLE_1241149 tptp.real) (BOUND_VARIABLE_1241150 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5038 BOUND_VARIABLE_1241149) BOUND_VARIABLE_1241150) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1241150 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1241150) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1241150) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241149) BOUND_VARIABLE_1241150))))))))))))) (let ((_let_2720 (forall ((BOUND_VARIABLE_1241139 tptp.nat) (BOUND_VARIABLE_1241140 tptp.nat)) (= (ho_4288 (ho_4287 k_5039 BOUND_VARIABLE_1241139) BOUND_VARIABLE_1241140) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1241140)) (ho_4290 k_4289 BOUND_VARIABLE_1241139)))))) (let ((_let_2721 (forall ((BOUND_VARIABLE_1241111 tptp.real) (BOUND_VARIABLE_1241112 tptp.real) (BOUND_VARIABLE_1241113 tptp.nat) (BOUND_VARIABLE_1241114 tptp.nat)) (let ((_let_1 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)))) (= (ho_4258 (ho_4265 (ho_4264 _let_1 k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4264 _let_1 k_4259) BOUND_VARIABLE_1241112) BOUND_VARIABLE_1241111)) BOUND_VARIABLE_1241114)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1241112) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241113) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1241114))) (ho_4245 (ho_4487 (ho_4740 (ho_4782 k_5040 BOUND_VARIABLE_1241111) BOUND_VARIABLE_1241112) BOUND_VARIABLE_1241113) BOUND_VARIABLE_1241114)))))) (let ((_let_2722 (forall ((BOUND_VARIABLE_1241089 tptp.nat) (BOUND_VARIABLE_1241090 tptp.nat) (BOUND_VARIABLE_1241091 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1241091)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241089) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))) BOUND_VARIABLE_1241090))) (ho_4288 (ho_4287 (ho_4303 k_5041 BOUND_VARIABLE_1241089) BOUND_VARIABLE_1241090) BOUND_VARIABLE_1241091))))))))) (let ((_let_2723 (forall ((BOUND_VARIABLE_1241061 tptp.rat) (BOUND_VARIABLE_1241062 tptp.rat) (BOUND_VARIABLE_1241063 tptp.nat) (BOUND_VARIABLE_1241064 tptp.nat)) (let ((_let_1 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)))) (= (ho_4442 (ho_4448 (ho_4447 _let_1 k_4697) (ho_4316 (ho_4799 k_4798 (ho_4442 (ho_4448 (ho_4447 _let_1 k_4443) BOUND_VARIABLE_1241062) BOUND_VARIABLE_1241061)) BOUND_VARIABLE_1241064)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1241062) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241063) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1241064))) (ho_4316 (ho_4338 (ho_4736 (ho_4815 k_5042 BOUND_VARIABLE_1241061) BOUND_VARIABLE_1241062) BOUND_VARIABLE_1241063) BOUND_VARIABLE_1241064)))))) (let ((_let_2724 (forall ((BOUND_VARIABLE_1241039 tptp.nat) (BOUND_VARIABLE_1241040 tptp.nat) (BOUND_VARIABLE_1241041 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1241041)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241039) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))) BOUND_VARIABLE_1241040))) (ho_4288 (ho_4287 (ho_4303 k_5043 BOUND_VARIABLE_1241039) BOUND_VARIABLE_1241040) BOUND_VARIABLE_1241041))))))))) (let ((_let_2725 (forall ((BOUND_VARIABLE_1241019 tptp.complex) (BOUND_VARIABLE_1241020 tptp.complex) (BOUND_VARIABLE_1241021 tptp.nat) (BOUND_VARIABLE_1241022 tptp.nat)) (= (ho_4767 (ho_4779 (ho_4778 (ho_4777 k_5044 BOUND_VARIABLE_1241019) BOUND_VARIABLE_1241020) BOUND_VARIABLE_1241021) BOUND_VARIABLE_1241022) (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1241020) BOUND_VARIABLE_1241019)) BOUND_VARIABLE_1241022)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1241020) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1241021) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1241022))))))) (let ((_let_2726 (forall ((BOUND_VARIABLE_1240997 tptp.nat) (BOUND_VARIABLE_1240998 tptp.nat) (BOUND_VARIABLE_1240999 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1240999)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240997) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))) BOUND_VARIABLE_1240998))) (ho_4288 (ho_4287 (ho_4303 k_5045 BOUND_VARIABLE_1240997) BOUND_VARIABLE_1240998) BOUND_VARIABLE_1240999))))))))) (let ((_let_2727 (forall ((BOUND_VARIABLE_1240946 tptp.real) (BOUND_VARIABLE_1240947 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5046 BOUND_VARIABLE_1240946) BOUND_VARIABLE_1240947) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240947 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240947) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1240947) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240946) BOUND_VARIABLE_1240947))))))))))))))))) (let ((_let_2728 (forall ((BOUND_VARIABLE_1240900 tptp.real) (BOUND_VARIABLE_1240901 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5047 BOUND_VARIABLE_1240900) BOUND_VARIABLE_1240901) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240901 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1240901) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1240901) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240900) BOUND_VARIABLE_1240901))))))))))))) (let ((_let_2729 (forall ((BOUND_VARIABLE_1240878 tptp.nat) (BOUND_VARIABLE_1240879 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1240878) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1240879) (ho_4406 (ho_4198 k_5048 BOUND_VARIABLE_1240878) BOUND_VARIABLE_1240879)))))))) (let ((_let_2730 (forall ((BOUND_VARIABLE_1240854 tptp.nat) (BOUND_VARIABLE_1240855 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)))) (let ((_let_4 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_5 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_5))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_8) _let_1)))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1240854) (ho_4442 (ho_4448 _let_7 _let_4) (ho_4442 (ho_4441 _let_5 k_4435) _let_4)))))) (= (ho_4316 (ho_4338 k_5051 BOUND_VARIABLE_1240854) BOUND_VARIABLE_1240855) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1240855 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 _let_8)))) _let_9) (ho_4442 (ho_4448 _let_7 _let_9) _let_4))))))))))))))) (let ((_let_2731 (forall ((BOUND_VARIABLE_1240818 tptp.nat) (BOUND_VARIABLE_1240819 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4216 (ho_4215 k_4221 _let_3) _let_5))) (let ((_let_7 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_5) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1240818) _let_6)) _let_2))))) (= (ho_4216 (ho_4215 k_5052 BOUND_VARIABLE_1240818) BOUND_VARIABLE_1240819) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1240819 _let_6)) _let_7) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 _let_7) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))))))))))) (let ((_let_2732 (forall ((BOUND_VARIABLE_1240794 tptp.nat) (BOUND_VARIABLE_1240795 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4193 k_4192 tptp.one))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4247 k_4246 _let_5)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1240794) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))))) (= (ho_4245 (ho_4487 k_5053 BOUND_VARIABLE_1240794) BOUND_VARIABLE_1240795) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1240795 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 _let_5))))) _let_6) (ho_4258 (ho_4265 _let_4 _let_6) _let_1)))))))))))) (let ((_let_2733 (forall ((BOUND_VARIABLE_1240770 tptp.nat) (BOUND_VARIABLE_1240771 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_3 (ho_4209 (ho_4211 k_4222 _let_2) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1240770) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))))) (= (ho_4335 (ho_4726 k_5054 BOUND_VARIABLE_1240770) BOUND_VARIABLE_1240771) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1240771 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 _let_2)))) _let_3) (ho_4209 (ho_4211 k_4210 _let_3) _let_1))))))))) (let ((_let_2734 (forall ((BOUND_VARIABLE_1240746 tptp.nat) (BOUND_VARIABLE_1240747 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4193 k_4192 tptp.one))) (let ((_let_3 (ho_4703 (ho_4705 k_4710 (ho_4701 k_4700 _let_2)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1240746) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))))) (= (ho_4767 (ho_4779 k_5055 BOUND_VARIABLE_1240746) BOUND_VARIABLE_1240747) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1240747 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 _let_2))))) _let_3) (ho_4703 (ho_4705 k_4704 _let_3) _let_1))))))))) (let ((_let_2735 (forall ((BOUND_VARIABLE_1240715 tptp.num) (BOUND_VARIABLE_1240716 tptp.int) (BOUND_VARIABLE_1240717 tptp.int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1240716))) (let ((_let_2 (ho_4196 k_4195 BOUND_VARIABLE_1240715))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1240717 (ho_4209 (ho_4211 k_4311 _let_2) BOUND_VARIABLE_1240717))) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4196 k_4195 tptp.one))) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1240717) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (ho_4428 (ho_4427 k_4426 _let_1) BOUND_VARIABLE_1240717)) (ho_4428 (ho_4427 (ho_5057 k_5056 BOUND_VARIABLE_1240715) BOUND_VARIABLE_1240716) BOUND_VARIABLE_1240717))))))) (let ((_let_2736 (forall ((BOUND_VARIABLE_1240684 tptp.num) (BOUND_VARIABLE_1240685 tptp.int) (BOUND_VARIABLE_1240686 tptp.int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1240685))) (let ((_let_2 (ho_4196 k_4195 BOUND_VARIABLE_1240684))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1240686 (ho_4209 (ho_4211 k_4311 _let_2) BOUND_VARIABLE_1240686))) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4196 k_4195 tptp.one))) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1240686) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (ho_4428 (ho_4427 k_4426 _let_1) BOUND_VARIABLE_1240686)) (ho_4428 (ho_4427 (ho_5057 k_5058 BOUND_VARIABLE_1240684) BOUND_VARIABLE_1240685) BOUND_VARIABLE_1240686))))))) (let ((_let_2737 (forall ((BOUND_VARIABLE_1240636 tptp.num) (BOUND_VARIABLE_1240637 tptp.nat) (BOUND_VARIABLE_1240638 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1240637) _let_2))))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1240636)))) (= (ho_5062 (ho_5061 (ho_5060 k_5059 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 _let_5)) (ho_4290 k_4289 BOUND_VARIABLE_1240638))) (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240638) _let_5))) (ho_4406 (ho_4198 k_4405 _let_4) BOUND_VARIABLE_1240638)) (ho_4406 (ho_4198 (ho_5064 k_5063 BOUND_VARIABLE_1240636) BOUND_VARIABLE_1240637) BOUND_VARIABLE_1240638)))))))))) (let ((_let_2738 (forall ((BOUND_VARIABLE_1240588 tptp.num) (BOUND_VARIABLE_1240589 tptp.nat) (BOUND_VARIABLE_1240590 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1240589) _let_2))))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1240588)))) (= (ho_5062 (ho_5061 (ho_5060 k_5059 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 _let_5)) (ho_4290 k_4289 BOUND_VARIABLE_1240590))) (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240590) _let_5))) (ho_4406 (ho_4198 k_4405 _let_4) BOUND_VARIABLE_1240590)) (ho_4406 (ho_4198 (ho_5064 k_5065 BOUND_VARIABLE_1240588) BOUND_VARIABLE_1240589) BOUND_VARIABLE_1240590)))))))))) (let ((_let_2739 (forall ((BOUND_VARIABLE_1240581 tptp.int) (BOUND_VARIABLE_1240582 tptp.nat)) (= (ho_4316 (ho_4315 k_5066 BOUND_VARIABLE_1240581) BOUND_VARIABLE_1240582) (ho_4318 k_4317 BOUND_VARIABLE_1240581))))) (let ((_let_2740 (forall ((BOUND_VARIABLE_1240574 tptp.int) (BOUND_VARIABLE_1240575 tptp.nat)) (= (ho_4316 (ho_4315 k_5067 BOUND_VARIABLE_1240574) BOUND_VARIABLE_1240575) (ho_4318 k_4317 BOUND_VARIABLE_1240574))))) (let ((_let_2741 (forall ((BOUND_VARIABLE_1240567 tptp.int) (BOUND_VARIABLE_1240568 tptp.nat)) (= (ho_4316 (ho_4315 k_5068 BOUND_VARIABLE_1240567) BOUND_VARIABLE_1240568) (ho_4318 k_4317 BOUND_VARIABLE_1240567))))) (let ((_let_2742 (forall ((BOUND_VARIABLE_1240560 tptp.int) (BOUND_VARIABLE_1240561 tptp.nat)) (= (ho_4316 (ho_4315 k_5069 BOUND_VARIABLE_1240560) BOUND_VARIABLE_1240561) (ho_4318 k_4317 BOUND_VARIABLE_1240560))))) (let ((_let_2743 (forall ((BOUND_VARIABLE_1240553 tptp.int) (BOUND_VARIABLE_1240554 tptp.nat)) (= (ho_4316 (ho_4315 k_5070 BOUND_VARIABLE_1240553) BOUND_VARIABLE_1240554) (ho_4318 k_4317 BOUND_VARIABLE_1240553))))) (let ((_let_2744 (forall ((BOUND_VARIABLE_1240541 tptp.int) (BOUND_VARIABLE_1240542 tptp.nat)) (= (ho_4318 k_4317 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) BOUND_VARIABLE_1240541)) (ho_4316 (ho_4315 k_5071 BOUND_VARIABLE_1240541) BOUND_VARIABLE_1240542))))) (let ((_let_2745 (forall ((BOUND_VARIABLE_1240477 tptp.int) (BOUND_VARIABLE_1240478 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1240477) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1240477)) BOUND_VARIABLE_1240477))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_5) _let_1)) _let_3))) (ho_4209 _let_2 _let_5)) _let_5)))) _let_3))) (= (ho_4316 (ho_4315 k_5072 BOUND_VARIABLE_1240477) BOUND_VARIABLE_1240478) (ho_4318 k_4317 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_5)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 BOUND_VARIABLE_1240477) (ho_4209 k_4594 _let_5))) _let_6) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1240477 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) _let_3)))) _let_3))))))))))))))) (let ((_let_2746 (forall ((BOUND_VARIABLE_1240451 tptp.num) (BOUND_VARIABLE_1240452 tptp.code_integer) (BOUND_VARIABLE_1240453 tptp.code_integer)) (let ((_let_1 (ho_4560 (ho_4564 k_4630 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1240452))) (let ((_let_2 (ho_4562 k_4561 BOUND_VARIABLE_1240451))) (let ((_let_3 (ho_4625 k_4624 BOUND_VARIABLE_1240453))) (= (ho_4572 (ho_4571 (ho_4629 k_5073 BOUND_VARIABLE_1240451) BOUND_VARIABLE_1240452) BOUND_VARIABLE_1240453) (ho_4576 (ho_4575 (ho_4574 k_4573 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 _let_2)) _let_3))) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4562 k_4561 tptp.one))) (ho_4560 (ho_4564 k_4563 BOUND_VARIABLE_1240453) (ho_4560 k_4559 _let_2)))) (ho_4572 (ho_4571 k_4570 _let_1) BOUND_VARIABLE_1240453))))))))) (let ((_let_2747 (forall ((BOUND_VARIABLE_1240420 tptp.num) (BOUND_VARIABLE_1240421 tptp.int) (BOUND_VARIABLE_1240422 tptp.int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1240421))) (let ((_let_2 (ho_4196 k_4195 BOUND_VARIABLE_1240420))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1240422 (ho_4209 (ho_4211 k_4311 _let_2) BOUND_VARIABLE_1240422))) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4196 k_4195 tptp.one))) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1240422) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (ho_4428 (ho_4427 k_4426 _let_1) BOUND_VARIABLE_1240422)) (ho_4428 (ho_4427 (ho_5057 k_5074 BOUND_VARIABLE_1240420) BOUND_VARIABLE_1240421) BOUND_VARIABLE_1240422))))))) (let ((_let_2748 (forall ((BOUND_VARIABLE_1240372 tptp.num) (BOUND_VARIABLE_1240373 tptp.nat) (BOUND_VARIABLE_1240374 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1240373) _let_2))))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1240372)))) (= (ho_5062 (ho_5061 (ho_5060 k_5059 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 _let_5)) (ho_4290 k_4289 BOUND_VARIABLE_1240374))) (ho_4406 (ho_4198 k_4405 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240374) _let_5))) (ho_4406 (ho_4198 k_4405 _let_4) BOUND_VARIABLE_1240374)) (ho_4406 (ho_4198 (ho_5064 k_5075 BOUND_VARIABLE_1240372) BOUND_VARIABLE_1240373) BOUND_VARIABLE_1240374)))))))))) (let ((_let_2749 (forall ((BOUND_VARIABLE_1240321 tptp.real) (BOUND_VARIABLE_1240322 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5076 BOUND_VARIABLE_1240321) BOUND_VARIABLE_1240322) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240322 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240322) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1240322) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240321) BOUND_VARIABLE_1240322))))))))))))))))) (let ((_let_2750 (forall ((BOUND_VARIABLE_1240275 tptp.real) (BOUND_VARIABLE_1240276 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5077 BOUND_VARIABLE_1240275) BOUND_VARIABLE_1240276) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240276 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1240276) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1240276) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240275) BOUND_VARIABLE_1240276))))))))))))) (let ((_let_2751 (forall ((BOUND_VARIABLE_1240224 tptp.real) (BOUND_VARIABLE_1240225 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5078 BOUND_VARIABLE_1240224) BOUND_VARIABLE_1240225) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240225 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240225) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1240225) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240224) BOUND_VARIABLE_1240225))))))))))))))))) (let ((_let_2752 (forall ((BOUND_VARIABLE_1240178 tptp.real) (BOUND_VARIABLE_1240179 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5079 BOUND_VARIABLE_1240178) BOUND_VARIABLE_1240179) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240179 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1240179) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1240179) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240178) BOUND_VARIABLE_1240179))))))))))))) (let ((_let_2753 (forall ((BOUND_VARIABLE_1240127 tptp.real) (BOUND_VARIABLE_1240128 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5080 BOUND_VARIABLE_1240127) BOUND_VARIABLE_1240128) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240128 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1240128) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1240128) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240127) BOUND_VARIABLE_1240128))))))))))))))))) (let ((_let_2754 (forall ((BOUND_VARIABLE_1240081 tptp.real) (BOUND_VARIABLE_1240082 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5081 BOUND_VARIABLE_1240081) BOUND_VARIABLE_1240082) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1240082 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1240082) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1240082) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1240081) BOUND_VARIABLE_1240082))))))))))))) (let ((_let_2755 (forall ((BOUND_VARIABLE_1290116 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1240066 tptp.nat) (BOUND_VARIABLE_1290114 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1240068 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1290116 BOUND_VARIABLE_1240066)) (ho_4245 BOUND_VARIABLE_1290114 BOUND_VARIABLE_1240068)) (ho_4245 (ho_4473 (ho_5084 (ho_5083 k_5082 BOUND_VARIABLE_1290116) BOUND_VARIABLE_1240066) BOUND_VARIABLE_1290114) BOUND_VARIABLE_1240068))))) (let ((_let_2756 (forall ((BOUND_VARIABLE_1290144 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1240040 tptp.nat) (BOUND_VARIABLE_1290140 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1240042 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1290144 BOUND_VARIABLE_1240040)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1290140 BOUND_VARIABLE_1240042)) _let_2))) (ho_4216 (ho_5088 (ho_5087 (ho_5086 k_5085 BOUND_VARIABLE_1290144) BOUND_VARIABLE_1240040) BOUND_VARIABLE_1290140) BOUND_VARIABLE_1240042)))))))) (let ((_let_2757 (forall ((BOUND_VARIABLE_1290179 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1240028 tptp.complex) (BOUND_VARIABLE_1290178 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1240030 tptp.complex)) (= (ho_4703 (ho_5092 (ho_5091 (ho_5090 k_5089 BOUND_VARIABLE_1290179) BOUND_VARIABLE_1240028) BOUND_VARIABLE_1290178) BOUND_VARIABLE_1240030) (ho_4703 (ho_4705 k_4710 (ho_4703 BOUND_VARIABLE_1290179 BOUND_VARIABLE_1240028)) (ho_4703 BOUND_VARIABLE_1290178 BOUND_VARIABLE_1240030)))))) (let ((_let_2758 (forall ((BOUND_VARIABLE_1290208 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1240016 tptp.int) (BOUND_VARIABLE_1290207 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1240018 tptp.int)) (= (ho_4209 (ho_5096 (ho_5095 (ho_5094 k_5093 BOUND_VARIABLE_1290208) BOUND_VARIABLE_1240016) BOUND_VARIABLE_1290207) BOUND_VARIABLE_1240018) (ho_4209 (ho_4211 k_4222 (ho_4209 BOUND_VARIABLE_1290208 BOUND_VARIABLE_1240016)) (ho_4209 BOUND_VARIABLE_1290207 BOUND_VARIABLE_1240018)))))) (let ((_let_2759 (forall ((BOUND_VARIABLE_1239964 tptp.real) (BOUND_VARIABLE_1239965 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5097 BOUND_VARIABLE_1239964) BOUND_VARIABLE_1239965) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239965 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239965) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239965) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239964) BOUND_VARIABLE_1239965))))))))))))))))) (let ((_let_2760 (forall ((BOUND_VARIABLE_1239918 tptp.real) (BOUND_VARIABLE_1239919 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5098 BOUND_VARIABLE_1239918) BOUND_VARIABLE_1239919) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239919 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239919) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239919) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239918) BOUND_VARIABLE_1239919))))))))))))) (let ((_let_2761 (forall ((BOUND_VARIABLE_1239867 tptp.real) (BOUND_VARIABLE_1239868 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5099 BOUND_VARIABLE_1239867) BOUND_VARIABLE_1239868) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239868 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239868) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239868) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239867) BOUND_VARIABLE_1239868))))))))))))))))) (let ((_let_2762 (forall ((BOUND_VARIABLE_1239821 tptp.real) (BOUND_VARIABLE_1239822 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5100 BOUND_VARIABLE_1239821) BOUND_VARIABLE_1239822) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239822 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239822) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239822) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239821) BOUND_VARIABLE_1239822))))))))))))) (let ((_let_2763 (forall ((BOUND_VARIABLE_1239770 tptp.real) (BOUND_VARIABLE_1239771 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5101 BOUND_VARIABLE_1239770) BOUND_VARIABLE_1239771) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239771 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239771) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239771) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239770) BOUND_VARIABLE_1239771))))))))))))))))) (let ((_let_2764 (forall ((BOUND_VARIABLE_1239724 tptp.real) (BOUND_VARIABLE_1239725 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5102 BOUND_VARIABLE_1239724) BOUND_VARIABLE_1239725) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239725 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239725) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239725) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239724) BOUND_VARIABLE_1239725))))))))))))) (let ((_let_2765 (forall ((BOUND_VARIABLE_1239673 tptp.real) (BOUND_VARIABLE_1239674 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5103 BOUND_VARIABLE_1239673) BOUND_VARIABLE_1239674) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239674 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239674) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239674) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239673) BOUND_VARIABLE_1239674))))))))))))))))) (let ((_let_2766 (forall ((BOUND_VARIABLE_1239627 tptp.real) (BOUND_VARIABLE_1239628 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5104 BOUND_VARIABLE_1239627) BOUND_VARIABLE_1239628) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239628 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239628) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239628) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239627) BOUND_VARIABLE_1239628))))))))))))) (let ((_let_2767 (forall ((BOUND_VARIABLE_1239576 tptp.real) (BOUND_VARIABLE_1239577 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5105 BOUND_VARIABLE_1239576) BOUND_VARIABLE_1239577) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239577 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 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(ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5106 BOUND_VARIABLE_1239530) BOUND_VARIABLE_1239531) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239531 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239531) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239531) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239530) BOUND_VARIABLE_1239531))))))))))))) (let ((_let_2769 (forall ((BOUND_VARIABLE_1239479 tptp.real) (BOUND_VARIABLE_1239480 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5107 BOUND_VARIABLE_1239479) BOUND_VARIABLE_1239480) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239480 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239480) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 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_let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239434 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239434) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239434) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239433) BOUND_VARIABLE_1239434))))))))))))) (let ((_let_2771 (forall ((BOUND_VARIABLE_1239382 tptp.real) (BOUND_VARIABLE_1239383 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5109 BOUND_VARIABLE_1239382) BOUND_VARIABLE_1239383) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239383 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239383) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239383) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239382) BOUND_VARIABLE_1239383))))))))))))))))) (let ((_let_2772 (forall ((BOUND_VARIABLE_1239336 tptp.real) (BOUND_VARIABLE_1239337 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5110 BOUND_VARIABLE_1239336) BOUND_VARIABLE_1239337) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239337 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239337) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239337) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239336) BOUND_VARIABLE_1239337))))))))))))) (let ((_let_2773 (forall ((BOUND_VARIABLE_1239285 tptp.real) (BOUND_VARIABLE_1239286 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5111 BOUND_VARIABLE_1239285) BOUND_VARIABLE_1239286) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239286 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1239286) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1239286) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239285) BOUND_VARIABLE_1239286))))))))))))))))) (let ((_let_2774 (forall ((BOUND_VARIABLE_1239239 tptp.real) (BOUND_VARIABLE_1239240 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5112 BOUND_VARIABLE_1239239) BOUND_VARIABLE_1239240) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1239240 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1239240) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1239240) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1239239) BOUND_VARIABLE_1239240))))))))))))) (let ((_let_2775 (forall ((BOUND_VARIABLE_1239231 tptp.set_int) (BOUND_VARIABLE_1239232 tptp.int)) (= (ho_4310 (ho_5114 k_5113 BOUND_VARIABLE_1239231) BOUND_VARIABLE_1239232) (ho_5117 (ho_5116 k_5115 BOUND_VARIABLE_1239232) BOUND_VARIABLE_1239231))))) (let ((_let_2776 (forall ((BOUND_VARIABLE_1239223 tptp.set_int) (BOUND_VARIABLE_1239224 tptp.int)) (= (ho_4310 (ho_5114 k_5118 BOUND_VARIABLE_1239223) BOUND_VARIABLE_1239224) (ho_5117 (ho_5116 k_5115 BOUND_VARIABLE_1239224) BOUND_VARIABLE_1239223))))) (let ((_let_2777 (forall ((BOUND_VARIABLE_1239215 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1239216 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_5120 k_5119 BOUND_VARIABLE_1239215) BOUND_VARIABLE_1239216) (ho_5123 (ho_5122 k_5121 BOUND_VARIABLE_1239216) BOUND_VARIABLE_1239215))))) (let ((_let_2778 (forall ((BOUND_VARIABLE_1239207 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1239208 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_5120 k_5124 BOUND_VARIABLE_1239207) BOUND_VARIABLE_1239208) (ho_5123 (ho_5122 k_5121 BOUND_VARIABLE_1239208) BOUND_VARIABLE_1239207))))) (let ((_let_2779 (forall ((BOUND_VARIABLE_1239199 tptp.set_complex) (BOUND_VARIABLE_1239200 tptp.complex)) (= (ho_5127 (ho_5126 k_5125 BOUND_VARIABLE_1239199) BOUND_VARIABLE_1239200) (ho_5130 (ho_5129 k_5128 BOUND_VARIABLE_1239200) BOUND_VARIABLE_1239199))))) (let ((_let_2780 (forall ((BOUND_VARIABLE_1239191 tptp.set_complex) (BOUND_VARIABLE_1239192 tptp.complex)) (= (ho_5127 (ho_5126 k_5131 BOUND_VARIABLE_1239191) BOUND_VARIABLE_1239192) (ho_5130 (ho_5129 k_5128 BOUND_VARIABLE_1239192) BOUND_VARIABLE_1239191))))) (let ((_let_2781 (forall ((BOUND_VARIABLE_1239183 tptp.set_real) (BOUND_VARIABLE_1239184 tptp.real)) (= (ho_4351 (ho_5133 k_5132 BOUND_VARIABLE_1239183) BOUND_VARIABLE_1239184) (ho_5136 (ho_5135 k_5134 BOUND_VARIABLE_1239184) BOUND_VARIABLE_1239183))))) (let ((_let_2782 (forall ((BOUND_VARIABLE_1239175 tptp.set_real) (BOUND_VARIABLE_1239176 tptp.real)) (= (ho_4351 (ho_5133 k_5137 BOUND_VARIABLE_1239175) BOUND_VARIABLE_1239176) (ho_5136 (ho_5135 k_5134 BOUND_VARIABLE_1239176) BOUND_VARIABLE_1239175))))) (let ((_let_2783 (forall ((BOUND_VARIABLE_1239167 tptp.set_nat) (BOUND_VARIABLE_1239168 tptp.nat)) (= (ho_4288 (ho_5139 k_5138 BOUND_VARIABLE_1239167) BOUND_VARIABLE_1239168) (ho_5142 (ho_5141 k_5140 BOUND_VARIABLE_1239168) BOUND_VARIABLE_1239167))))) (let ((_let_2784 (forall ((BOUND_VARIABLE_1239159 tptp.set_nat) (BOUND_VARIABLE_1239160 tptp.nat)) (= (ho_4288 (ho_5139 k_5143 BOUND_VARIABLE_1239159) BOUND_VARIABLE_1239160) (ho_5142 (ho_5141 k_5140 BOUND_VARIABLE_1239160) BOUND_VARIABLE_1239159))))) (let ((_let_2785 (forall ((BOUND_VARIABLE_1239142 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1239143 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5144 BOUND_VARIABLE_1239142) BOUND_VARIABLE_1239143) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239143 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1239142) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1239142))))))))))) (let ((_let_2786 (forall ((BOUND_VARIABLE_1239125 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1239126 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5145 BOUND_VARIABLE_1239125) BOUND_VARIABLE_1239126) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239126 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1239125) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1239125))))))))))) (let ((_let_2787 (forall ((BOUND_VARIABLE_1239108 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1239109 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5146 BOUND_VARIABLE_1239108) BOUND_VARIABLE_1239109) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239109 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1239108) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1239108))))))))))) (let ((_let_2788 (forall ((BOUND_VARIABLE_1239091 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1239092 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5147 BOUND_VARIABLE_1239091) BOUND_VARIABLE_1239092) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239092 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1239091) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1239091))))))))))) (let ((_let_2789 (forall ((BOUND_VARIABLE_1239074 tptp.list_int) (BOUND_VARIABLE_1239075 tptp.int)) (= (ho_4310 (ho_5149 k_5148 BOUND_VARIABLE_1239074) BOUND_VARIABLE_1239075) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239075 (ho_4335 (ho_4640 k_4639 BOUND_VARIABLE_1239074) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 BOUND_VARIABLE_1239074))))))))))) (let ((_let_2790 (forall ((BOUND_VARIABLE_1239057 tptp.list_nat) (BOUND_VARIABLE_1239058 tptp.nat)) (= (ho_4288 (ho_5151 k_5150 BOUND_VARIABLE_1239057) BOUND_VARIABLE_1239058) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239058 (ho_4216 (ho_4468 k_4467 BOUND_VARIABLE_1239057) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 BOUND_VARIABLE_1239057))))))))))) (let ((_let_2791 (forall ((BOUND_VARIABLE_1239040 tptp.list_o) (BOUND_VARIABLE_1239041 Bool)) (= (ho_5154 (ho_5153 k_5152 BOUND_VARIABLE_1239040) BOUND_VARIABLE_1239041) (not (forall ((I3 tptp.nat)) (or (= (not BOUND_VARIABLE_1239041) (ho_4288 (ho_5158 k_5157 BOUND_VARIABLE_1239040) I3)) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_5156 k_5155 BOUND_VARIABLE_1239040))))))))))) (let ((_let_2792 (forall ((BOUND_VARIABLE_1239023 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1239024 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5159 BOUND_VARIABLE_1239023) BOUND_VARIABLE_1239024) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239024 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1239023) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1239023))))))))))) (let ((_let_2793 (forall ((BOUND_VARIABLE_1239006 tptp.list_complex) (BOUND_VARIABLE_1239007 tptp.complex)) (= (ho_5127 (ho_5161 k_5160 BOUND_VARIABLE_1239006) BOUND_VARIABLE_1239007) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1239007 (ho_4767 (ho_5165 k_5164 BOUND_VARIABLE_1239006) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_5163 k_5162 BOUND_VARIABLE_1239006))))))))))) (let ((_let_2794 (forall ((BOUND_VARIABLE_1238989 tptp.list_int) (BOUND_VARIABLE_1238990 tptp.int)) (= (ho_4310 (ho_5149 k_5166 BOUND_VARIABLE_1238989) BOUND_VARIABLE_1238990) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1238990 (ho_4335 (ho_4640 k_4639 BOUND_VARIABLE_1238989) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 BOUND_VARIABLE_1238989))))))))))) (let ((_let_2795 (forall ((BOUND_VARIABLE_1238972 tptp.list_nat) (BOUND_VARIABLE_1238973 tptp.nat)) (= (ho_4288 (ho_5151 k_5167 BOUND_VARIABLE_1238972) BOUND_VARIABLE_1238973) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1238973 (ho_4216 (ho_4468 k_4467 BOUND_VARIABLE_1238972) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 BOUND_VARIABLE_1238972))))))))))) (let ((_let_2796 (forall ((BOUND_VARIABLE_1238955 tptp.list_o) (BOUND_VARIABLE_1238956 Bool)) (= (ho_5154 (ho_5153 k_5168 BOUND_VARIABLE_1238955) BOUND_VARIABLE_1238956) (not (forall ((I3 tptp.nat)) (or (= (not BOUND_VARIABLE_1238956) (ho_4288 (ho_5158 k_5157 BOUND_VARIABLE_1238955) I3)) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_5156 k_5155 BOUND_VARIABLE_1238955))))))))))) (let ((_let_2797 (forall ((BOUND_VARIABLE_1238938 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1238939 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5169 BOUND_VARIABLE_1238938) BOUND_VARIABLE_1238939) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1238939 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1238938) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1238938))))))))))) (let ((_let_2798 (forall ((BOUND_VARIABLE_1238921 tptp.list_complex) (BOUND_VARIABLE_1238922 tptp.complex)) (= (ho_5127 (ho_5161 k_5170 BOUND_VARIABLE_1238921) BOUND_VARIABLE_1238922) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1238922 (ho_4767 (ho_5165 k_5164 BOUND_VARIABLE_1238921) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_5163 k_5162 BOUND_VARIABLE_1238921))))))))))) (let ((_let_2799 (forall ((BOUND_VARIABLE_1238875 tptp.real) (BOUND_VARIABLE_1238876 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5171 BOUND_VARIABLE_1238875) BOUND_VARIABLE_1238876) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1238876 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1238876) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1238876) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1238875) BOUND_VARIABLE_1238876))))))))))))) (let ((_let_2800 (forall ((BOUND_VARIABLE_1238868 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_5172 BOUND_VARIABLE_1238868))))))))) (let ((_let_2801 (forall ((BOUND_VARIABLE_1291157 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1238858 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1291157 BOUND_VARIABLE_1238858)) (ho_4316 (ho_4249 k_5173 BOUND_VARIABLE_1291157) BOUND_VARIABLE_1238858))))) (let ((_let_2802 (forall ((BOUND_VARIABLE_1238842 tptp.product_prod_int_int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238842)) (ho_4587 k_4586 BOUND_VARIABLE_1238842)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (= (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2))) _let_2)) _let_1)) (ho_4582 k_5174 BOUND_VARIABLE_1238842))))))) (let ((_let_2803 (forall ((BOUND_VARIABLE_1238823 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4588 BOUND_VARIABLE_1238823))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_1)) (ho_4428 (ho_4427 k_4426 _let_3) _let_2)) (ho_4428 (ho_4427 k_4426 (ho_4587 k_4586 BOUND_VARIABLE_1238823)) _let_1)) (ho_4432 k_5175 BOUND_VARIABLE_1238823)))))))) (let ((_let_2804 (forall ((BOUND_VARIABLE_1238804 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4588 BOUND_VARIABLE_1238804))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_1)) (ho_4428 (ho_4427 k_4426 _let_3) _let_2)) (ho_4428 (ho_4427 k_4426 (ho_4587 k_4586 BOUND_VARIABLE_1238804)) _let_1)) (ho_4432 k_5176 BOUND_VARIABLE_1238804)))))))) (let ((_let_2805 (forall ((BOUND_VARIABLE_1238797 Bool) (BOUND_VARIABLE_1238798 Bool)) (= (= BOUND_VARIABLE_1238797 BOUND_VARIABLE_1238798) (ho_5154 (ho_5178 k_5177 BOUND_VARIABLE_1238797) BOUND_VARIABLE_1238798))))) (let ((_let_2806 (forall ((BOUND_VARIABLE_1238782 tptp.product_prod_int_int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238782)) (ho_4587 k_4586 BOUND_VARIABLE_1238782)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (= (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2))) _let_2)) _let_1)) (ho_4582 k_5179 BOUND_VARIABLE_1238782))))))) (let ((_let_2807 (forall ((BOUND_VARIABLE_1238767 tptp.product_prod_int_int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238767)) (ho_4587 k_4586 BOUND_VARIABLE_1238767)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (= (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2))) _let_2)) _let_1)) (ho_4582 k_5180 BOUND_VARIABLE_1238767))))))) (let ((_let_2808 (forall ((BOUND_VARIABLE_1238751 tptp.product_prod_int_int) (BOUND_VARIABLE_1238752 tptp.product_prod_int_int)) (= (ho_4432 (ho_4431 k_5181 BOUND_VARIABLE_1238751) BOUND_VARIABLE_1238752) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238751)) (ho_4587 k_4588 BOUND_VARIABLE_1238752))) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4586 BOUND_VARIABLE_1238751)) (ho_4587 k_4586 BOUND_VARIABLE_1238752))))))) (let ((_let_2809 (forall ((BOUND_VARIABLE_1238735 tptp.product_prod_int_int) (BOUND_VARIABLE_1238736 tptp.product_prod_int_int)) (= (ho_4432 (ho_4431 k_5182 BOUND_VARIABLE_1238735) BOUND_VARIABLE_1238736) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238735)) (ho_4587 k_4588 BOUND_VARIABLE_1238736))) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4586 BOUND_VARIABLE_1238735)) (ho_4587 k_4586 BOUND_VARIABLE_1238736))))))) (let ((_let_2810 (forall ((BOUND_VARIABLE_1238720 tptp.product_prod_int_int)) (= (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4587 k_4588 BOUND_VARIABLE_1238720))) (ho_4587 k_4586 BOUND_VARIABLE_1238720)) (ho_4432 k_5183 BOUND_VARIABLE_1238720))))) (let ((_let_2811 (forall ((BOUND_VARIABLE_1238705 tptp.product_prod_int_int)) (= (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4587 k_4588 BOUND_VARIABLE_1238705))) (ho_4587 k_4586 BOUND_VARIABLE_1238705)) (ho_4432 k_5184 BOUND_VARIABLE_1238705))))) (let ((_let_2812 (forall ((BOUND_VARIABLE_1238678 tptp.product_prod_int_int) (BOUND_VARIABLE_1238679 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4586 BOUND_VARIABLE_1238679))) (let ((_let_2 (ho_4587 k_4586 BOUND_VARIABLE_1238678))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3)))) (= (ho_4582 (ho_5186 k_5185 BOUND_VARIABLE_1238678) BOUND_VARIABLE_1238679) (and (not (= _let_4 _let_2)) (not (= _let_4 _let_1)) (= (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238679)) _let_2) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238678)) _let_1))))))))))) (let ((_let_2813 (forall ((BOUND_VARIABLE_1238671 tptp.int) (BOUND_VARIABLE_1238672 tptp.int)) (= (= BOUND_VARIABLE_1238671 BOUND_VARIABLE_1238672) (ho_4310 (ho_4309 k_5187 BOUND_VARIABLE_1238671) BOUND_VARIABLE_1238672))))) (let ((_let_2814 (forall ((BOUND_VARIABLE_1238664 tptp.int) (BOUND_VARIABLE_1238665 tptp.int)) (= (= BOUND_VARIABLE_1238664 BOUND_VARIABLE_1238665) (ho_4310 (ho_4309 k_5188 BOUND_VARIABLE_1238664) BOUND_VARIABLE_1238665))))) (let ((_let_2815 (forall ((BOUND_VARIABLE_1238646 tptp.int) (BOUND_VARIABLE_1238647 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4428 (ho_4427 k_5189 BOUND_VARIABLE_1238646) BOUND_VARIABLE_1238647) (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1238647 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 BOUND_VARIABLE_1238646) BOUND_VARIABLE_1238647)))))))) (let ((_let_2816 (forall ((BOUND_VARIABLE_1238628 tptp.int) (BOUND_VARIABLE_1238629 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4428 (ho_4427 k_5190 BOUND_VARIABLE_1238628) BOUND_VARIABLE_1238629) (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1238629 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 BOUND_VARIABLE_1238628) BOUND_VARIABLE_1238629)))))))) (let ((_let_2817 (forall ((BOUND_VARIABLE_1238601 tptp.product_prod_int_int) (BOUND_VARIABLE_1238602 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4586 BOUND_VARIABLE_1238602))) (let ((_let_2 (ho_4587 k_4586 BOUND_VARIABLE_1238601))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3)))) (= (ho_4582 (ho_5186 k_5191 BOUND_VARIABLE_1238601) BOUND_VARIABLE_1238602) (and (not (= _let_4 _let_2)) (not (= _let_4 _let_1)) (= (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238602)) _let_2) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238601)) _let_1))))))))))) (let ((_let_2818 (forall ((BOUND_VARIABLE_1238581 tptp.product_prod_int_int) (BOUND_VARIABLE_1238582 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4586 BOUND_VARIABLE_1238582))) (let ((_let_2 (ho_4587 k_4586 BOUND_VARIABLE_1238581))) (= (ho_4432 (ho_4431 k_5192 BOUND_VARIABLE_1238581) BOUND_VARIABLE_1238582) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238581)) _let_1)) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238582)) _let_2))) (ho_4209 (ho_4211 k_4222 _let_2) _let_1)))))))) (let ((_let_2819 (forall ((BOUND_VARIABLE_1238561 tptp.product_prod_int_int) (BOUND_VARIABLE_1238562 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4586 BOUND_VARIABLE_1238562))) (let ((_let_2 (ho_4587 k_4586 BOUND_VARIABLE_1238561))) (= (ho_4432 (ho_4431 k_5193 BOUND_VARIABLE_1238561) BOUND_VARIABLE_1238562) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238561)) _let_1)) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1238562)) _let_2))) (ho_4209 (ho_4211 k_4222 _let_2) _let_1)))))))) (let ((_let_2820 (forall ((BOUND_VARIABLE_1238549 tptp.real) (BOUND_VARIABLE_1238550 tptp.real)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4259) BOUND_VARIABLE_1238550) BOUND_VARIABLE_1238549) (ho_4258 (ho_4265 k_5194 BOUND_VARIABLE_1238549) BOUND_VARIABLE_1238550))))) (let ((_let_2821 (forall ((BOUND_VARIABLE_1238513 tptp.nat) (BOUND_VARIABLE_1238514 tptp.nat)) (let ((_let_1 (ho_5196 k_5195 BOUND_VARIABLE_1238514))) (let ((_let_2 (ho_4562 k_4561 tptp.one))) (let ((_let_3 (ho_4560 (ho_4564 k_4563 _let_2) (ho_4560 k_4559 _let_2)))) (let ((_let_4 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 _let_1) _let_3)) (ho_4560 k_4559 _let_1)) _let_1))) (let ((_let_5 (ho_5196 k_5195 BOUND_VARIABLE_1238513))) (let ((_let_6 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 _let_5) _let_3)) (ho_4560 k_4559 _let_5)) _let_5))) (let ((_let_7 (ho_4571 k_4570 _let_3))) (= (ho_5202 (ho_5201 (ho_5200 k_5199 k_4610) k_4610) (ho_4576 (ho_4575 (ho_4574 k_4573 (= _let_3 _let_5)) (ho_4572 _let_7 _let_3)) (ho_4576 (ho_4575 (ho_4574 k_4573 (= _let_3 _let_1)) (ho_4572 _let_7 _let_5)) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 _let_6) _let_4)) (ho_4560 (ho_4564 k_5197 _let_6) _let_4))))) (ho_4406 (ho_4198 k_5203 BOUND_VARIABLE_1238513) BOUND_VARIABLE_1238514)))))))))))) (let ((_let_2822 (forall ((BOUND_VARIABLE_1291491 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1238494 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4288 BOUND_VARIABLE_1291491 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1238494) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4288 (ho_5205 k_5204 BOUND_VARIABLE_1291491) BOUND_VARIABLE_1238494)))))))) (let ((_let_2823 (forall ((BOUND_VARIABLE_1238442 tptp.real) (BOUND_VARIABLE_1238443 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5206 BOUND_VARIABLE_1238442) BOUND_VARIABLE_1238443) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1238443 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1238443) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1238443) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1238442) BOUND_VARIABLE_1238443))))))))))))))))) (let ((_let_2824 (forall ((BOUND_VARIABLE_1238396 tptp.real) (BOUND_VARIABLE_1238397 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5207 BOUND_VARIABLE_1238396) BOUND_VARIABLE_1238397) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1238397 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1238397) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1238397) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1238396) BOUND_VARIABLE_1238397))))))))))))) (let ((_let_2825 (forall ((BOUND_VARIABLE_1238351 tptp.nat) (BOUND_VARIABLE_1238352 tptp.nat) (BOUND_VARIABLE_1238353 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4407 BOUND_VARIABLE_1238351) BOUND_VARIABLE_1238352)) BOUND_VARIABLE_1238353) (ho_5062 (ho_5210 (ho_5209 k_5208 BOUND_VARIABLE_1238351) BOUND_VARIABLE_1238352) BOUND_VARIABLE_1238353))))) (let ((_let_2826 (forall ((BOUND_VARIABLE_1238306 tptp.nat) (BOUND_VARIABLE_1238307 tptp.nat) (BOUND_VARIABLE_1238308 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4410 BOUND_VARIABLE_1238306) BOUND_VARIABLE_1238307)) BOUND_VARIABLE_1238308) (ho_5062 (ho_5210 (ho_5209 k_5211 BOUND_VARIABLE_1238306) BOUND_VARIABLE_1238307) BOUND_VARIABLE_1238308))))) (let ((_let_2827 (forall ((BOUND_VARIABLE_1238261 tptp.nat) (BOUND_VARIABLE_1238262 tptp.nat) (BOUND_VARIABLE_1238263 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4411 BOUND_VARIABLE_1238261) BOUND_VARIABLE_1238262)) BOUND_VARIABLE_1238263) (ho_5062 (ho_5210 (ho_5209 k_5212 BOUND_VARIABLE_1238261) BOUND_VARIABLE_1238262) BOUND_VARIABLE_1238263))))) (let ((_let_2828 (forall ((BOUND_VARIABLE_1238216 tptp.nat) (BOUND_VARIABLE_1238217 tptp.nat) (BOUND_VARIABLE_1238218 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4412 BOUND_VARIABLE_1238216) BOUND_VARIABLE_1238217)) BOUND_VARIABLE_1238218) (ho_5062 (ho_5210 (ho_5209 k_5213 BOUND_VARIABLE_1238216) BOUND_VARIABLE_1238217) BOUND_VARIABLE_1238218))))) (let ((_let_2829 (forall ((BOUND_VARIABLE_1238209 Bool) (BOUND_VARIABLE_1238210 Bool)) (= (= BOUND_VARIABLE_1238209 BOUND_VARIABLE_1238210) (ho_5154 (ho_5178 k_5214 BOUND_VARIABLE_1238209) BOUND_VARIABLE_1238210))))) (let ((_let_2830 (forall ((BOUND_VARIABLE_1238162 tptp.nat) (BOUND_VARIABLE_1238163 tptp.nat) (BOUND_VARIABLE_1238164 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4413 BOUND_VARIABLE_1238162) BOUND_VARIABLE_1238163)) BOUND_VARIABLE_1238164) (ho_4549 (ho_4552 (ho_4551 k_5215 BOUND_VARIABLE_1238162) BOUND_VARIABLE_1238163) BOUND_VARIABLE_1238164))))) (let ((_let_2831 (forall ((BOUND_VARIABLE_1238115 tptp.nat) (BOUND_VARIABLE_1238116 tptp.nat) (BOUND_VARIABLE_1238117 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4414 BOUND_VARIABLE_1238115) BOUND_VARIABLE_1238116)) BOUND_VARIABLE_1238117) (ho_4549 (ho_4552 (ho_4551 k_5216 BOUND_VARIABLE_1238115) BOUND_VARIABLE_1238116) BOUND_VARIABLE_1238117))))) (let ((_let_2832 (forall ((BOUND_VARIABLE_1238108 Bool) (BOUND_VARIABLE_1238109 Bool)) (= (= BOUND_VARIABLE_1238108 BOUND_VARIABLE_1238109) (ho_5154 (ho_5178 k_5217 BOUND_VARIABLE_1238108) BOUND_VARIABLE_1238109))))) (let ((_let_2833 (forall ((BOUND_VARIABLE_1238061 tptp.nat) (BOUND_VARIABLE_1238062 tptp.nat) (BOUND_VARIABLE_1238063 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4415 BOUND_VARIABLE_1238061) BOUND_VARIABLE_1238062)) BOUND_VARIABLE_1238063) (ho_4549 (ho_4552 (ho_4551 k_5218 BOUND_VARIABLE_1238061) BOUND_VARIABLE_1238062) BOUND_VARIABLE_1238063))))) (let ((_let_2834 (forall ((BOUND_VARIABLE_1238014 tptp.nat) (BOUND_VARIABLE_1238015 tptp.nat) (BOUND_VARIABLE_1238016 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4416 BOUND_VARIABLE_1238014) BOUND_VARIABLE_1238015)) BOUND_VARIABLE_1238016) (ho_4549 (ho_4552 (ho_4551 k_5219 BOUND_VARIABLE_1238014) BOUND_VARIABLE_1238015) BOUND_VARIABLE_1238016))))) (let ((_let_2835 (forall ((BOUND_VARIABLE_1291689 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1238007 tptp.nat) (BOUND_VARIABLE_1238008 tptp.nat)) (= (ho_4316 (ho_4338 (ho_4838 k_5220 BOUND_VARIABLE_1291689) BOUND_VARIABLE_1238007) BOUND_VARIABLE_1238008) (ho_4316 BOUND_VARIABLE_1291689 BOUND_VARIABLE_1238007))))) (let ((_let_2836 (forall ((BOUND_VARIABLE_1291701 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237999 tptp.nat) (BOUND_VARIABLE_1238000 tptp.nat)) (= (ho_4316 (ho_4338 (ho_4838 k_5221 BOUND_VARIABLE_1291701) BOUND_VARIABLE_1237999) BOUND_VARIABLE_1238000) (ho_4316 BOUND_VARIABLE_1291701 BOUND_VARIABLE_1237999))))) (let ((_let_2837 (forall ((BOUND_VARIABLE_1237992 tptp.rat) (BOUND_VARIABLE_1237993 tptp.nat)) (= BOUND_VARIABLE_1237992 (ho_4316 (ho_4799 k_5222 BOUND_VARIABLE_1237992) BOUND_VARIABLE_1237993))))) (let ((_let_2838 (forall ((BOUND_VARIABLE_1291720 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237985 tptp.nat) (BOUND_VARIABLE_1237986 tptp.nat)) (= (ho_4316 (ho_4338 (ho_4838 k_5223 BOUND_VARIABLE_1291720) BOUND_VARIABLE_1237985) BOUND_VARIABLE_1237986) (ho_4316 BOUND_VARIABLE_1291720 BOUND_VARIABLE_1237985))))) (let ((_let_2839 (forall ((BOUND_VARIABLE_1237976 tptp.nat) (BOUND_VARIABLE_1237977 tptp.nat)) (= (ho_4406 (ho_4198 k_5224 BOUND_VARIABLE_1237976) BOUND_VARIABLE_1237977) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1237977) BOUND_VARIABLE_1237976))))) (let ((_let_2840 (forall ((BOUND_VARIABLE_1237968 tptp.nat) (BOUND_VARIABLE_1237969 tptp.nat)) (= (ho_4406 (ho_4198 k_5225 BOUND_VARIABLE_1237968) BOUND_VARIABLE_1237969) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1237969) BOUND_VARIABLE_1237968))))) (let ((_let_2841 (forall ((BOUND_VARIABLE_1237927 tptp.nat) (BOUND_VARIABLE_1237928 tptp.nat) (BOUND_VARIABLE_1237929 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4417 BOUND_VARIABLE_1237927) BOUND_VARIABLE_1237928)) BOUND_VARIABLE_1237929) (ho_4549 (ho_4552 (ho_4551 k_5226 BOUND_VARIABLE_1237927) BOUND_VARIABLE_1237928) BOUND_VARIABLE_1237929))))) (let ((_let_2842 (forall ((BOUND_VARIABLE_1237846 tptp.nat) (BOUND_VARIABLE_1237847 tptp.nat) (BOUND_VARIABLE_1237848 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4418 BOUND_VARIABLE_1237846) BOUND_VARIABLE_1237847)) BOUND_VARIABLE_1237848) (ho_5062 (ho_5210 (ho_5209 k_5227 BOUND_VARIABLE_1237846) BOUND_VARIABLE_1237847) BOUND_VARIABLE_1237848))))) (let ((_let_2843 (forall ((BOUND_VARIABLE_1237765 tptp.nat) (BOUND_VARIABLE_1237766 tptp.nat) (BOUND_VARIABLE_1237767 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4419 BOUND_VARIABLE_1237765) BOUND_VARIABLE_1237766)) BOUND_VARIABLE_1237767) (ho_5062 (ho_5210 (ho_5209 k_5228 BOUND_VARIABLE_1237765) BOUND_VARIABLE_1237766) BOUND_VARIABLE_1237767))))) (let ((_let_2844 (forall ((BOUND_VARIABLE_1237720 tptp.nat) (BOUND_VARIABLE_1237721 tptp.nat) (BOUND_VARIABLE_1237722 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4420 BOUND_VARIABLE_1237720) BOUND_VARIABLE_1237721)) BOUND_VARIABLE_1237722) (ho_5062 (ho_5210 (ho_5209 k_5229 BOUND_VARIABLE_1237720) BOUND_VARIABLE_1237721) BOUND_VARIABLE_1237722))))) (let ((_let_2845 (forall ((BOUND_VARIABLE_1237675 tptp.nat) (BOUND_VARIABLE_1237676 tptp.nat) (BOUND_VARIABLE_1237677 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4421 BOUND_VARIABLE_1237675) BOUND_VARIABLE_1237676)) BOUND_VARIABLE_1237677) (ho_5062 (ho_5210 (ho_5209 k_5230 BOUND_VARIABLE_1237675) BOUND_VARIABLE_1237676) BOUND_VARIABLE_1237677))))) (let ((_let_2846 (forall ((BOUND_VARIABLE_1237668 Bool) (BOUND_VARIABLE_1237669 Bool)) (= (= BOUND_VARIABLE_1237668 BOUND_VARIABLE_1237669) (ho_5154 (ho_5178 k_5231 BOUND_VARIABLE_1237668) BOUND_VARIABLE_1237669))))) (let ((_let_2847 (forall ((BOUND_VARIABLE_1237621 tptp.nat) (BOUND_VARIABLE_1237622 tptp.nat) (BOUND_VARIABLE_1237623 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4422 BOUND_VARIABLE_1237621) BOUND_VARIABLE_1237622)) BOUND_VARIABLE_1237623) (ho_4549 (ho_4552 (ho_4551 k_5232 BOUND_VARIABLE_1237621) BOUND_VARIABLE_1237622) BOUND_VARIABLE_1237623))))) (let ((_let_2848 (forall ((BOUND_VARIABLE_1237614 Bool) (BOUND_VARIABLE_1237615 Bool)) (= (= BOUND_VARIABLE_1237614 BOUND_VARIABLE_1237615) (ho_5154 (ho_5178 k_5233 BOUND_VARIABLE_1237614) BOUND_VARIABLE_1237615))))) (let ((_let_2849 (forall ((BOUND_VARIABLE_1237567 tptp.nat) (BOUND_VARIABLE_1237568 tptp.nat) (BOUND_VARIABLE_1237569 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4423 BOUND_VARIABLE_1237567) BOUND_VARIABLE_1237568)) BOUND_VARIABLE_1237569) (ho_4549 (ho_4552 (ho_4551 k_5234 BOUND_VARIABLE_1237567) BOUND_VARIABLE_1237568) BOUND_VARIABLE_1237569))))) (let ((_let_2850 (forall ((BOUND_VARIABLE_1237559 tptp.nat) (BOUND_VARIABLE_1237560 tptp.nat)) (= (ho_4406 (ho_4198 k_5235 BOUND_VARIABLE_1237559) BOUND_VARIABLE_1237560) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1237560) BOUND_VARIABLE_1237559))))) (let ((_let_2851 (forall ((BOUND_VARIABLE_1237552 tptp.nat) (BOUND_VARIABLE_1237553 tptp.nat)) (= (= BOUND_VARIABLE_1237552 BOUND_VARIABLE_1237553) (ho_4288 (ho_4287 k_5236 BOUND_VARIABLE_1237552) BOUND_VARIABLE_1237553))))) (let ((_let_2852 (forall ((BOUND_VARIABLE_1237545 tptp.nat)) (= (ho_4406 k_5237 BOUND_VARIABLE_1237545) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1237545) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))))))) (let ((_let_2853 (forall ((BOUND_VARIABLE_1237464 tptp.nat) (BOUND_VARIABLE_1237465 tptp.nat) (BOUND_VARIABLE_1237466 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4424 BOUND_VARIABLE_1237464) BOUND_VARIABLE_1237465)) BOUND_VARIABLE_1237466) (ho_5062 (ho_5210 (ho_5209 k_5238 BOUND_VARIABLE_1237464) BOUND_VARIABLE_1237465) BOUND_VARIABLE_1237466))))) (let ((_let_2854 (forall ((BOUND_VARIABLE_1237445 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4588 BOUND_VARIABLE_1237445))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (= (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_3 _let_1)) (ho_4428 (ho_4427 k_4426 _let_3) _let_2)) (ho_4428 (ho_4427 k_4426 (ho_4587 k_4586 BOUND_VARIABLE_1237445)) _let_1)) (ho_4432 k_5239 BOUND_VARIABLE_1237445)))))))) (let ((_let_2855 (forall ((BOUND_VARIABLE_1237438 Bool) (BOUND_VARIABLE_1237439 Bool)) (= (= BOUND_VARIABLE_1237438 BOUND_VARIABLE_1237439) (ho_5154 (ho_5178 k_5240 BOUND_VARIABLE_1237438) BOUND_VARIABLE_1237439))))) (let ((_let_2856 (forall ((BOUND_VARIABLE_1237423 tptp.product_prod_int_int)) (let ((_let_1 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1237423)) (ho_4587 k_4586 BOUND_VARIABLE_1237423)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (= (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2))) _let_2)) _let_1)) (ho_4582 k_5241 BOUND_VARIABLE_1237423))))))) (let ((_let_2857 (forall ((BOUND_VARIABLE_1237407 tptp.rat)) (let ((_let_1 (ho_4437 k_4436 BOUND_VARIABLE_1237407))) (let ((_let_2 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 _let_1)) (ho_4587 k_4586 _let_1)))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (= (= _let_2 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3))) _let_3)) _let_2)) (ho_5243 k_5242 BOUND_VARIABLE_1237407)))))))) (let ((_let_2858 (forall ((BOUND_VARIABLE_1237391 tptp.product_prod_int_int) (BOUND_VARIABLE_1237392 tptp.product_prod_int_int)) (= (ho_4432 (ho_4431 k_5244 BOUND_VARIABLE_1237391) BOUND_VARIABLE_1237392) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1237391)) (ho_4587 k_4588 BOUND_VARIABLE_1237392))) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4586 BOUND_VARIABLE_1237391)) (ho_4587 k_4586 BOUND_VARIABLE_1237392))))))) (let ((_let_2859 (forall ((BOUND_VARIABLE_1237376 tptp.product_prod_int_int)) (= (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4587 k_4588 BOUND_VARIABLE_1237376))) (ho_4587 k_4586 BOUND_VARIABLE_1237376)) (ho_4432 k_5245 BOUND_VARIABLE_1237376))))) (let ((_let_2860 (forall ((BOUND_VARIABLE_1237369 tptp.int) (BOUND_VARIABLE_1237370 tptp.int)) (= (= BOUND_VARIABLE_1237369 BOUND_VARIABLE_1237370) (ho_4310 (ho_4309 k_5246 BOUND_VARIABLE_1237369) BOUND_VARIABLE_1237370))))) (let ((_let_2861 (forall ((BOUND_VARIABLE_1237362 tptp.int) (BOUND_VARIABLE_1237363 tptp.int)) (= (= BOUND_VARIABLE_1237362 BOUND_VARIABLE_1237363) (ho_4310 (ho_4309 k_5247 BOUND_VARIABLE_1237362) BOUND_VARIABLE_1237363))))) (let ((_let_2862 (forall ((BOUND_VARIABLE_1237344 tptp.int) (BOUND_VARIABLE_1237345 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4428 (ho_4427 k_5248 BOUND_VARIABLE_1237344) BOUND_VARIABLE_1237345) (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1237345 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 BOUND_VARIABLE_1237344) BOUND_VARIABLE_1237345)))))))) (let ((_let_2863 (forall ((BOUND_VARIABLE_1237324 tptp.int) (BOUND_VARIABLE_1237325 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4318 (ho_5250 k_5249 BOUND_VARIABLE_1237324) BOUND_VARIABLE_1237325) (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1237325 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 BOUND_VARIABLE_1237324) BOUND_VARIABLE_1237325))))))))) (let ((_let_2864 (forall ((BOUND_VARIABLE_1237304 tptp.product_prod_int_int) (BOUND_VARIABLE_1237305 tptp.product_prod_int_int)) (let ((_let_1 (ho_4587 k_4586 BOUND_VARIABLE_1237305))) (let ((_let_2 (ho_4587 k_4586 BOUND_VARIABLE_1237304))) (= (ho_4432 (ho_4431 k_5251 BOUND_VARIABLE_1237304) BOUND_VARIABLE_1237305) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1237304)) _let_1)) (ho_4209 (ho_4211 k_4222 (ho_4587 k_4588 BOUND_VARIABLE_1237305)) _let_2))) (ho_4209 (ho_4211 k_4222 _let_2) _let_1)))))))) (let ((_let_2865 (forall ((BOUND_VARIABLE_1292026 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237235 tptp.nat)) (= (ho_4316 (ho_4249 (ho_4260 (ho_5254 k_5253 (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292026 N2))) (let ((_let_2 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_3 (ho_4441 _let_2 k_4435))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_4 _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_4)) (ho_4428 (ho_4427 k_4426 _let_4) _let_4))))) (let ((_let_7 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_2) k_4443) _let_6) (ho_4442 _let_3 _let_6)))) (let ((_let_8 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_7 (ho_4442 (ho_4448 k_5252 _let_7) _let_1)) (not (= _let_7 _let_1)))) (ho_4442 _let_3 _let_1)) _let_1))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 K3)) (ho_4290 k_4289 N2))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_8)) (not (= R5 _let_8)))))))))))))))))))))))) k_4425) (ho_4249 k_4450 BOUND_VARIABLE_1292026)) BOUND_VARIABLE_1237235) (ho_4316 (ho_4249 k_5255 BOUND_VARIABLE_1292026) BOUND_VARIABLE_1237235))))) (let ((_let_2866 (forall ((BOUND_VARIABLE_1292081 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292079 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237221 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1292081 BOUND_VARIABLE_1237221)) (ho_4316 BOUND_VARIABLE_1292079 BOUND_VARIABLE_1237221)) (ho_4316 (ho_4249 (ho_4260 k_5256 BOUND_VARIABLE_1292081) BOUND_VARIABLE_1292079) BOUND_VARIABLE_1237221))))) (let ((_let_2867 (forall ((BOUND_VARIABLE_1292097 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292095 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237206 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4443) (ho_4316 BOUND_VARIABLE_1292097 BOUND_VARIABLE_1237206)) (ho_4316 BOUND_VARIABLE_1292095 BOUND_VARIABLE_1237206)) (ho_4316 (ho_4249 (ho_4260 k_5257 BOUND_VARIABLE_1292097) BOUND_VARIABLE_1292095) BOUND_VARIABLE_1237206))))) (let ((_let_2868 (forall ((BOUND_VARIABLE_1292111 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237194 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4435) (ho_4316 BOUND_VARIABLE_1292111 BOUND_VARIABLE_1237194)) (ho_4316 (ho_4249 k_5258 BOUND_VARIABLE_1292111) BOUND_VARIABLE_1237194))))) (let ((_let_2869 (forall ((BOUND_VARIABLE_1292122 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1237132 tptp.real)) (= (and (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_235021 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_2 (ho_4441 _let_1 k_4435))) (let ((_let_3 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443))) (let ((_let_4 (ho_4442 (ho_4448 _let_3 (ho_4316 BOUND_VARIABLE_1292122 M6)) (ho_4442 _let_2 (ho_4316 BOUND_VARIABLE_1292122 BOUND_VARIABLE_235021))))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_5 _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_5))))) (let ((_let_8 (ho_4442 (ho_4448 _let_3 _let_7) (ho_4442 _let_2 _let_7)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_8 (ho_4442 (ho_4448 k_5252 _let_8) _let_4)) (not (= _let_8 _let_4)))) (ho_4442 _let_2 _let_4)) _let_4))) (let ((_let_10 (ho_4292 k_4304 (ho_4290 k_4289 K3)))) (or (not (ho_4293 _let_10 (ho_4290 k_4289 M6))) (not (ho_4293 _let_10 (ho_4290 k_4289 BOUND_VARIABLE_235021))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_9)) (not (= R5 _let_9))))))))))))))))))))))))) (= BOUND_VARIABLE_1237132 (ho_4251 k_4250 BOUND_VARIABLE_1292122))) (ho_4351 (ho_5260 k_5259 BOUND_VARIABLE_1292122) BOUND_VARIABLE_1237132))))) (let ((_let_2870 (forall ((BOUND_VARIABLE_1237124 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))) (ho_4316 k_5261 BOUND_VARIABLE_1237124))))))) (let ((_let_2871 (forall ((BOUND_VARIABLE_1237117 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_5262 BOUND_VARIABLE_1237117))))))))) (let ((_let_2872 (forall ((BOUND_VARIABLE_1237110 Bool) (BOUND_VARIABLE_1237111 Bool)) (= (= BOUND_VARIABLE_1237110 BOUND_VARIABLE_1237111) (ho_5154 (ho_5178 k_5263 BOUND_VARIABLE_1237110) BOUND_VARIABLE_1237111))))) (let ((_let_2873 (forall ((BOUND_VARIABLE_1237103 tptp.real) (BOUND_VARIABLE_1237104 tptp.real)) (= (= BOUND_VARIABLE_1237103 BOUND_VARIABLE_1237104) (ho_4351 (ho_4508 k_5264 BOUND_VARIABLE_1237103) BOUND_VARIABLE_1237104))))) (let ((_let_2874 (forall ((BOUND_VARIABLE_1292201 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236993 tptp.real)) (= (and (= BOUND_VARIABLE_1236993 (ho_4251 k_4250 BOUND_VARIABLE_1292201)) (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_235021 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_2 (ho_4441 _let_1 k_4435))) (let ((_let_3 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443))) (let ((_let_4 (ho_4442 (ho_4448 _let_3 (ho_4316 BOUND_VARIABLE_1292201 M6)) (ho_4442 _let_2 (ho_4316 BOUND_VARIABLE_1292201 BOUND_VARIABLE_235021))))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_5 _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_5))))) (let ((_let_8 (ho_4442 (ho_4448 _let_3 _let_7) (ho_4442 _let_2 _let_7)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_8 (ho_4442 (ho_4448 k_5252 _let_8) _let_4)) (not (= _let_8 _let_4)))) (ho_4442 _let_2 _let_4)) _let_4))) (let ((_let_10 (ho_4292 k_4304 (ho_4290 k_4289 K3)))) (or (not (ho_4293 _let_10 (ho_4290 k_4289 M6))) (not (ho_4293 _let_10 (ho_4290 k_4289 BOUND_VARIABLE_235021))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_9)) (not (= R5 _let_9))))))))))))))))))))))))) (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292201 N2))) (let ((_let_2 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_3 (ho_4441 _let_2 k_4435))) (let ((_let_4 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_2) k_4443))) (let ((_let_5 (ho_4442 (ho_4448 _let_4 _let_1) (ho_4442 _let_3 _let_1)))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_8 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_6 _let_7)) (ho_4428 (ho_4427 k_4426 _let_7) _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_6))))) (let ((_let_9 (ho_4442 (ho_4448 _let_4 _let_8) (ho_4442 _let_3 _let_8)))) (let ((_let_10 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_9 (ho_4442 (ho_4448 k_5252 _let_9) _let_5)) (not (= _let_9 _let_5)))) (ho_4442 _let_3 _let_5)) _let_5))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 K3)) (ho_4290 k_4289 N2))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_10)) (not (= R5 _let_10)))))))))))))))))))))))))) (ho_4351 (ho_5260 k_5265 BOUND_VARIABLE_1292201) BOUND_VARIABLE_1236993))))) (let ((_let_2875 (forall ((BOUND_VARIABLE_1236985 Bool) (BOUND_VARIABLE_1236986 Bool)) (= (= BOUND_VARIABLE_1236985 BOUND_VARIABLE_1236986) (ho_5154 (ho_5178 k_5266 BOUND_VARIABLE_1236985) BOUND_VARIABLE_1236986))))) (let ((_let_2876 (forall ((BOUND_VARIABLE_1292271 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235727 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292271 N2))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_235727)) (ho_4290 k_4289 N2))) (and (= _let_1 (ho_4442 (ho_4448 k_5252 _let_1) R5)) (not (= R5 _let_1))))))))))))))) (ho_5268 k_5267 BOUND_VARIABLE_1292271))))) (let ((_let_2877 (forall ((BOUND_VARIABLE_1236934 tptp.real)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235444 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 (ho_4253 k_4252 BOUND_VARIABLE_1236934) N2))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_235444)) (ho_4290 k_4289 N2))) (and (= _let_1 (ho_4442 (ho_4448 k_5252 _let_1) R5)) (not (= R5 _let_1))))))))))))))) (ho_4351 k_5269 BOUND_VARIABLE_1236934))))) (let ((_let_2878 (forall ((BOUND_VARIABLE_1292334 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236865 tptp.nat)) (= (ho_4316 (ho_4249 (ho_4260 (ho_5254 k_5253 (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292334 N2))) (let ((_let_2 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_3 (ho_4441 _let_2 k_4435))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_4 _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_4)) (ho_4428 (ho_4427 k_4426 _let_4) _let_4))))) (let ((_let_7 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_2) k_4443) _let_6) (ho_4442 _let_3 _let_6)))) (let ((_let_8 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_7 (ho_4442 (ho_4448 k_5252 _let_7) _let_1)) (not (= _let_7 _let_1)))) (ho_4442 _let_3 _let_1)) _let_1))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 K3)) (ho_4290 k_4289 N2))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_8)) (not (= R5 _let_8)))))))))))))))))))))))) k_4451) (ho_4249 k_4452 BOUND_VARIABLE_1292334)) BOUND_VARIABLE_1236865) (ho_4316 (ho_4249 k_5270 BOUND_VARIABLE_1292334) BOUND_VARIABLE_1236865))))) (let ((_let_2879 (forall ((BOUND_VARIABLE_1292370 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236795 tptp.nat)) (= (ho_4316 (ho_4249 (ho_4260 (ho_5254 k_5253 (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292370 N2))) (let ((_let_2 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_3 (ho_4441 _let_2 k_4435))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_4 _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_4)) (ho_4428 (ho_4427 k_4426 _let_4) _let_4))))) (let ((_let_7 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_2) k_4443) _let_6) (ho_4442 _let_3 _let_6)))) (let ((_let_8 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_7 (ho_4442 (ho_4448 k_5252 _let_7) _let_1)) (not (= _let_7 _let_1)))) (ho_4442 _let_3 _let_1)) _let_1))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 K3)) (ho_4290 k_4289 N2))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_8)) (not (= R5 _let_8)))))))))))))))))))))))) k_4453) (ho_4249 k_4454 BOUND_VARIABLE_1292370)) BOUND_VARIABLE_1236795) (ho_4316 (ho_4249 k_5271 BOUND_VARIABLE_1292370) BOUND_VARIABLE_1236795))))) (let ((_let_2880 (forall ((BOUND_VARIABLE_1236787 tptp.nat) (BOUND_VARIABLE_1236788 tptp.nat)) (= (= BOUND_VARIABLE_1236787 BOUND_VARIABLE_1236788) (ho_4288 (ho_4287 k_5272 BOUND_VARIABLE_1236787) BOUND_VARIABLE_1236788))))) (let ((_let_2881 (forall ((BOUND_VARIABLE_1236780 tptp.nat) (BOUND_VARIABLE_1236781 tptp.nat)) (= (= BOUND_VARIABLE_1236780 BOUND_VARIABLE_1236781) (ho_4288 (ho_4287 k_5273 BOUND_VARIABLE_1236780) BOUND_VARIABLE_1236781))))) (let ((_let_2882 (forall ((BOUND_VARIABLE_1236773 Bool) (BOUND_VARIABLE_1236774 Bool)) (= (= BOUND_VARIABLE_1236773 BOUND_VARIABLE_1236774) (ho_5154 (ho_5178 k_5274 BOUND_VARIABLE_1236773) BOUND_VARIABLE_1236774))))) (let ((_let_2883 (forall ((BOUND_VARIABLE_1236766 tptp.int) (BOUND_VARIABLE_1236767 tptp.int)) (= (= BOUND_VARIABLE_1236766 BOUND_VARIABLE_1236767) (ho_4310 (ho_4309 k_5275 BOUND_VARIABLE_1236766) BOUND_VARIABLE_1236767))))) (let ((_let_2884 (forall ((BOUND_VARIABLE_1236759 tptp.int) (BOUND_VARIABLE_1236760 tptp.int)) (= (= BOUND_VARIABLE_1236759 BOUND_VARIABLE_1236760) (ho_4310 (ho_4309 k_5276 BOUND_VARIABLE_1236759) BOUND_VARIABLE_1236760))))) (let ((_let_2885 (forall ((BOUND_VARIABLE_1236752 Bool) (BOUND_VARIABLE_1236753 Bool)) (= (= BOUND_VARIABLE_1236752 BOUND_VARIABLE_1236753) (ho_5154 (ho_5178 k_5277 BOUND_VARIABLE_1236752) BOUND_VARIABLE_1236753))))) (let ((_let_2886 (forall ((BOUND_VARIABLE_1236745 tptp.num) (BOUND_VARIABLE_1236746 tptp.num)) (= (= BOUND_VARIABLE_1236745 BOUND_VARIABLE_1236746) (ho_5280 (ho_5279 k_5278 BOUND_VARIABLE_1236745) BOUND_VARIABLE_1236746))))) (let ((_let_2887 (forall ((BOUND_VARIABLE_1236738 tptp.num) (BOUND_VARIABLE_1236739 tptp.num)) (= (= BOUND_VARIABLE_1236738 BOUND_VARIABLE_1236739) (ho_5280 (ho_5279 k_5281 BOUND_VARIABLE_1236738) BOUND_VARIABLE_1236739))))) (let ((_let_2888 (forall ((BOUND_VARIABLE_1236731 tptp.int) (BOUND_VARIABLE_1236732 tptp.int)) (= (= BOUND_VARIABLE_1236731 BOUND_VARIABLE_1236732) (ho_4310 (ho_4309 k_5282 BOUND_VARIABLE_1236731) BOUND_VARIABLE_1236732))))) (let ((_let_2889 (forall ((BOUND_VARIABLE_1236716 tptp.num) (BOUND_VARIABLE_1236717 tptp.num)) (= (ho_4209 (ho_4211 k_4210 (ho_4196 k_4195 BOUND_VARIABLE_1236716)) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4196 k_4195 BOUND_VARIABLE_1236717))) (ho_4196 (ho_5284 k_5283 BOUND_VARIABLE_1236716) BOUND_VARIABLE_1236717))))) (let ((_let_2890 (forall ((BOUND_VARIABLE_1236701 tptp.num) (BOUND_VARIABLE_1236702 tptp.num)) (= (ho_4209 (ho_4211 k_4210 (ho_4196 k_4195 BOUND_VARIABLE_1236701)) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4196 k_4195 BOUND_VARIABLE_1236702))) (ho_4196 (ho_5284 k_5285 BOUND_VARIABLE_1236701) BOUND_VARIABLE_1236702))))) (let ((_let_2891 (forall ((BOUND_VARIABLE_1236694 tptp.int) (BOUND_VARIABLE_1236695 tptp.int)) (= (= BOUND_VARIABLE_1236694 BOUND_VARIABLE_1236695) (ho_4310 (ho_4309 k_5286 BOUND_VARIABLE_1236694) BOUND_VARIABLE_1236695))))) (let ((_let_2892 (forall ((BOUND_VARIABLE_1236687 tptp.int) (BOUND_VARIABLE_1236688 tptp.int)) (= (= BOUND_VARIABLE_1236687 BOUND_VARIABLE_1236688) (ho_4310 (ho_4309 k_5287 BOUND_VARIABLE_1236687) BOUND_VARIABLE_1236688))))) (let ((_let_2893 (forall ((BOUND_VARIABLE_1236680 tptp.int) (BOUND_VARIABLE_1236681 tptp.int)) (= (= BOUND_VARIABLE_1236680 BOUND_VARIABLE_1236681) (ho_4310 (ho_4309 k_5288 BOUND_VARIABLE_1236680) BOUND_VARIABLE_1236681))))) (let ((_let_2894 (forall ((BOUND_VARIABLE_1236673 tptp.nat) (BOUND_VARIABLE_1236674 tptp.nat)) (= (= BOUND_VARIABLE_1236673 BOUND_VARIABLE_1236674) (ho_4288 (ho_4287 k_5289 BOUND_VARIABLE_1236673) BOUND_VARIABLE_1236674))))) (let ((_let_2895 (forall ((BOUND_VARIABLE_1236666 tptp.nat) (BOUND_VARIABLE_1236667 tptp.nat)) (= (= BOUND_VARIABLE_1236666 BOUND_VARIABLE_1236667) (ho_4288 (ho_4287 k_5290 BOUND_VARIABLE_1236666) BOUND_VARIABLE_1236667))))) (let ((_let_2896 (forall ((BOUND_VARIABLE_1236659 tptp.nat) (BOUND_VARIABLE_1236660 tptp.nat)) (= (= BOUND_VARIABLE_1236659 BOUND_VARIABLE_1236660) (ho_4288 (ho_4287 k_5291 BOUND_VARIABLE_1236659) BOUND_VARIABLE_1236660))))) (let ((_let_2897 (forall ((BOUND_VARIABLE_1236652 tptp.int) (BOUND_VARIABLE_1236653 tptp.int)) (= (= BOUND_VARIABLE_1236652 BOUND_VARIABLE_1236653) (ho_4310 (ho_4309 k_5292 BOUND_VARIABLE_1236652) BOUND_VARIABLE_1236653))))) (let ((_let_2898 (forall ((BOUND_VARIABLE_1236645 tptp.int) (BOUND_VARIABLE_1236646 tptp.int)) (= (= BOUND_VARIABLE_1236645 BOUND_VARIABLE_1236646) (ho_4310 (ho_4309 k_5293 BOUND_VARIABLE_1236645) BOUND_VARIABLE_1236646))))) (let ((_let_2899 (forall ((BOUND_VARIABLE_1236638 tptp.int)) (= (ho_4209 k_5294 BOUND_VARIABLE_1236638) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1236638) BOUND_VARIABLE_1236638))))) (let ((_let_2900 (forall ((BOUND_VARIABLE_1236631 tptp.int)) (= (ho_4209 k_5295 BOUND_VARIABLE_1236631) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1236631) BOUND_VARIABLE_1236631))))) (let ((_let_2901 (forall ((BOUND_VARIABLE_1236624 tptp.nat) (BOUND_VARIABLE_1236625 tptp.nat)) (= (= BOUND_VARIABLE_1236624 BOUND_VARIABLE_1236625) (ho_4288 (ho_4287 k_5296 BOUND_VARIABLE_1236624) BOUND_VARIABLE_1236625))))) (let ((_let_2902 (forall ((BOUND_VARIABLE_1236617 tptp.nat) (BOUND_VARIABLE_1236618 tptp.nat)) (= (= BOUND_VARIABLE_1236617 BOUND_VARIABLE_1236618) (ho_4288 (ho_4287 k_5297 BOUND_VARIABLE_1236617) BOUND_VARIABLE_1236618))))) (let ((_let_2903 (forall ((BOUND_VARIABLE_1236610 tptp.nat) (BOUND_VARIABLE_1236611 tptp.nat)) (= (= BOUND_VARIABLE_1236610 BOUND_VARIABLE_1236611) (ho_4288 (ho_4287 k_5298 BOUND_VARIABLE_1236610) BOUND_VARIABLE_1236611))))) (let ((_let_2904 (forall ((BOUND_VARIABLE_1236603 tptp.nat) (BOUND_VARIABLE_1236604 tptp.nat)) (= (= BOUND_VARIABLE_1236603 BOUND_VARIABLE_1236604) (ho_4288 (ho_4287 k_5299 BOUND_VARIABLE_1236603) BOUND_VARIABLE_1236604))))) (let ((_let_2905 (forall ((BOUND_VARIABLE_1236596 tptp.nat) (BOUND_VARIABLE_1236597 tptp.nat)) (= (= BOUND_VARIABLE_1236596 BOUND_VARIABLE_1236597) (ho_4288 (ho_4287 k_5300 BOUND_VARIABLE_1236596) BOUND_VARIABLE_1236597))))) (let ((_let_2906 (forall ((BOUND_VARIABLE_1236589 tptp.int) (BOUND_VARIABLE_1236590 tptp.int)) (= (= BOUND_VARIABLE_1236589 BOUND_VARIABLE_1236590) (ho_4310 (ho_4309 k_5301 BOUND_VARIABLE_1236589) BOUND_VARIABLE_1236590))))) (let ((_let_2907 (forall ((BOUND_VARIABLE_1236582 tptp.int) (BOUND_VARIABLE_1236583 tptp.int)) (= (= BOUND_VARIABLE_1236582 BOUND_VARIABLE_1236583) (ho_4310 (ho_4309 k_5302 BOUND_VARIABLE_1236582) BOUND_VARIABLE_1236583))))) (let ((_let_2908 (forall ((BOUND_VARIABLE_1236575 tptp.int) (BOUND_VARIABLE_1236576 tptp.int)) (= (= BOUND_VARIABLE_1236575 BOUND_VARIABLE_1236576) (ho_4310 (ho_4309 k_5303 BOUND_VARIABLE_1236575) BOUND_VARIABLE_1236576))))) (let ((_let_2909 (forall ((BOUND_VARIABLE_1236568 tptp.nat) (BOUND_VARIABLE_1236569 tptp.nat)) (= (= BOUND_VARIABLE_1236568 BOUND_VARIABLE_1236569) (ho_4288 (ho_4287 k_5304 BOUND_VARIABLE_1236568) BOUND_VARIABLE_1236569))))) (let ((_let_2910 (forall ((BOUND_VARIABLE_1236561 tptp.nat) (BOUND_VARIABLE_1236562 tptp.nat)) (= (= BOUND_VARIABLE_1236561 BOUND_VARIABLE_1236562) (ho_4288 (ho_4287 k_5305 BOUND_VARIABLE_1236561) BOUND_VARIABLE_1236562))))) (let ((_let_2911 (forall ((BOUND_VARIABLE_1236554 tptp.nat) (BOUND_VARIABLE_1236555 tptp.nat)) (= (= BOUND_VARIABLE_1236554 BOUND_VARIABLE_1236555) (ho_4288 (ho_4287 k_5306 BOUND_VARIABLE_1236554) BOUND_VARIABLE_1236555))))) (let ((_let_2912 (forall ((BOUND_VARIABLE_1236547 tptp.nat) (BOUND_VARIABLE_1236548 tptp.nat)) (= (= BOUND_VARIABLE_1236547 BOUND_VARIABLE_1236548) (ho_4288 (ho_4287 k_5307 BOUND_VARIABLE_1236547) BOUND_VARIABLE_1236548))))) (let ((_let_2913 (forall ((BOUND_VARIABLE_1236540 tptp.nat) (BOUND_VARIABLE_1236541 tptp.nat)) (= (= BOUND_VARIABLE_1236540 BOUND_VARIABLE_1236541) (ho_4288 (ho_4287 k_5308 BOUND_VARIABLE_1236540) BOUND_VARIABLE_1236541))))) (let ((_let_2914 (forall ((BOUND_VARIABLE_1236533 Bool) (BOUND_VARIABLE_1236534 Bool)) (= (= BOUND_VARIABLE_1236533 BOUND_VARIABLE_1236534) (ho_5154 (ho_5178 k_5309 BOUND_VARIABLE_1236533) BOUND_VARIABLE_1236534))))) (let ((_let_2915 (forall ((BOUND_VARIABLE_1292672 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292670 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236520 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1292672 BOUND_VARIABLE_1236520)) (ho_4316 BOUND_VARIABLE_1292670 BOUND_VARIABLE_1236520)) (ho_4316 (ho_4249 (ho_4260 k_5310 BOUND_VARIABLE_1292672) BOUND_VARIABLE_1292670) BOUND_VARIABLE_1236520))))) (let ((_let_2916 (forall ((BOUND_VARIABLE_1292688 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292686 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236505 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1292688 BOUND_VARIABLE_1236505)) (ho_4316 BOUND_VARIABLE_1292686 BOUND_VARIABLE_1236505)) (ho_4316 (ho_4249 (ho_4260 k_5311 BOUND_VARIABLE_1292688) BOUND_VARIABLE_1292686) BOUND_VARIABLE_1236505))))) (let ((_let_2917 (forall ((BOUND_VARIABLE_1292702 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236493 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4435) (ho_4316 BOUND_VARIABLE_1292702 BOUND_VARIABLE_1236493)) (ho_4316 (ho_4249 k_5312 BOUND_VARIABLE_1292702) BOUND_VARIABLE_1236493))))) (let ((_let_2918 (forall ((BOUND_VARIABLE_1292713 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236482 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4435) (ho_4316 BOUND_VARIABLE_1292713 BOUND_VARIABLE_1236482)) (ho_4316 (ho_4249 k_5313 BOUND_VARIABLE_1292713) BOUND_VARIABLE_1236482))))) (let ((_let_2919 (forall ((BOUND_VARIABLE_1292726 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292724 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236468 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4443) (ho_4316 BOUND_VARIABLE_1292726 BOUND_VARIABLE_1236468)) (ho_4316 BOUND_VARIABLE_1292724 BOUND_VARIABLE_1236468)) (ho_4316 (ho_4249 (ho_4260 k_5314 BOUND_VARIABLE_1292726) BOUND_VARIABLE_1292724) BOUND_VARIABLE_1236468))))) (let ((_let_2920 (forall ((BOUND_VARIABLE_1292742 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292740 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236453 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4443) (ho_4316 BOUND_VARIABLE_1292742 BOUND_VARIABLE_1236453)) (ho_4316 BOUND_VARIABLE_1292740 BOUND_VARIABLE_1236453)) (ho_4316 (ho_4249 (ho_4260 k_5315 BOUND_VARIABLE_1292742) BOUND_VARIABLE_1292740) BOUND_VARIABLE_1236453))))) (let ((_let_2921 (forall ((BOUND_VARIABLE_1292759 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292756 |u_(-> tptp.nat tptp.rat)|)) (= (and (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_235021 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_2 (ho_4441 _let_1 k_4435))) (let ((_let_3 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443))) (let ((_let_4 (ho_4442 (ho_4448 _let_3 (ho_4316 BOUND_VARIABLE_1292759 M6)) (ho_4442 _let_2 (ho_4316 BOUND_VARIABLE_1292759 BOUND_VARIABLE_235021))))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_5 _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_5))))) (let ((_let_8 (ho_4442 (ho_4448 _let_3 _let_7) (ho_4442 _let_2 _let_7)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_8 (ho_4442 (ho_4448 k_5252 _let_8) _let_4)) (not (= _let_8 _let_4)))) (ho_4442 _let_2 _let_4)) _let_4))) (let ((_let_10 (ho_4292 k_4304 (ho_4290 k_4289 K3)))) (or (not (ho_4293 _let_10 (ho_4290 k_4289 M6))) (not (ho_4293 _let_10 (ho_4290 k_4289 BOUND_VARIABLE_235021))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_9)) (not (= R5 _let_9))))))))))))))))))))))))) (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_235021 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_2 (ho_4441 _let_1 k_4435))) (let ((_let_3 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443))) (let ((_let_4 (ho_4442 (ho_4448 _let_3 (ho_4316 BOUND_VARIABLE_1292756 M6)) (ho_4442 _let_2 (ho_4316 BOUND_VARIABLE_1292756 BOUND_VARIABLE_235021))))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_5 _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_5))))) (let ((_let_8 (ho_4442 (ho_4448 _let_3 _let_7) (ho_4442 _let_2 _let_7)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_8 (ho_4442 (ho_4448 k_5252 _let_8) _let_4)) (not (= _let_8 _let_4)))) (ho_4442 _let_2 _let_4)) _let_4))) (let ((_let_10 (ho_4292 k_4304 (ho_4290 k_4289 K3)))) (or (not (ho_4293 _let_10 (ho_4290 k_4289 M6))) (not (ho_4293 _let_10 (ho_4290 k_4289 BOUND_VARIABLE_235021))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_9)) (not (= R5 _let_9))))))))))))))))))))))))) (forall ((R5 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_2 (ho_4441 _let_1 k_4435))) (let ((_let_3 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443))) (let ((_let_4 (ho_4442 (ho_4448 _let_3 (ho_4316 BOUND_VARIABLE_1292759 N2)) (ho_4442 _let_2 (ho_4316 BOUND_VARIABLE_1292756 N2))))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_5 _let_6)) (ho_4428 (ho_4427 k_4426 _let_6) _let_5)) (ho_4428 (ho_4427 k_4426 _let_5) _let_5))))) (let ((_let_8 (ho_4442 (ho_4448 _let_3 _let_7) (ho_4442 _let_2 _let_7)))) (let ((_let_9 (ho_4442 (ho_4448 (ho_5050 k_5049 (and (= _let_8 (ho_4442 (ho_4448 k_5252 _let_8) _let_4)) (not (= _let_8 _let_4)))) (ho_4442 _let_2 _let_4)) _let_4))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 K3)) (ho_4290 k_4289 N2))) (and (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_9)) (not (= R5 _let_9))))))))))))))))))))))))) (ho_5268 (ho_5317 k_5316 BOUND_VARIABLE_1292759) BOUND_VARIABLE_1292756))))) (let ((_let_2922 (forall ((BOUND_VARIABLE_1236284 Bool) (BOUND_VARIABLE_1236285 Bool)) (= (= BOUND_VARIABLE_1236284 BOUND_VARIABLE_1236285) (ho_5154 (ho_5178 k_5318 BOUND_VARIABLE_1236284) BOUND_VARIABLE_1236285))))) (let ((_let_2923 (forall ((BOUND_VARIABLE_1292856 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235573 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292856 N2))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_235573)) (ho_4290 k_4289 N2))) (and (= _let_1 (ho_4442 (ho_4448 k_5252 _let_1) R5)) (not (= R5 _let_1))))))))))))))) (ho_5268 k_5319 BOUND_VARIABLE_1292856))))) (let ((_let_2924 (forall ((BOUND_VARIABLE_1292886 |u_(-> tptp.nat tptp.rat)|)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235602 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4316 BOUND_VARIABLE_1292886 N2))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_235602)) (ho_4290 k_4289 N2))) (and (= _let_1 (ho_4442 (ho_4448 k_5252 _let_1) R5)) (not (= R5 _let_1))))))))))))))) (ho_5268 k_5320 BOUND_VARIABLE_1292886))))) (let ((_let_2925 (forall ((BOUND_VARIABLE_1292918 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292916 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236217 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1292918 BOUND_VARIABLE_1236217)) (ho_4316 BOUND_VARIABLE_1292916 BOUND_VARIABLE_1236217)) (ho_4316 (ho_4249 (ho_4260 k_5321 BOUND_VARIABLE_1292918) BOUND_VARIABLE_1292916) BOUND_VARIABLE_1236217))))) (let ((_let_2926 (forall ((BOUND_VARIABLE_1292934 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1292932 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236202 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4443) (ho_4316 BOUND_VARIABLE_1292934 BOUND_VARIABLE_1236202)) (ho_4316 BOUND_VARIABLE_1292932 BOUND_VARIABLE_1236202)) (ho_4316 (ho_4249 (ho_4260 k_5322 BOUND_VARIABLE_1292934) BOUND_VARIABLE_1292932) BOUND_VARIABLE_1236202))))) (let ((_let_2927 (forall ((BOUND_VARIABLE_1292948 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236190 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4435) (ho_4316 BOUND_VARIABLE_1292948 BOUND_VARIABLE_1236190)) (ho_4316 (ho_4249 k_5323 BOUND_VARIABLE_1292948) BOUND_VARIABLE_1236190))))) (let ((_let_2928 (forall ((BOUND_VARIABLE_1236182 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_5324 BOUND_VARIABLE_1236182))))))))) (let ((_let_2929 (forall ((BOUND_VARIABLE_1292964 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236172 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1292964 BOUND_VARIABLE_1236172)) (ho_4316 (ho_4249 k_5325 BOUND_VARIABLE_1292964) BOUND_VARIABLE_1236172))))) (let ((_let_2930 (forall ((BOUND_VARIABLE_1236129 tptp.real) (BOUND_VARIABLE_1236130 tptp.real)) (= (not (forall ((R5 tptp.rat) (BOUND_VARIABLE_235444 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (or (not (= R5 (ho_4442 (ho_4448 k_5252 R5) _let_5))) (= R5 _let_5) (not (forall ((N2 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4316 (ho_4253 k_4252 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) BOUND_VARIABLE_1236130) (ho_4258 (ho_4257 _let_1 k_4248) BOUND_VARIABLE_1236129))) N2))) (or (not (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_235444)) (ho_4290 k_4289 N2))) (and (= _let_2 (ho_4442 (ho_4448 k_5252 _let_2) R5)) (not (= R5 _let_2)))))))))))))))) (ho_4351 (ho_4508 k_5326 BOUND_VARIABLE_1236129) BOUND_VARIABLE_1236130))))) (let ((_let_2931 (forall ((BOUND_VARIABLE_1292999 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236119 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4449) (ho_4316 BOUND_VARIABLE_1292999 BOUND_VARIABLE_1236119)) (ho_4316 (ho_4249 k_5327 BOUND_VARIABLE_1292999) BOUND_VARIABLE_1236119))))) (let ((_let_2932 (forall ((BOUND_VARIABLE_1293013 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1293010 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236103 tptp.nat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443) (ho_4316 BOUND_VARIABLE_1293013 BOUND_VARIABLE_1236103)) (ho_4442 (ho_4441 _let_1 k_4435) (ho_4316 BOUND_VARIABLE_1293010 BOUND_VARIABLE_1236103))) (ho_4316 (ho_4249 (ho_4260 k_5328 BOUND_VARIABLE_1293013) BOUND_VARIABLE_1293010) BOUND_VARIABLE_1236103)))))) (let ((_let_2933 (forall ((BOUND_VARIABLE_1293029 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1293027 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236088 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1293029 BOUND_VARIABLE_1236088)) (ho_4316 BOUND_VARIABLE_1293027 BOUND_VARIABLE_1236088)) (ho_4316 (ho_4249 (ho_4260 k_5329 BOUND_VARIABLE_1293029) BOUND_VARIABLE_1293027) BOUND_VARIABLE_1236088))))) (let ((_let_2934 (forall ((BOUND_VARIABLE_1293045 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1293043 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236073 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4443) (ho_4316 BOUND_VARIABLE_1293045 BOUND_VARIABLE_1236073)) (ho_4316 BOUND_VARIABLE_1293043 BOUND_VARIABLE_1236073)) (ho_4316 (ho_4249 (ho_4260 k_5330 BOUND_VARIABLE_1293045) BOUND_VARIABLE_1293043) BOUND_VARIABLE_1236073))))) (let ((_let_2935 (forall ((BOUND_VARIABLE_1293059 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1236061 tptp.nat)) (= (ho_4442 (ho_4441 (ho_4440 (ho_4439 k_4438 k_4436) k_4433) k_4435) (ho_4316 BOUND_VARIABLE_1293059 BOUND_VARIABLE_1236061)) (ho_4316 (ho_4249 k_5331 BOUND_VARIABLE_1293059) BOUND_VARIABLE_1236061))))) (let ((_let_2936 (forall ((BOUND_VARIABLE_1236053 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (= (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))) (ho_4316 k_5332 BOUND_VARIABLE_1236053))))))) (let ((_let_2937 (forall ((BOUND_VARIABLE_1236046 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)) (ho_4316 k_5333 BOUND_VARIABLE_1236046))))))))) (let ((_let_2938 (forall ((BOUND_VARIABLE_1236027 tptp.nat)) (= (ho_4251 k_4250 (ho_4338 k_4459 BOUND_VARIABLE_1236027)) (ho_4245 k_5334 BOUND_VARIABLE_1236027))))) (let ((_let_2939 (forall ((BOUND_VARIABLE_1236010 tptp.list_int) (BOUND_VARIABLE_1236011 tptp.int)) (= (ho_4310 (ho_5149 k_5335 BOUND_VARIABLE_1236010) BOUND_VARIABLE_1236011) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1236011 (ho_4335 (ho_4640 k_4639 BOUND_VARIABLE_1236010) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 BOUND_VARIABLE_1236010))))))))))) (let ((_let_2940 (forall ((BOUND_VARIABLE_1235993 tptp.list_nat) (BOUND_VARIABLE_1235994 tptp.nat)) (= (ho_4288 (ho_5151 k_5336 BOUND_VARIABLE_1235993) BOUND_VARIABLE_1235994) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1235994 (ho_4216 (ho_4468 k_4467 BOUND_VARIABLE_1235993) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 BOUND_VARIABLE_1235993))))))))))) (let ((_let_2941 (forall ((BOUND_VARIABLE_1235937 tptp.nat) (BOUND_VARIABLE_1235938 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235937) _let_2))) (let ((_let_5 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235938) _let_2)))) _let_2))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_5) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) _let_2)))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) _let_4)) (ho_4216 (ho_4215 k_5337 BOUND_VARIABLE_1235937) BOUND_VARIABLE_1235938)))))))))) (let ((_let_2942 (forall ((BOUND_VARIABLE_1235920 tptp.nat) (BOUND_VARIABLE_1235921 tptp.nat) (BOUND_VARIABLE_1235922 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 BOUND_VARIABLE_1235922))) (let ((_let_2 (ho_4290 k_4289 BOUND_VARIABLE_1235921))) (let ((_let_3 (ho_4290 k_4289 BOUND_VARIABLE_1235920))) (= (ho_4288 (ho_4287 (ho_4303 k_5338 BOUND_VARIABLE_1235920) BOUND_VARIABLE_1235921) BOUND_VARIABLE_1235922) (and (ho_4293 (ho_4292 k_4291 _let_2) _let_3) (ho_4293 (ho_4292 k_4291 _let_1) _let_3) (ho_4293 (ho_4292 k_4304 _let_2) _let_1))))))))) (let ((_let_2943 (forall ((BOUND_VARIABLE_1235910 tptp.nat) (BOUND_VARIABLE_1235911 tptp.nat)) (= (ho_4288 (ho_4287 k_5339 BOUND_VARIABLE_1235910) BOUND_VARIABLE_1235911) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1235911)) (ho_4290 k_4289 BOUND_VARIABLE_1235910)))))) (let ((_let_2944 (forall ((BOUND_VARIABLE_1235890 tptp.nat) (BOUND_VARIABLE_1235891 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (= BOUND_VARIABLE_1235891 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235890) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4288 (ho_4287 k_5340 BOUND_VARIABLE_1235890) BOUND_VARIABLE_1235891)))))))) (let ((_let_2945 (forall ((BOUND_VARIABLE_1235841 tptp.nat) (BOUND_VARIABLE_1235842 tptp.nat) (BOUND_VARIABLE_1235843 tptp.nat) (BOUND_VARIABLE_1235844 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1235841) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235842) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235843) _let_2)))))) (or (not (= BOUND_VARIABLE_1235844 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_5341 BOUND_VARIABLE_1235841) BOUND_VARIABLE_1235842) BOUND_VARIABLE_1235843) BOUND_VARIABLE_1235844))))) (let ((_let_2946 (forall ((BOUND_VARIABLE_1235821 tptp.nat) (BOUND_VARIABLE_1235822 tptp.nat) (BOUND_VARIABLE_1235823 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5342 BOUND_VARIABLE_1235821) BOUND_VARIABLE_1235822) BOUND_VARIABLE_1235823) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1235821) BOUND_VARIABLE_1235822))) (or (not (= BOUND_VARIABLE_1235823 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_2947 (forall ((BOUND_VARIABLE_1235773 tptp.nat) (BOUND_VARIABLE_1235774 tptp.nat) (BOUND_VARIABLE_1235775 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1235773) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235773) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235774) _let_2)))))) (or (not (= BOUND_VARIABLE_1235775 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5343 BOUND_VARIABLE_1235773) BOUND_VARIABLE_1235774) BOUND_VARIABLE_1235775))))) (let ((_let_2948 (forall ((BOUND_VARIABLE_1235736 tptp.nat) (BOUND_VARIABLE_1235737 tptp.nat) (BOUND_VARIABLE_1235738 tptp.nat)) (= (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1235736 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235738) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))) (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1235737 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235738) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5344 BOUND_VARIABLE_1235736) BOUND_VARIABLE_1235737) BOUND_VARIABLE_1235738))))) (let ((_let_2949 (forall ((BOUND_VARIABLE_1235695 tptp.nat) (BOUND_VARIABLE_1235696 tptp.nat)) (let ((_let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4216 (ho_4215 k_5347 BOUND_VARIABLE_1235695) BOUND_VARIABLE_1235696) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1235696 _let_1)) _let_1) (ho_5346 k_5345 (ho_4516 k_4515 (ho_4287 (ho_4303 k_4460 BOUND_VARIABLE_1235696) BOUND_VARIABLE_1235695))))))))) (let ((_let_2950 (forall ((BOUND_VARIABLE_1235683 tptp.nat) (BOUND_VARIABLE_1235684 tptp.nat) (BOUND_VARIABLE_1235685 tptp.list_nat)) (= (ho_5351 (ho_5350 (ho_5349 k_5348 BOUND_VARIABLE_1235683) BOUND_VARIABLE_1235684) BOUND_VARIABLE_1235685) (and (= BOUND_VARIABLE_1235683 (ho_4466 k_4465 BOUND_VARIABLE_1235685)) (= BOUND_VARIABLE_1235684 (ho_4466 k_5352 BOUND_VARIABLE_1235685))))))) (let ((_let_2951 (forall ((BOUND_VARIABLE_1235671 tptp.nat) (BOUND_VARIABLE_1235672 tptp.nat) (BOUND_VARIABLE_1235673 tptp.list_nat)) (= (ho_5351 (ho_5350 (ho_5349 k_5353 BOUND_VARIABLE_1235671) BOUND_VARIABLE_1235672) BOUND_VARIABLE_1235673) (and (= BOUND_VARIABLE_1235671 (ho_4466 k_4465 BOUND_VARIABLE_1235673)) (= BOUND_VARIABLE_1235672 (ho_4466 k_5352 BOUND_VARIABLE_1235673))))))) (let ((_let_2952 (forall ((BOUND_VARIABLE_1235657 tptp.nat) (BOUND_VARIABLE_1235658 tptp.nat) (BOUND_VARIABLE_1235659 tptp.list_nat)) (= (ho_5351 (ho_5350 (ho_5349 k_5354 BOUND_VARIABLE_1235657) BOUND_VARIABLE_1235658) BOUND_VARIABLE_1235659) (and (= (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1235657) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4466 k_4465 BOUND_VARIABLE_1235659)) (= BOUND_VARIABLE_1235658 (ho_4466 k_5352 BOUND_VARIABLE_1235659))))))) (let ((_let_2953 (forall ((BOUND_VARIABLE_1235631 tptp.nat) (BOUND_VARIABLE_1235632 tptp.nat) (BOUND_VARIABLE_1235633 tptp.list_nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (= BOUND_VARIABLE_1235631 (ho_4466 k_4465 BOUND_VARIABLE_1235633)) (= BOUND_VARIABLE_1235632 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4466 k_5352 BOUND_VARIABLE_1235633)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_5351 (ho_5350 (ho_5349 k_5355 BOUND_VARIABLE_1235631) BOUND_VARIABLE_1235632) BOUND_VARIABLE_1235633)))))))) (let ((_let_2954 (forall ((BOUND_VARIABLE_1235626 tptp.nat)) (= BOUND_VARIABLE_1235626 (ho_4216 k_5356 BOUND_VARIABLE_1235626))))) (let ((_let_2955 (forall ((BOUND_VARIABLE_1235606 tptp.nat) (BOUND_VARIABLE_1235607 tptp.nat) (BOUND_VARIABLE_1235608 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5357 BOUND_VARIABLE_1235606) BOUND_VARIABLE_1235607) BOUND_VARIABLE_1235608) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1235606) BOUND_VARIABLE_1235607))) (or (not (= BOUND_VARIABLE_1235608 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_2956 (forall ((BOUND_VARIABLE_1235561 tptp.nat) (BOUND_VARIABLE_1235562 tptp.nat) (BOUND_VARIABLE_1235563 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235561) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1235562))) (or (not (= BOUND_VARIABLE_1235563 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5358 BOUND_VARIABLE_1235561) BOUND_VARIABLE_1235562) BOUND_VARIABLE_1235563))))) (let ((_let_2957 (forall ((BOUND_VARIABLE_1235506 tptp.nat) (BOUND_VARIABLE_1235507 tptp.nat) (BOUND_VARIABLE_1235508 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235506) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235507) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1235508 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5359 BOUND_VARIABLE_1235506) BOUND_VARIABLE_1235507) BOUND_VARIABLE_1235508))))) (let ((_let_2958 (forall ((BOUND_VARIABLE_1235461 tptp.nat) (BOUND_VARIABLE_1235462 tptp.nat) (BOUND_VARIABLE_1235463 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235461) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1235462))) (or (not (= BOUND_VARIABLE_1235463 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5360 BOUND_VARIABLE_1235461) BOUND_VARIABLE_1235462) BOUND_VARIABLE_1235463))))) (let ((_let_2959 (forall ((BOUND_VARIABLE_1235406 tptp.nat) (BOUND_VARIABLE_1235407 tptp.nat) (BOUND_VARIABLE_1235408 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235406) _let_2)) _let_4))) _let_2)) _let_4))) BOUND_VARIABLE_1235407))) (or (not (= BOUND_VARIABLE_1235408 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5361 BOUND_VARIABLE_1235406) BOUND_VARIABLE_1235407) BOUND_VARIABLE_1235408))))) (let ((_let_2960 (forall ((BOUND_VARIABLE_1235351 tptp.nat) (BOUND_VARIABLE_1235352 tptp.nat) (BOUND_VARIABLE_1235353 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235351) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235352) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1235353 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5362 BOUND_VARIABLE_1235351) BOUND_VARIABLE_1235352) BOUND_VARIABLE_1235353))))) (let ((_let_2961 (forall ((BOUND_VARIABLE_1235286 tptp.nat) (BOUND_VARIABLE_1235287 tptp.nat) (BOUND_VARIABLE_1235288 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235286) _let_2)) _let_4))) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235287) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1235288 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5363 BOUND_VARIABLE_1235286) BOUND_VARIABLE_1235287) BOUND_VARIABLE_1235288))))) (let ((_let_2962 (forall ((BOUND_VARIABLE_1235262 tptp.nat) (BOUND_VARIABLE_1235263 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1235263)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235262) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5364 BOUND_VARIABLE_1235262) BOUND_VARIABLE_1235263)))))))) (let ((_let_2963 (forall ((BOUND_VARIABLE_1235252 tptp.nat) (BOUND_VARIABLE_1235253 tptp.nat)) (= (ho_4288 (ho_4287 k_5365 BOUND_VARIABLE_1235252) BOUND_VARIABLE_1235253) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1235253)) (ho_4290 k_4289 BOUND_VARIABLE_1235252)))))) (let ((_let_2964 (forall ((BOUND_VARIABLE_1235228 tptp.nat) (BOUND_VARIABLE_1235229 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1235229)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235228) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5366 BOUND_VARIABLE_1235228) BOUND_VARIABLE_1235229)))))))) (let ((_let_2965 (forall ((BOUND_VARIABLE_1235218 tptp.nat) (BOUND_VARIABLE_1235219 tptp.nat)) (= (ho_4288 (ho_4287 k_5367 BOUND_VARIABLE_1235218) BOUND_VARIABLE_1235219) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1235219)) (ho_4290 k_4289 BOUND_VARIABLE_1235218)))))) (let ((_let_2966 (forall ((BOUND_VARIABLE_1235208 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1235208) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))) (ho_4216 k_5368 BOUND_VARIABLE_1235208))))))))) (let ((_let_2967 (forall ((BOUND_VARIABLE_1235189 tptp.nat)) (= (ho_4516 k_4515 (ho_4287 k_4461 BOUND_VARIABLE_1235189)) (ho_5370 k_5369 BOUND_VARIABLE_1235189))))) (let ((_let_2968 (forall ((BOUND_VARIABLE_1235140 tptp.nat)) (= (ho_4516 k_4515 (ho_4287 k_4469 BOUND_VARIABLE_1235140)) (ho_5370 k_5371 BOUND_VARIABLE_1235140))))) (let ((_let_2969 (forall ((BOUND_VARIABLE_1235121 tptp.nat)) (= (ho_4516 k_4515 (ho_4287 k_4470 BOUND_VARIABLE_1235121)) (ho_5370 k_5372 BOUND_VARIABLE_1235121))))) (let ((_let_2970 (forall ((BOUND_VARIABLE_1235082 tptp.nat)) (= (ho_4516 k_4515 (ho_4287 k_4471 BOUND_VARIABLE_1235082)) (ho_5370 k_5373 BOUND_VARIABLE_1235082))))) (let ((_let_2971 (forall ((BOUND_VARIABLE_1235048 tptp.nat) (BOUND_VARIABLE_1235049 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_5376 (ho_5379 (ho_5378 k_5377 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1235048)) (ho_4290 k_4289 BOUND_VARIABLE_1235049))) (ho_5376 (ho_5375 k_5374 BOUND_VARIABLE_1235048) (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235048) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1235049))) tptp.nil_nat) (ho_4464 (ho_4463 k_5380 BOUND_VARIABLE_1235048) BOUND_VARIABLE_1235049)))))))) (let ((_let_2972 (forall ((BOUND_VARIABLE_1235026 tptp.nat) (BOUND_VARIABLE_1235027 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235027) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1235026) _let_2))) (ho_4216 (ho_4215 k_5381 BOUND_VARIABLE_1235026) BOUND_VARIABLE_1235027)))))))) (let ((_let_2973 (forall ((BOUND_VARIABLE_1235006 tptp.nat) (BOUND_VARIABLE_1235007 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_5382 BOUND_VARIABLE_1235007) BOUND_VARIABLE_1235006)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (ho_4216 (ho_4215 k_5383 BOUND_VARIABLE_1235006) BOUND_VARIABLE_1235007)))))))) (let ((_let_2974 (forall ((BOUND_VARIABLE_1234986 tptp.nat) (BOUND_VARIABLE_1234987 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_5382 BOUND_VARIABLE_1234986) BOUND_VARIABLE_1234987)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (ho_4216 (ho_4215 k_5384 BOUND_VARIABLE_1234986) BOUND_VARIABLE_1234987)))))))) (let ((_let_2975 (forall ((BOUND_VARIABLE_1234979 tptp.int) (BOUND_VARIABLE_1234980 tptp.nat)) (= (ho_4316 (ho_4315 k_5385 BOUND_VARIABLE_1234979) BOUND_VARIABLE_1234980) (ho_4318 k_4317 BOUND_VARIABLE_1234979))))) (let ((_let_2976 (forall ((BOUND_VARIABLE_1234971 tptp.nat) (BOUND_VARIABLE_1234972 tptp.nat)) (= (ho_4216 (ho_4215 k_5386 BOUND_VARIABLE_1234971) BOUND_VARIABLE_1234972) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1234972) BOUND_VARIABLE_1234971))))) (let ((_let_2977 (forall ((BOUND_VARIABLE_1234918 tptp.nat) (BOUND_VARIABLE_1234919 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1234919 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5387 BOUND_VARIABLE_1234918) BOUND_VARIABLE_1234919) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1234919 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1234919) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1234919)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1234919)) BOUND_VARIABLE_1234919)) BOUND_VARIABLE_1234918)))))))))))))) (let ((_let_2978 (forall ((BOUND_VARIABLE_1293831 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1293830 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1234911 tptp.nat)) (= (ho_4245 (ho_5390 (ho_5389 k_5388 BOUND_VARIABLE_1293831) BOUND_VARIABLE_1293830) BOUND_VARIABLE_1234911) (ho_4245 BOUND_VARIABLE_1293831 (ho_4216 BOUND_VARIABLE_1293830 BOUND_VARIABLE_1234911)))))) (let ((_let_2979 (forall ((BOUND_VARIABLE_1234899 tptp.nat) (BOUND_VARIABLE_1234900 tptp.nat)) (= (ho_4216 (ho_4215 k_5391 BOUND_VARIABLE_1234899) BOUND_VARIABLE_1234900) (ho_4216 (ho_4215 k_4223 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1234899) BOUND_VARIABLE_1234900)) BOUND_VARIABLE_1234900))))) (let ((_let_2980 (forall ((BOUND_VARIABLE_1234877 tptp.nat) (BOUND_VARIABLE_1234878 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234877) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234878) _let_2))) (ho_4216 (ho_4215 k_5392 BOUND_VARIABLE_1234877) BOUND_VARIABLE_1234878)))))))) (let ((_let_2981 (forall ((BOUND_VARIABLE_1234859 tptp.int) (BOUND_VARIABLE_1234860 tptp.int)) (= (ho_4636 (ho_4635 k_5393 BOUND_VARIABLE_1234859) BOUND_VARIABLE_1234860) (ho_5396 (ho_5399 (ho_5398 k_5397 (= BOUND_VARIABLE_1234860 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1234859) BOUND_VARIABLE_1234860))) (ho_5396 (ho_5395 k_5394 BOUND_VARIABLE_1234859) (ho_4636 (ho_4635 k_4634 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1234859) (ho_4196 k_4195 tptp.one))) BOUND_VARIABLE_1234860))) tptp.nil_int))))) (let ((_let_2982 (forall ((BOUND_VARIABLE_1293909 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1234852 tptp.real)) (= (ho_4258 (ho_4946 k_5400 BOUND_VARIABLE_1293909) BOUND_VARIABLE_1234852) (ho_4258 k_5401 (ho_4258 BOUND_VARIABLE_1293909 BOUND_VARIABLE_1234852)))))) (let ((_let_2983 (forall ((BOUND_VARIABLE_1293921 |u_(-> tptp.real Bool)|) (BOUND_VARIABLE_1234837 tptp.real) (BOUND_VARIABLE_1234838 tptp.real)) (= (ho_4351 BOUND_VARIABLE_1293921 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4259) BOUND_VARIABLE_1234838) BOUND_VARIABLE_1234837)) (ho_4351 (ho_4508 (ho_5403 k_5402 BOUND_VARIABLE_1293921) BOUND_VARIABLE_1234837) BOUND_VARIABLE_1234838))))) (let ((_let_2984 (forall ((BOUND_VARIABLE_1234814 tptp.real) (BOUND_VARIABLE_1234815 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 k_5404 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_2) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1234814) BOUND_VARIABLE_1234815))) (ho_4258 (ho_4265 _let_4 _let_2) (ho_4258 (ho_4257 _let_1 k_4274) BOUND_VARIABLE_1234815))) (ho_4258 (ho_4265 k_5405 BOUND_VARIABLE_1234814) BOUND_VARIABLE_1234815))))))))) (let ((_let_2985 (forall ((BOUND_VARIABLE_1293955 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1234805 tptp.nat) (BOUND_VARIABLE_1234806 tptp.real)) (= (ho_4258 (ho_4273 (ho_4272 k_5406 BOUND_VARIABLE_1293955) BOUND_VARIABLE_1234805) BOUND_VARIABLE_1234806) (ho_4245 (ho_4244 k_4243 (ho_4258 BOUND_VARIABLE_1293955 BOUND_VARIABLE_1234806)) BOUND_VARIABLE_1234805))))) (let ((_let_2986 (forall ((BOUND_VARIABLE_1293970 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1234784 tptp.nat) (BOUND_VARIABLE_1234785 tptp.real)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_4243 (ho_4258 BOUND_VARIABLE_1293970 BOUND_VARIABLE_1234785)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234784) _let_2)))) (ho_4258 (ho_4273 (ho_4272 k_5407 BOUND_VARIABLE_1293970) BOUND_VARIABLE_1234784) BOUND_VARIABLE_1234785)))))))) (let ((_let_2987 (forall ((BOUND_VARIABLE_1234766 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (= (ho_4351 k_5408 BOUND_VARIABLE_1234766) (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1234766)) (not (= BOUND_VARIABLE_1234766 _let_4))))))))))) (let ((_let_2988 (forall ((BOUND_VARIABLE_1234746 tptp.real) (BOUND_VARIABLE_1234747 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (= (ho_4258 (ho_4265 k_5404 (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) (ho_4247 k_4246 tptp.one)) (ho_4258 (ho_4265 (ho_4264 _let_2 k_4275) BOUND_VARIABLE_1234746) (ho_4258 (ho_4257 _let_1 k_4274) BOUND_VARIABLE_1234747)))) BOUND_VARIABLE_1234747) (ho_4258 (ho_4265 k_5409 BOUND_VARIABLE_1234746) BOUND_VARIABLE_1234747))))))) (let ((_let_2989 (forall ((BOUND_VARIABLE_1234729 tptp.nat) (BOUND_VARIABLE_1234730 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1234730) BOUND_VARIABLE_1234729)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 k_5410 BOUND_VARIABLE_1234730))) (ho_4258 (ho_4273 k_5411 BOUND_VARIABLE_1234729) BOUND_VARIABLE_1234730)))))) (let ((_let_2990 (forall ((BOUND_VARIABLE_1234719 tptp.nat) (BOUND_VARIABLE_1234720 tptp.nat)) (= (ho_4288 (ho_4287 k_5412 BOUND_VARIABLE_1234719) BOUND_VARIABLE_1234720) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1234719)) (ho_4290 k_4289 BOUND_VARIABLE_1234720)))))) (let ((_let_2991 (forall ((BOUND_VARIABLE_1294039 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1234695 tptp.nat) (BOUND_VARIABLE_1234696 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4288 BOUND_VARIABLE_1294039 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234696) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234695) _let_2)))) (ho_4288 (ho_4287 (ho_5414 k_5413 BOUND_VARIABLE_1294039) BOUND_VARIABLE_1234695) BOUND_VARIABLE_1234696)))))))) (let ((_let_2992 (forall ((BOUND_VARIABLE_1294062 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1234670 tptp.nat) (BOUND_VARIABLE_1234671 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4288 BOUND_VARIABLE_1294062 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234671) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234670) _let_2)))) (ho_4288 (ho_4287 (ho_5414 k_5415 BOUND_VARIABLE_1294062) BOUND_VARIABLE_1234670) BOUND_VARIABLE_1234671)))))))) (let ((_let_2993 (forall ((BOUND_VARIABLE_1294079 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1234650 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4288 BOUND_VARIABLE_1294079 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234650) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4288 (ho_5205 k_5416 BOUND_VARIABLE_1294079) BOUND_VARIABLE_1234650)))))))) (let ((_let_2994 (forall ((BOUND_VARIABLE_1294091 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234598 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4472 BOUND_VARIABLE_1294091)) (ho_4516 k_4515 (ho_4287 k_4474 BOUND_VARIABLE_1234598))) (ho_4245 (ho_4473 k_5417 BOUND_VARIABLE_1294091) BOUND_VARIABLE_1234598))))) (let ((_let_2995 (forall ((BOUND_VARIABLE_1294103 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234583 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234583)) (ho_4245 BOUND_VARIABLE_1294103 BOUND_VARIABLE_1234583)) (ho_4245 (ho_4473 k_5418 BOUND_VARIABLE_1294103) BOUND_VARIABLE_1234583)))))) (let ((_let_2996 (forall ((BOUND_VARIABLE_1294116 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234568 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234568)) (ho_4245 BOUND_VARIABLE_1294116 BOUND_VARIABLE_1234568)) (ho_4245 (ho_4473 k_5419 BOUND_VARIABLE_1294116) BOUND_VARIABLE_1234568)))))) (let ((_let_2997 (forall ((BOUND_VARIABLE_1294129 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234553 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234553)) (ho_4245 BOUND_VARIABLE_1294129 BOUND_VARIABLE_1234553)) (ho_4245 (ho_4473 k_5420 BOUND_VARIABLE_1294129) BOUND_VARIABLE_1234553)))))) (let ((_let_2998 (forall ((BOUND_VARIABLE_1234520 tptp.nat) (BOUND_VARIABLE_1234521 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1234521)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234520) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5421 BOUND_VARIABLE_1234520) BOUND_VARIABLE_1234521)))))))) (let ((_let_2999 (forall ((BOUND_VARIABLE_1294164 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234469 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4475 BOUND_VARIABLE_1294164)) (ho_4516 k_4515 (ho_4287 k_4476 BOUND_VARIABLE_1234469))) (ho_4245 (ho_4473 k_5422 BOUND_VARIABLE_1294164) BOUND_VARIABLE_1234469))))) (let ((_let_3000 (forall ((BOUND_VARIABLE_1294176 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234454 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234454)) (ho_4245 BOUND_VARIABLE_1294176 BOUND_VARIABLE_1234454)) (ho_4245 (ho_4473 k_5423 BOUND_VARIABLE_1294176) BOUND_VARIABLE_1234454)))))) (let ((_let_3001 (forall ((BOUND_VARIABLE_1294189 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234439 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234439)) (ho_4245 BOUND_VARIABLE_1294189 BOUND_VARIABLE_1234439)) (ho_4245 (ho_4473 k_5424 BOUND_VARIABLE_1294189) BOUND_VARIABLE_1234439)))))) (let ((_let_3002 (forall ((BOUND_VARIABLE_1234416 tptp.nat) (BOUND_VARIABLE_1234417 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1234417)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234416) _let_2))))) (ho_4288 (ho_4287 k_5425 BOUND_VARIABLE_1234416) BOUND_VARIABLE_1234417)))))))) (let ((_let_3003 (forall ((BOUND_VARIABLE_1294219 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234375 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4477 BOUND_VARIABLE_1294219)) (ho_4516 k_4515 (ho_4287 k_4478 BOUND_VARIABLE_1234375))) (ho_4245 (ho_4473 k_5426 BOUND_VARIABLE_1294219) BOUND_VARIABLE_1234375))))) (let ((_let_3004 (forall ((BOUND_VARIABLE_1294231 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234360 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234360)) (ho_4245 BOUND_VARIABLE_1294231 BOUND_VARIABLE_1234360)) (ho_4245 (ho_4473 k_5427 BOUND_VARIABLE_1294231) BOUND_VARIABLE_1234360)))))) (let ((_let_3005 (forall ((BOUND_VARIABLE_1234327 tptp.nat) (BOUND_VARIABLE_1234328 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1234328)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234327) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5428 BOUND_VARIABLE_1234327) BOUND_VARIABLE_1234328)))))))) (let ((_let_3006 (forall ((BOUND_VARIABLE_1294266 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234276 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4479 BOUND_VARIABLE_1294266)) (ho_4516 k_4515 (ho_4287 k_4480 BOUND_VARIABLE_1234276))) (ho_4245 (ho_4473 k_5429 BOUND_VARIABLE_1294266) BOUND_VARIABLE_1234276))))) (let ((_let_3007 (forall ((BOUND_VARIABLE_1294280 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234234 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4481 BOUND_VARIABLE_1294280)) (ho_4516 k_4515 (ho_4287 k_4482 BOUND_VARIABLE_1234234))) (ho_4245 (ho_4473 k_5430 BOUND_VARIABLE_1294280) BOUND_VARIABLE_1234234))))) (let ((_let_3008 (forall ((BOUND_VARIABLE_1294292 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234219 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234219)) (ho_4245 BOUND_VARIABLE_1294292 BOUND_VARIABLE_1234219)) (ho_4245 (ho_4473 k_5431 BOUND_VARIABLE_1294292) BOUND_VARIABLE_1234219)))))) (let ((_let_3009 (forall ((BOUND_VARIABLE_1294305 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234204 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234204)) (ho_4245 BOUND_VARIABLE_1294305 BOUND_VARIABLE_1234204)) (ho_4245 (ho_4473 k_5432 BOUND_VARIABLE_1294305) BOUND_VARIABLE_1234204)))))) (let ((_let_3010 (forall ((BOUND_VARIABLE_1294318 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234189 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234189)) (ho_4245 BOUND_VARIABLE_1294318 BOUND_VARIABLE_1234189)) (ho_4245 (ho_4473 k_5433 BOUND_VARIABLE_1294318) BOUND_VARIABLE_1234189)))))) (let ((_let_3011 (forall ((BOUND_VARIABLE_1234166 tptp.nat) (BOUND_VARIABLE_1234167 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1234167)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234166) _let_2))))) (ho_4288 (ho_4287 k_5434 BOUND_VARIABLE_1234166) BOUND_VARIABLE_1234167)))))))) (let ((_let_3012 (forall ((BOUND_VARIABLE_1234123 tptp.real) (BOUND_VARIABLE_1234124 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1234124) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4264 _let_7 k_4275))) (= (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 _let_5) (ho_4258 (ho_4257 _let_6 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) _let_4) (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) _let_5) (ho_4258 (ho_4257 _let_6 k_4248) _let_5)))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1234123) _let_4)) (ho_4245 (ho_4244 k_5435 BOUND_VARIABLE_1234123) BOUND_VARIABLE_1234124))))))))))))) (let ((_let_3013 (forall ((BOUND_VARIABLE_1294373 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234082 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4473 k_4483 BOUND_VARIABLE_1294373)) (ho_4516 k_4515 (ho_4287 k_4484 BOUND_VARIABLE_1234082))) (ho_4245 (ho_4473 k_5436 BOUND_VARIABLE_1294373) BOUND_VARIABLE_1234082))))) (let ((_let_3014 (forall ((BOUND_VARIABLE_1294385 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234067 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1234067)) (ho_4245 BOUND_VARIABLE_1294385 BOUND_VARIABLE_1234067)) (ho_4245 (ho_4473 k_5437 BOUND_VARIABLE_1294385) BOUND_VARIABLE_1234067)))))) (let ((_let_3015 (forall ((BOUND_VARIABLE_1294398 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1234041 tptp.nat)) (= (ho_4348 k_4347 (ho_4487 (ho_4486 k_4485 BOUND_VARIABLE_1294398) BOUND_VARIABLE_1234041)) (ho_4245 (ho_4473 k_5438 BOUND_VARIABLE_1294398) BOUND_VARIABLE_1234041))))) (let ((_let_3016 (forall ((BOUND_VARIABLE_1294418 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1294411 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1234008 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4264 _let_2 k_4275))) (let ((_let_4 (ho_4265 _let_3 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))))) (= (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) (ho_4245 BOUND_VARIABLE_1294418 BOUND_VARIABLE_1234008)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4258 (ho_4265 _let_3 (ho_4251 k_4250 (ho_4338 (ho_4489 k_4488 BOUND_VARIABLE_1294411) BOUND_VARIABLE_1234008))) (ho_4258 _let_4 (ho_4258 _let_4 (ho_4506 k_4505 k_4504)))))) (ho_4245 (ho_5441 (ho_5440 k_5439 BOUND_VARIABLE_1294418) BOUND_VARIABLE_1294411) BOUND_VARIABLE_1234008))))))))) (let ((_let_3017 (forall ((BOUND_VARIABLE_1294440 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233972 tptp.real) (BOUND_VARIABLE_1233973 tptp.nat)) (= (ho_4348 k_4347 (ho_4244 (ho_4492 (ho_4491 k_4490 BOUND_VARIABLE_1294440) BOUND_VARIABLE_1233973) BOUND_VARIABLE_1233972)) (ho_4245 (ho_4244 (ho_4512 k_5442 BOUND_VARIABLE_1294440) BOUND_VARIABLE_1233972) BOUND_VARIABLE_1233973))))) (let ((_let_3018 (forall ((BOUND_VARIABLE_1294462 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1294455 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1233938 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4264 _let_2 k_4275))) (let ((_let_4 (ho_4265 _let_3 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))))) (= (ho_4258 (ho_4265 (ho_4264 _let_2 k_4259) (ho_4245 BOUND_VARIABLE_1294462 BOUND_VARIABLE_1233938)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4258 (ho_4265 _let_3 (ho_4251 k_4250 (ho_4338 (ho_4489 k_4493 BOUND_VARIABLE_1294455) BOUND_VARIABLE_1233938))) (ho_4258 _let_4 (ho_4258 _let_4 (ho_4506 k_4505 k_4504)))))) (ho_4245 (ho_5441 (ho_5440 k_5443 BOUND_VARIABLE_1294462) BOUND_VARIABLE_1294455) BOUND_VARIABLE_1233938))))))))) (let ((_let_3019 (forall ((BOUND_VARIABLE_1294476 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233922 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233922)) (ho_4245 BOUND_VARIABLE_1294476 BOUND_VARIABLE_1233922)) (ho_4245 (ho_4473 k_5444 BOUND_VARIABLE_1294476) BOUND_VARIABLE_1233922)))))) (let ((_let_3020 (forall ((BOUND_VARIABLE_1294489 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233907 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233907)) (ho_4245 BOUND_VARIABLE_1294489 BOUND_VARIABLE_1233907)) (ho_4245 (ho_4473 k_5445 BOUND_VARIABLE_1294489) BOUND_VARIABLE_1233907)))))) (let ((_let_3021 (forall ((BOUND_VARIABLE_1233874 tptp.real) (BOUND_VARIABLE_1233875 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4265 (ho_4264 _let_4 k_4259) _let_1))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_8 (ho_4219 k_4218 k_4217))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) BOUND_VARIABLE_1233874) (ho_4258 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_8 BOUND_VARIABLE_1233875) _let_7)) (ho_4209 (ho_4220 _let_8 (ho_4213 k_4212 _let_6)) _let_7)))) (ho_4258 _let_5 (ho_4258 _let_3 _let_1))))))) (ho_4245 (ho_4244 k_5446 BOUND_VARIABLE_1233874) BOUND_VARIABLE_1233875))))))))))))) (let ((_let_3022 (forall ((BOUND_VARIABLE_1233850 tptp.real) (BOUND_VARIABLE_1233851 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4265 (ho_4264 _let_3 k_4259) _let_1))) (= (ho_4245 (ho_4244 k_4243 (ho_4258 _let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) BOUND_VARIABLE_1233850) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1233851) (ho_4258 _let_4 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))))) BOUND_VARIABLE_1233851) (ho_4245 (ho_4244 k_5447 BOUND_VARIABLE_1233850) BOUND_VARIABLE_1233851))))))))) (let ((_let_3023 (forall ((BOUND_VARIABLE_1233820 tptp.real) (BOUND_VARIABLE_1233821 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (= (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1233820) (ho_4258 _let_3 (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_7 BOUND_VARIABLE_1233821) _let_6)) (ho_4209 (ho_4220 _let_7 (ho_4213 k_4212 _let_5)) _let_6)))) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 _let_3 _let_1)))))) (ho_4245 (ho_4244 k_5448 BOUND_VARIABLE_1233820) BOUND_VARIABLE_1233821)))))))))))) (let ((_let_3024 (forall ((BOUND_VARIABLE_1233808 tptp.real) (BOUND_VARIABLE_1233809 tptp.nat)) (= (ho_4258 (ho_4257 (ho_4256 (ho_4255 k_4254 k_4252) k_4250) k_4274) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1233808) BOUND_VARIABLE_1233809)) (ho_4245 (ho_4244 k_5449 BOUND_VARIABLE_1233808) BOUND_VARIABLE_1233809))))) (let ((_let_3025 (forall ((BOUND_VARIABLE_1233791 tptp.real) (BOUND_VARIABLE_1233792 tptp.real) (BOUND_VARIABLE_1233793 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) BOUND_VARIABLE_1233791) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1233792) BOUND_VARIABLE_1233793))) (ho_4245 (ho_4244 (ho_5451 k_5450 BOUND_VARIABLE_1233791) BOUND_VARIABLE_1233792) BOUND_VARIABLE_1233793)))))) (let ((_let_3026 (forall ((BOUND_VARIABLE_1233763 tptp.real) (BOUND_VARIABLE_1233764 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (= (ho_4258 (ho_4265 _let_3 BOUND_VARIABLE_1233763) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 BOUND_VARIABLE_1233764) _let_5)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 _let_4)) _let_5)))) (ho_4258 (ho_4265 _let_3 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) (ho_4245 (ho_4244 k_5452 BOUND_VARIABLE_1233763) BOUND_VARIABLE_1233764))))))))))) (let ((_let_3027 (forall ((BOUND_VARIABLE_1233740 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3)))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (= (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1233740) _let_4)) (ho_4209 (ho_4220 _let_5 (ho_4213 k_4212 _let_3)) _let_4)))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (ho_4245 k_5453 BOUND_VARIABLE_1233740)))))))))) (let ((_let_3028 (forall ((BOUND_VARIABLE_1233712 tptp.real) (BOUND_VARIABLE_1233713 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4245 (ho_4244 k_5454 BOUND_VARIABLE_1233712) BOUND_VARIABLE_1233713) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1233713 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4494 BOUND_VARIABLE_1233713)) BOUND_VARIABLE_1233712)))))))) (let ((_let_3029 (forall ((BOUND_VARIABLE_1294625 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233702 tptp.nat)) (= (ho_4258 (ho_4257 (ho_4256 (ho_4255 k_4254 k_4252) k_4250) k_4274) (ho_4245 BOUND_VARIABLE_1294625 BOUND_VARIABLE_1233702)) (ho_4245 (ho_4473 k_5455 BOUND_VARIABLE_1294625) BOUND_VARIABLE_1233702))))) (let ((_let_3030 (forall ((BOUND_VARIABLE_1294639 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1294636 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233686 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_4245 BOUND_VARIABLE_1294639 BOUND_VARIABLE_1233686)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4245 BOUND_VARIABLE_1294636 BOUND_VARIABLE_1233686))) (ho_4245 (ho_4473 (ho_5457 k_5456 BOUND_VARIABLE_1294639) BOUND_VARIABLE_1294636) BOUND_VARIABLE_1233686)))))) (let ((_let_3031 (forall ((BOUND_VARIABLE_1233653 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (= (ho_4245 k_5458 BOUND_VARIABLE_1233653) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1233653 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_3) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4495 BOUND_VARIABLE_1233653)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1233653) _let_3)))))))))) (let ((_let_3032 (forall ((BOUND_VARIABLE_1233631 tptp.nat) (BOUND_VARIABLE_1233632 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233631) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233632) _let_2))) (ho_4216 (ho_4215 k_5459 BOUND_VARIABLE_1233631) BOUND_VARIABLE_1233632)))))))) (let ((_let_3033 (forall ((BOUND_VARIABLE_1233609 tptp.nat) (BOUND_VARIABLE_1233610 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233610) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233609) _let_2))) (ho_4216 (ho_4215 k_5460 BOUND_VARIABLE_1233609) BOUND_VARIABLE_1233610)))))))) (let ((_let_3034 (forall ((BOUND_VARIABLE_1294699 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233595 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233595)) (ho_4245 BOUND_VARIABLE_1294699 BOUND_VARIABLE_1233595)) (ho_4245 (ho_4473 k_5461 BOUND_VARIABLE_1294699) BOUND_VARIABLE_1233595)))))) (let ((_let_3035 (forall ((BOUND_VARIABLE_1294712 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233580 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233580)) (ho_4245 BOUND_VARIABLE_1294712 BOUND_VARIABLE_1233580)) (ho_4245 (ho_4473 k_5462 BOUND_VARIABLE_1294712) BOUND_VARIABLE_1233580)))))) (let ((_let_3036 (forall ((BOUND_VARIABLE_1233557 tptp.nat) (BOUND_VARIABLE_1233558 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233558)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233557) _let_2))))) (ho_4288 (ho_4287 k_5463 BOUND_VARIABLE_1233557) BOUND_VARIABLE_1233558)))))))) (let ((_let_3037 (forall ((BOUND_VARIABLE_1294740 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233543 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233543)) (ho_4245 BOUND_VARIABLE_1294740 BOUND_VARIABLE_1233543)) (ho_4245 (ho_4473 k_5464 BOUND_VARIABLE_1294740) BOUND_VARIABLE_1233543)))))) (let ((_let_3038 (forall ((BOUND_VARIABLE_1233510 tptp.nat) (BOUND_VARIABLE_1233511 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233511)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233510) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5465 BOUND_VARIABLE_1233510) BOUND_VARIABLE_1233511)))))))) (let ((_let_3039 (forall ((BOUND_VARIABLE_1294773 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233496 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233496)) (ho_4245 BOUND_VARIABLE_1294773 BOUND_VARIABLE_1233496)) (ho_4245 (ho_4473 k_5466 BOUND_VARIABLE_1294773) BOUND_VARIABLE_1233496)))))) (let ((_let_3040 (forall ((BOUND_VARIABLE_1294786 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233481 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233481)) (ho_4245 BOUND_VARIABLE_1294786 BOUND_VARIABLE_1233481)) (ho_4245 (ho_4473 k_5467 BOUND_VARIABLE_1294786) BOUND_VARIABLE_1233481)))))) (let ((_let_3041 (forall ((BOUND_VARIABLE_1233448 tptp.nat) (BOUND_VARIABLE_1233449 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233449)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233448) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5468 BOUND_VARIABLE_1233448) BOUND_VARIABLE_1233449)))))))) (let ((_let_3042 (forall ((BOUND_VARIABLE_1294819 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1233434 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233434)) (ho_4245 BOUND_VARIABLE_1294819 BOUND_VARIABLE_1233434)) (ho_4245 (ho_4473 k_5469 BOUND_VARIABLE_1294819) BOUND_VARIABLE_1233434)))))) (let ((_let_3043 (forall ((BOUND_VARIABLE_1233411 tptp.nat) (BOUND_VARIABLE_1233412 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233412)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233411) _let_2))))) (ho_4288 (ho_4287 k_5470 BOUND_VARIABLE_1233411) BOUND_VARIABLE_1233412)))))))) (let ((_let_3044 (forall ((BOUND_VARIABLE_1233371 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4348 k_4347 (ho_4244 k_4496 BOUND_VARIABLE_1233371))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4348 k_4347 (ho_4244 k_4497 BOUND_VARIABLE_1233371)))) (ho_4258 k_5471 BOUND_VARIABLE_1233371)))))) (let ((_let_3045 (forall ((BOUND_VARIABLE_1233343 tptp.nat) (BOUND_VARIABLE_1233344 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4273 k_5472 BOUND_VARIABLE_1233343) BOUND_VARIABLE_1233344) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1233343 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4498 BOUND_VARIABLE_1233343)) BOUND_VARIABLE_1233344)))))))) (let ((_let_3046 (forall ((BOUND_VARIABLE_1233320 tptp.real)) (= (ho_4348 k_4347 (ho_4244 k_4499 BOUND_VARIABLE_1233320)) (ho_4258 k_5473 BOUND_VARIABLE_1233320))))) (let ((_let_3047 (forall ((BOUND_VARIABLE_1233293 tptp.real) (BOUND_VARIABLE_1233294 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_4) k_4275) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4257 _let_4 k_4248) (ho_4247 k_4246 tptp.one))) BOUND_VARIABLE_1233294)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1233293) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233294) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2))))) (ho_4245 (ho_4244 k_5474 BOUND_VARIABLE_1233293) BOUND_VARIABLE_1233294))))))))) (let ((_let_3048 (forall ((BOUND_VARIABLE_1294918 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1233175 tptp.real) (BOUND_VARIABLE_1233176 tptp.nat) (BOUND_VARIABLE_1233177 tptp.nat) (BOUND_VARIABLE_1233178 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_9 (ho_4219 k_4218 k_4217))) (let ((_let_10 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_9 BOUND_VARIABLE_1233176) _let_8)) (ho_4209 (ho_4220 _let_9 _let_7) _let_8)))) BOUND_VARIABLE_1233177))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1294918 BOUND_VARIABLE_1233177) BOUND_VARIABLE_1233178)) (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 (ho_4519 (ho_4518 k_4517 (ho_4244 (ho_4492 (ho_4501 k_4500 BOUND_VARIABLE_1294918) BOUND_VARIABLE_1233177) BOUND_VARIABLE_1233178)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4502 BOUND_VARIABLE_1233176) BOUND_VARIABLE_1233177)))) (ho_4258 (ho_4265 _let_11 BOUND_VARIABLE_1233175) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1233178) _let_10)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_10) _let_7)) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))))))) (ho_4258 (ho_4273 (ho_4715 (ho_4714 (ho_5476 k_5475 BOUND_VARIABLE_1294918) BOUND_VARIABLE_1233175) BOUND_VARIABLE_1233176) BOUND_VARIABLE_1233177) BOUND_VARIABLE_1233178)))))))))))))))) (let ((_let_3049 (forall ((BOUND_VARIABLE_1233116 tptp.nat) (BOUND_VARIABLE_1294968 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1233118 tptp.real) (BOUND_VARIABLE_1233119 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4196 k_4195 tptp.one))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4209 (ho_4211 k_4210 _let_5) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_5)))) (let ((_let_8 (ho_4219 k_4218 k_4217))) (let ((_let_9 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4273 BOUND_VARIABLE_1294968 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_8 BOUND_VARIABLE_1233116) _let_7)) (ho_4209 (ho_4220 _let_8 _let_6) _let_7)))) _let_7)) (ho_4209 (ho_4220 _let_8 BOUND_VARIABLE_1233119) _let_7)))) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1233119) _let_6)) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1233118) BOUND_VARIABLE_1233119)) (ho_4245 (ho_4244 (ho_5479 (ho_5478 k_5477 BOUND_VARIABLE_1233116) BOUND_VARIABLE_1294968) BOUND_VARIABLE_1233118) BOUND_VARIABLE_1233119)))))))))))))) (let ((_let_3050 (forall ((BOUND_VARIABLE_1233077 tptp.nat) (BOUND_VARIABLE_1233078 tptp.nat) (BOUND_VARIABLE_1233079 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233079)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233077) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1233078) _let_2)) _let_4))))) (ho_4288 (ho_4287 (ho_4303 k_5480 BOUND_VARIABLE_1233077) BOUND_VARIABLE_1233078) BOUND_VARIABLE_1233079))))))))) (let ((_let_3051 (forall ((BOUND_VARIABLE_1295030 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1233038 tptp.real) (BOUND_VARIABLE_1233039 tptp.real) (BOUND_VARIABLE_1233040 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4273 BOUND_VARIABLE_1295030 BOUND_VARIABLE_1233040) BOUND_VARIABLE_1233039)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1233040) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 _let_2 _let_5)))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1233038) (ho_4258 _let_2 BOUND_VARIABLE_1233039))) BOUND_VARIABLE_1233040)) (ho_4245 (ho_4244 (ho_5451 (ho_5482 k_5481 BOUND_VARIABLE_1295030) BOUND_VARIABLE_1233038) BOUND_VARIABLE_1233039) BOUND_VARIABLE_1233040))))))))))) (let ((_let_3052 (forall ((BOUND_VARIABLE_1233027 tptp.nat) (BOUND_VARIABLE_1233028 tptp.nat)) (= (ho_4288 (ho_4287 k_5483 BOUND_VARIABLE_1233027) BOUND_VARIABLE_1233028) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1233028)) (ho_4290 k_4289 BOUND_VARIABLE_1233027)))))) (let ((_let_3053 (forall ((BOUND_VARIABLE_1295074 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232988 tptp.real) (BOUND_VARIABLE_1232989 tptp.real) (BOUND_VARIABLE_1232990 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4273 BOUND_VARIABLE_1295074 BOUND_VARIABLE_1232990) BOUND_VARIABLE_1232989)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232990) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 _let_2 _let_5)))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1232988) (ho_4258 _let_2 BOUND_VARIABLE_1232989))) BOUND_VARIABLE_1232990)) (ho_4245 (ho_4244 (ho_5451 (ho_5482 k_5484 BOUND_VARIABLE_1295074) BOUND_VARIABLE_1232988) BOUND_VARIABLE_1232989) BOUND_VARIABLE_1232990))))))))))) (let ((_let_3054 (forall ((BOUND_VARIABLE_1232977 tptp.nat) (BOUND_VARIABLE_1232978 tptp.nat)) (= (ho_4288 (ho_4287 k_5485 BOUND_VARIABLE_1232977) BOUND_VARIABLE_1232978) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232978)) (ho_4290 k_4289 BOUND_VARIABLE_1232977)))))) (let ((_let_3055 (forall ((BOUND_VARIABLE_1295114 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232938 tptp.real) (BOUND_VARIABLE_1232939 tptp.real) (BOUND_VARIABLE_1232940 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4273 BOUND_VARIABLE_1295114 BOUND_VARIABLE_1232940) BOUND_VARIABLE_1232939)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232940) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 _let_2 _let_5)))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1232938) (ho_4258 _let_2 BOUND_VARIABLE_1232939))) BOUND_VARIABLE_1232940)) (ho_4245 (ho_4244 (ho_5451 (ho_5482 k_5486 BOUND_VARIABLE_1295114) BOUND_VARIABLE_1232938) BOUND_VARIABLE_1232939) BOUND_VARIABLE_1232940))))))))))) (let ((_let_3056 (forall ((BOUND_VARIABLE_1232927 tptp.nat) (BOUND_VARIABLE_1232928 tptp.nat)) (= (ho_4288 (ho_4287 k_5487 BOUND_VARIABLE_1232927) BOUND_VARIABLE_1232928) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232928)) (ho_4290 k_4289 BOUND_VARIABLE_1232927)))))) (let ((_let_3057 (forall ((BOUND_VARIABLE_1295151 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232896 tptp.real) (BOUND_VARIABLE_1232897 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295151 BOUND_VARIABLE_1232897) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232897) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232896) BOUND_VARIABLE_1232897)) (ho_4245 (ho_4244 (ho_5479 k_5488 BOUND_VARIABLE_1295151) BOUND_VARIABLE_1232896) BOUND_VARIABLE_1232897)))))))))) (let ((_let_3058 (forall ((BOUND_VARIABLE_1232885 tptp.nat) (BOUND_VARIABLE_1232886 tptp.nat)) (= (ho_4288 (ho_4287 k_5489 BOUND_VARIABLE_1232885) BOUND_VARIABLE_1232886) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232886)) (ho_4290 k_4289 BOUND_VARIABLE_1232885)))))) (let ((_let_3059 (forall ((BOUND_VARIABLE_1295186 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232854 tptp.real) (BOUND_VARIABLE_1232855 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295186 BOUND_VARIABLE_1232855) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232855) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232854) BOUND_VARIABLE_1232855)) (ho_4245 (ho_4244 (ho_5479 k_5490 BOUND_VARIABLE_1295186) BOUND_VARIABLE_1232854) BOUND_VARIABLE_1232855)))))))))) (let ((_let_3060 (forall ((BOUND_VARIABLE_1232843 tptp.nat) (BOUND_VARIABLE_1232844 tptp.nat)) (= (ho_4288 (ho_4287 k_5491 BOUND_VARIABLE_1232843) BOUND_VARIABLE_1232844) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232844)) (ho_4290 k_4289 BOUND_VARIABLE_1232843)))))) (let ((_let_3061 (forall ((BOUND_VARIABLE_1295221 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232812 tptp.real) (BOUND_VARIABLE_1232813 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295221 BOUND_VARIABLE_1232813) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232813) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232812) BOUND_VARIABLE_1232813)) (ho_4245 (ho_4244 (ho_5479 k_5492 BOUND_VARIABLE_1295221) BOUND_VARIABLE_1232812) BOUND_VARIABLE_1232813)))))))))) (let ((_let_3062 (forall ((BOUND_VARIABLE_1232801 tptp.nat) (BOUND_VARIABLE_1232802 tptp.nat)) (= (ho_4288 (ho_4287 k_5493 BOUND_VARIABLE_1232801) BOUND_VARIABLE_1232802) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232802)) (ho_4290 k_4289 BOUND_VARIABLE_1232801)))))) (let ((_let_3063 (forall ((BOUND_VARIABLE_1295256 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232770 tptp.real) (BOUND_VARIABLE_1232771 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295256 BOUND_VARIABLE_1232771) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232771) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232770) BOUND_VARIABLE_1232771)) (ho_4245 (ho_4244 (ho_5479 k_5494 BOUND_VARIABLE_1295256) BOUND_VARIABLE_1232770) BOUND_VARIABLE_1232771)))))))))) (let ((_let_3064 (forall ((BOUND_VARIABLE_1232759 tptp.nat) (BOUND_VARIABLE_1232760 tptp.nat)) (= (ho_4288 (ho_4287 k_5495 BOUND_VARIABLE_1232759) BOUND_VARIABLE_1232760) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232760)) (ho_4290 k_4289 BOUND_VARIABLE_1232759)))))) (let ((_let_3065 (forall ((BOUND_VARIABLE_1295291 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232728 tptp.real) (BOUND_VARIABLE_1232729 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295291 BOUND_VARIABLE_1232729) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232729) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232728) BOUND_VARIABLE_1232729)) (ho_4245 (ho_4244 (ho_5479 k_5496 BOUND_VARIABLE_1295291) BOUND_VARIABLE_1232728) BOUND_VARIABLE_1232729)))))))))) (let ((_let_3066 (forall ((BOUND_VARIABLE_1232717 tptp.nat) (BOUND_VARIABLE_1232718 tptp.nat)) (= (ho_4288 (ho_4287 k_5497 BOUND_VARIABLE_1232717) BOUND_VARIABLE_1232718) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232718)) (ho_4290 k_4289 BOUND_VARIABLE_1232717)))))) (let ((_let_3067 (forall ((BOUND_VARIABLE_1232689 tptp.nat) (BOUND_VARIABLE_1232690 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4273 k_5498 BOUND_VARIABLE_1232689) BOUND_VARIABLE_1232690) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1232689 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4503 BOUND_VARIABLE_1232689)) BOUND_VARIABLE_1232690)))))))) (let ((_let_3068 (forall ((BOUND_VARIABLE_1232636 tptp.nat) (BOUND_VARIABLE_1232637 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1232637 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5499 BOUND_VARIABLE_1232636) BOUND_VARIABLE_1232637) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1232637 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1232637) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1232637)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1232637)) BOUND_VARIABLE_1232637)) BOUND_VARIABLE_1232636)))))))))))))) (let ((_let_3069 (forall ((BOUND_VARIABLE_1295370 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232605 tptp.real) (BOUND_VARIABLE_1232606 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295370 BOUND_VARIABLE_1232606) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232606) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232605) BOUND_VARIABLE_1232606)) (ho_4245 (ho_4244 (ho_5479 k_5500 BOUND_VARIABLE_1295370) BOUND_VARIABLE_1232605) BOUND_VARIABLE_1232606)))))))))) (let ((_let_3070 (forall ((BOUND_VARIABLE_1232594 tptp.nat) (BOUND_VARIABLE_1232595 tptp.nat)) (= (ho_4288 (ho_4287 k_5501 BOUND_VARIABLE_1232594) BOUND_VARIABLE_1232595) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232595)) (ho_4290 k_4289 BOUND_VARIABLE_1232594)))))) (let ((_let_3071 (forall ((BOUND_VARIABLE_1295405 |u_(-> tptp.nat tptp.real tptp.real)|) (BOUND_VARIABLE_1232563 tptp.real) (BOUND_VARIABLE_1232564 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4273 BOUND_VARIABLE_1295405 BOUND_VARIABLE_1232564) _let_4)) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) BOUND_VARIABLE_1232564) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_4)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232563) BOUND_VARIABLE_1232564)) (ho_4245 (ho_4244 (ho_5479 k_5502 BOUND_VARIABLE_1295405) BOUND_VARIABLE_1232563) BOUND_VARIABLE_1232564)))))))))) (let ((_let_3072 (forall ((BOUND_VARIABLE_1232552 tptp.nat) (BOUND_VARIABLE_1232553 tptp.nat)) (= (ho_4288 (ho_4287 k_5503 BOUND_VARIABLE_1232552) BOUND_VARIABLE_1232553) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232553)) (ho_4290 k_4289 BOUND_VARIABLE_1232552)))))) (let ((_let_3073 (forall ((BOUND_VARIABLE_1232533 tptp.real)) (= (ho_4506 k_4505 (ho_4508 k_4507 BOUND_VARIABLE_1232533)) (ho_4258 k_5504 BOUND_VARIABLE_1232533))))) (let ((_let_3074 (forall ((BOUND_VARIABLE_1232514 tptp.real)) (= (ho_4506 k_4505 (ho_4508 k_4509 BOUND_VARIABLE_1232514)) (ho_4258 k_5505 BOUND_VARIABLE_1232514))))) (let ((_let_3075 (forall ((BOUND_VARIABLE_1232486 tptp.nat) (BOUND_VARIABLE_1232487 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4273 k_5506 BOUND_VARIABLE_1232486) BOUND_VARIABLE_1232487) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1232486 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4510 BOUND_VARIABLE_1232486)) BOUND_VARIABLE_1232487)))))))) (let ((_let_3076 (forall ((BOUND_VARIABLE_1232433 tptp.nat) (BOUND_VARIABLE_1232434 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1232434 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5507 BOUND_VARIABLE_1232433) BOUND_VARIABLE_1232434) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1232434 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1232434) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1232434)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1232434)) BOUND_VARIABLE_1232434)) BOUND_VARIABLE_1232433)))))))))))))) (let ((_let_3077 (forall ((BOUND_VARIABLE_1295500 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1232400 tptp.real) (BOUND_VARIABLE_1232401 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 (ho_4245 BOUND_VARIABLE_1295500 BOUND_VARIABLE_1232401)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 BOUND_VARIABLE_1232401) _let_5)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 _let_4)) _let_5)))) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232400) BOUND_VARIABLE_1232401)) (ho_4245 (ho_4244 (ho_4512 k_5508 BOUND_VARIABLE_1295500) BOUND_VARIABLE_1232400) BOUND_VARIABLE_1232401)))))))))))) (let ((_let_3078 (forall ((BOUND_VARIABLE_1295516 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1232372 tptp.real)) (= (ho_4348 k_4347 (ho_4244 (ho_4512 k_4511 BOUND_VARIABLE_1295516) BOUND_VARIABLE_1232372)) (ho_4258 (ho_5510 k_5509 BOUND_VARIABLE_1295516) BOUND_VARIABLE_1232372))))) (let ((_let_3079 (forall ((BOUND_VARIABLE_1295541 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1232338 tptp.real) (BOUND_VARIABLE_1232339 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4196 k_4195 tptp.one))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_4)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 (ho_4245 BOUND_VARIABLE_1295541 BOUND_VARIABLE_1232339)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 BOUND_VARIABLE_1232339) _let_5)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 _let_4)) _let_5)))) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232338) BOUND_VARIABLE_1232339)) (ho_4245 (ho_4244 (ho_4512 k_5511 BOUND_VARIABLE_1295541) BOUND_VARIABLE_1232338) BOUND_VARIABLE_1232339)))))))))))) (let ((_let_3080 (forall ((BOUND_VARIABLE_1232314 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (= (ho_4258 k_5512 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1232314) (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_2 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_2))) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_3 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232314) _let_2)) _let_1))))) (ho_4258 k_5513 BOUND_VARIABLE_1232314))))))))) (let ((_let_3081 (forall ((BOUND_VARIABLE_1232303 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_3 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_3))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) BOUND_VARIABLE_1232303)) (ho_4258 k_5514 BOUND_VARIABLE_1232303)))))))) (let ((_let_3082 (forall ((BOUND_VARIABLE_1232278 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4274))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4265 (ho_4264 _let_3 k_4259) (ho_4247 k_4246 tptp.one)))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 k_5512 (ho_4258 (ho_4265 _let_5 (ho_4258 _let_4 BOUND_VARIABLE_1232278)) (ho_4258 _let_2 (ho_4258 _let_4 (ho_4258 (ho_4257 _let_1 k_4248) BOUND_VARIABLE_1232278)))))) (ho_4258 _let_2 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (ho_4258 k_5515 BOUND_VARIABLE_1232278)))))))))) (let ((_let_3083 (forall ((BOUND_VARIABLE_1295597 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1295596 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1232269 tptp.real)) (= (ho_4258 (ho_4946 (ho_5517 k_5516 BOUND_VARIABLE_1295597) BOUND_VARIABLE_1295596) BOUND_VARIABLE_1232269) (ho_4258 (ho_4265 k_5404 (ho_4258 BOUND_VARIABLE_1295597 BOUND_VARIABLE_1232269)) (ho_4258 BOUND_VARIABLE_1295596 BOUND_VARIABLE_1232269)))))) (let ((_let_3084 (forall ((BOUND_VARIABLE_1295616 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1232258 tptp.real) (BOUND_VARIABLE_1232259 tptp.real)) (= (ho_4258 (ho_4265 (ho_5519 k_5518 BOUND_VARIABLE_1295616) BOUND_VARIABLE_1232258) BOUND_VARIABLE_1232259) (ho_4258 (ho_4265 k_5404 (ho_4258 BOUND_VARIABLE_1295616 BOUND_VARIABLE_1232259)) BOUND_VARIABLE_1232258))))) (let ((_let_3085 (forall ((BOUND_VARIABLE_1295634 |u_(-> tptp.real tptp.nat tptp.real)|) (BOUND_VARIABLE_1232249 tptp.nat) (BOUND_VARIABLE_1232250 tptp.real)) (= (ho_4258 (ho_4273 (ho_5521 k_5520 BOUND_VARIABLE_1295634) BOUND_VARIABLE_1232249) BOUND_VARIABLE_1232250) (ho_4245 (ho_4244 BOUND_VARIABLE_1295634 BOUND_VARIABLE_1232250) BOUND_VARIABLE_1232249))))) (let ((_let_3086 (forall ((BOUND_VARIABLE_1295650 |u_(-> tptp.real tptp.nat tptp.real)|) (BOUND_VARIABLE_1232241 tptp.real)) (= (ho_4258 (ho_5523 k_5522 BOUND_VARIABLE_1295650) BOUND_VARIABLE_1232241) (ho_4348 k_4347 (ho_4244 BOUND_VARIABLE_1295650 BOUND_VARIABLE_1232241)))))) (let ((_let_3087 (forall ((BOUND_VARIABLE_1232232 tptp.real) (BOUND_VARIABLE_1232233 tptp.real)) (= (ho_4258 (ho_4265 k_5524 BOUND_VARIABLE_1232232) BOUND_VARIABLE_1232233) (ho_4258 (ho_4265 k_5404 BOUND_VARIABLE_1232233) BOUND_VARIABLE_1232232))))) (let ((_let_3088 (forall ((BOUND_VARIABLE_1295675 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1232223 tptp.nat) (BOUND_VARIABLE_1232224 tptp.real)) (= (ho_4258 (ho_4273 (ho_4272 k_5525 BOUND_VARIABLE_1295675) BOUND_VARIABLE_1232223) BOUND_VARIABLE_1232224) (ho_4245 (ho_4244 k_4243 (ho_4258 BOUND_VARIABLE_1295675 BOUND_VARIABLE_1232224)) BOUND_VARIABLE_1232223))))) (let ((_let_3089 (forall ((BOUND_VARIABLE_1232214 tptp.nat) (BOUND_VARIABLE_1232215 tptp.real)) (= (ho_4258 (ho_4273 k_5526 BOUND_VARIABLE_1232214) BOUND_VARIABLE_1232215) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1232215) BOUND_VARIABLE_1232214))))) (let ((_let_3090 (forall ((BOUND_VARIABLE_1232161 tptp.nat) (BOUND_VARIABLE_1232162 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1232162 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5527 BOUND_VARIABLE_1232161) BOUND_VARIABLE_1232162) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1232162 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1232162) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1232162)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1232162)) BOUND_VARIABLE_1232162)) BOUND_VARIABLE_1232161)))))))))))))) (let ((_let_3091 (forall ((BOUND_VARIABLE_1232133 tptp.nat) (BOUND_VARIABLE_1232134 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4273 k_5528 BOUND_VARIABLE_1232133) BOUND_VARIABLE_1232134) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1232133 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4513 BOUND_VARIABLE_1232133)) BOUND_VARIABLE_1232134)))))))) (let ((_let_3092 (forall ((BOUND_VARIABLE_1232091 tptp.nat) (BOUND_VARIABLE_1232092 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3)))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_3)) _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 _let_6) _let_4)) (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1232091) _let_4))))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) (ho_4273 k_4514 BOUND_VARIABLE_1232091)) BOUND_VARIABLE_1232092)) (ho_4258 (ho_4273 k_5529 BOUND_VARIABLE_1232091) BOUND_VARIABLE_1232092))))))))))) (let ((_let_3093 (forall ((BOUND_VARIABLE_1232030 tptp.nat) (BOUND_VARIABLE_1232031 tptp.real)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4257 _let_4 k_4248))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4258 _let_5 _let_6))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_9 (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) _let_6) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1232031 _let_9))) (let ((_let_11 (not _let_10))) (= (ho_4258 (ho_4273 k_5530 BOUND_VARIABLE_1232030) BOUND_VARIABLE_1232031) (ho_4258 (ho_4265 (ho_4264 _let_8 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_10) _let_9) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1232031 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1232031) _let_9)) _let_11)) _let_6) _let_7))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_9 (ho_4258 (ho_4265 k_4349 _let_9) BOUND_VARIABLE_1232031)) _let_11)) (ho_4258 _let_5 BOUND_VARIABLE_1232031)) BOUND_VARIABLE_1232031)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1232030) _let_2)))))))))))))))))))) (let ((_let_3094 (forall ((BOUND_VARIABLE_1232020 tptp.nat)) (= (ho_4288 k_5531 BOUND_VARIABLE_1232020) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 (ho_4193 k_4192 (ho_4193 k_4192 (ho_4193 k_4192 (ho_4193 k_4192 (ho_4193 k_4192 (ho_4193 k_4192 _let_1)))))))))))) (or (not (= BOUND_VARIABLE_1232020 (ho_4216 (ho_4468 k_4467 _let_2) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_2))))))))))))) (let ((_let_3095 (forall ((BOUND_VARIABLE_1232009 tptp.int) (BOUND_VARIABLE_1232010 tptp.nat)) (= (ho_4288 (ho_5533 k_5532 BOUND_VARIABLE_1232009) BOUND_VARIABLE_1232010) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1232010)) (ho_4290 k_4289 (ho_4213 k_4212 BOUND_VARIABLE_1232009))))))) (let ((_let_3096 (forall ((BOUND_VARIABLE_1231974 tptp.int) (BOUND_VARIABLE_1231975 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (let ((_let_3 (ho_4636 (ho_4635 k_4634 (ho_4209 (ho_4211 k_4210 _let_1) _let_2)) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1231974) _let_2)))) (or (not (= BOUND_VARIABLE_1231975 (ho_4335 (ho_4640 k_4639 _let_3) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_3)))))))))) (ho_4310 (ho_4309 k_5534 BOUND_VARIABLE_1231974) BOUND_VARIABLE_1231975))))) (let ((_let_3097 (forall ((BOUND_VARIABLE_1231947 tptp.nat) (BOUND_VARIABLE_1231948 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231948) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1231948) BOUND_VARIABLE_1231947)) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231947) _let_2)))) (ho_4216 (ho_4215 k_5535 BOUND_VARIABLE_1231947) BOUND_VARIABLE_1231948)))))))) (let ((_let_3098 (forall ((BOUND_VARIABLE_1231929 tptp.nat) (BOUND_VARIABLE_1231930 tptp.nat)) (= (ho_4288 (ho_4287 k_5536 BOUND_VARIABLE_1231929) BOUND_VARIABLE_1231930) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1231929))) (or (not (= BOUND_VARIABLE_1231930 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3099 (forall ((BOUND_VARIABLE_1231921 tptp.int) (BOUND_VARIABLE_1231922 tptp.int)) (= (ho_4209 (ho_4211 k_5537 BOUND_VARIABLE_1231921) BOUND_VARIABLE_1231922) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1231922) BOUND_VARIABLE_1231921))))) (let ((_let_3100 (forall ((BOUND_VARIABLE_1231878 tptp.int) (BOUND_VARIABLE_1231879 tptp.int) (BOUND_VARIABLE_1231880 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4636 (ho_4635 k_4634 (ho_4209 (ho_4211 k_4210 _let_1) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1231878) (ho_4209 _let_2 BOUND_VARIABLE_1231879))) _let_3)))) (or (not (= BOUND_VARIABLE_1231880 (ho_4335 (ho_4640 k_4639 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_4))))))))))) (ho_4310 (ho_4309 (ho_4308 k_5538 BOUND_VARIABLE_1231878) BOUND_VARIABLE_1231879) BOUND_VARIABLE_1231880))))) (let ((_let_3101 (forall ((BOUND_VARIABLE_1231841 tptp.int) (BOUND_VARIABLE_1231842 tptp.int) (BOUND_VARIABLE_1231843 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1231841) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1231842) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4196 k_4195 tptp.one)))))) (or (not (= BOUND_VARIABLE_1231843 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))) (ho_4310 (ho_4309 (ho_4308 k_5539 BOUND_VARIABLE_1231841) BOUND_VARIABLE_1231842) BOUND_VARIABLE_1231843))))) (let ((_let_3102 (forall ((BOUND_VARIABLE_1295954 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1231806 tptp.real)) (= (forall ((X2 tptp.real)) (let ((_let_1 (= X2 BOUND_VARIABLE_1231806))) (or (not (ho_5136 (ho_5135 k_5134 X2) (ho_5542 (ho_5541 k_5540 (ho_4473 k_4520 BOUND_VARIABLE_1295954)) tptp.top_top_set_nat))) (and (= BOUND_VARIABLE_1231806 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1231806) X2)) (not _let_1)) _let_1))) (ho_4351 (ho_5544 k_5543 BOUND_VARIABLE_1295954) BOUND_VARIABLE_1231806))))) (let ((_let_3103 (forall ((BOUND_VARIABLE_1231782 tptp.set_int)) (= (not (forall ((K3 tptp.int)) (not (forall ((X2 tptp.int)) (let ((_let_1 (ho_5116 k_5115 X2))) (or (not (ho_5117 _let_1 (ho_5551 (ho_5550 k_5549 k_5548) BOUND_VARIABLE_1231782))) (ho_5117 _let_1 (ho_5547 k_5546 (ho_4309 k_5545 K3))))))))) (ho_5117 k_5552 BOUND_VARIABLE_1231782))))) (let ((_let_3104 (forall ((BOUND_VARIABLE_1231750 tptp.set_int)) (= (not (forall ((K3 tptp.int)) (not (forall ((X2 tptp.int)) (let ((_let_1 (ho_5116 k_5115 X2))) (or (not (ho_5117 _let_1 (ho_5551 (ho_5550 k_5549 k_5548) BOUND_VARIABLE_1231750))) (ho_5117 _let_1 (ho_5547 k_5546 (ho_4309 k_4521 K3))))))))) (ho_5117 k_5553 BOUND_VARIABLE_1231750))))) (let ((_let_3105 (forall ((BOUND_VARIABLE_1231726 tptp.nat) (BOUND_VARIABLE_1231727 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1231727)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231726) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5554 BOUND_VARIABLE_1231726) BOUND_VARIABLE_1231727)))))))) (let ((_let_3106 (forall ((BOUND_VARIABLE_1231716 tptp.nat) (BOUND_VARIABLE_1231717 tptp.nat)) (= (ho_4288 (ho_4287 k_5555 BOUND_VARIABLE_1231716) BOUND_VARIABLE_1231717) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1231717)) (ho_4290 k_4289 BOUND_VARIABLE_1231716)))))) (let ((_let_3107 (forall ((BOUND_VARIABLE_1231692 tptp.nat) (BOUND_VARIABLE_1231693 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1231693)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231692) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5556 BOUND_VARIABLE_1231692) BOUND_VARIABLE_1231693)))))))) (let ((_let_3108 (forall ((BOUND_VARIABLE_1231682 tptp.nat) (BOUND_VARIABLE_1231683 tptp.nat)) (= (ho_4288 (ho_4287 k_5557 BOUND_VARIABLE_1231682) BOUND_VARIABLE_1231683) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1231683)) (ho_4290 k_4289 BOUND_VARIABLE_1231682)))))) (let ((_let_3109 (forall ((BOUND_VARIABLE_1231640 tptp.nat) (BOUND_VARIABLE_1231641 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1231640) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1231641 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5558 BOUND_VARIABLE_1231640) BOUND_VARIABLE_1231641))))) (let ((_let_3110 (forall ((BOUND_VARIABLE_1231622 tptp.nat) (BOUND_VARIABLE_1231623 tptp.nat)) (= (ho_4288 (ho_4287 k_5559 BOUND_VARIABLE_1231622) BOUND_VARIABLE_1231623) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1231622))) (or (not (= BOUND_VARIABLE_1231623 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3111 (forall ((BOUND_VARIABLE_1231570 tptp.nat) (BOUND_VARIABLE_1231571 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1231570) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1231571 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_5560 BOUND_VARIABLE_1231570) BOUND_VARIABLE_1231571))))) (let ((_let_3112 (forall ((BOUND_VARIABLE_1231528 tptp.nat) (BOUND_VARIABLE_1231529 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1231528) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1231529 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5561 BOUND_VARIABLE_1231528) BOUND_VARIABLE_1231529))))) (let ((_let_3113 (forall ((BOUND_VARIABLE_1231518 tptp.nat) (BOUND_VARIABLE_1231519 tptp.nat)) (= (ho_4288 (ho_4287 k_5562 BOUND_VARIABLE_1231518) BOUND_VARIABLE_1231519) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1231519)) (ho_4290 k_4289 BOUND_VARIABLE_1231518)))))) (let ((_let_3114 (forall ((BOUND_VARIABLE_1231466 tptp.nat) (BOUND_VARIABLE_1231467 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1231466) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1231467 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_5563 BOUND_VARIABLE_1231466) BOUND_VARIABLE_1231467))))) (let ((_let_3115 (forall ((BOUND_VARIABLE_1231456 tptp.nat) (BOUND_VARIABLE_1231457 tptp.nat)) (= (ho_4288 (ho_4287 k_5564 BOUND_VARIABLE_1231456) BOUND_VARIABLE_1231457) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1231457)) (ho_4290 k_4289 BOUND_VARIABLE_1231456)))))) (let ((_let_3116 (forall ((BOUND_VARIABLE_1231414 tptp.nat) (BOUND_VARIABLE_1231415 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1231414) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1231415 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5565 BOUND_VARIABLE_1231414) BOUND_VARIABLE_1231415))))) (let ((_let_3117 (forall ((BOUND_VARIABLE_1231394 tptp.nat) (BOUND_VARIABLE_1231395 tptp.nat) (BOUND_VARIABLE_1231396 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5566 BOUND_VARIABLE_1231394) BOUND_VARIABLE_1231395) BOUND_VARIABLE_1231396) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1231394) BOUND_VARIABLE_1231395))) (or (not (= BOUND_VARIABLE_1231396 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3118 (forall ((BOUND_VARIABLE_1231339 tptp.nat) (BOUND_VARIABLE_1231340 tptp.nat) (BOUND_VARIABLE_1231341 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231339) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231340) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1231341 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5567 BOUND_VARIABLE_1231339) BOUND_VARIABLE_1231340) BOUND_VARIABLE_1231341))))) (let ((_let_3119 (forall ((BOUND_VARIABLE_1231295 tptp.nat) (BOUND_VARIABLE_1231296 tptp.nat) (BOUND_VARIABLE_1231297 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1231295) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231296) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1231297 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5568 BOUND_VARIABLE_1231295) BOUND_VARIABLE_1231296) BOUND_VARIABLE_1231297))))) (let ((_let_3120 (forall ((BOUND_VARIABLE_1231230 tptp.nat) (BOUND_VARIABLE_1231231 tptp.nat) (BOUND_VARIABLE_1231232 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231230) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1231231) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1231232 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5569 BOUND_VARIABLE_1231230) BOUND_VARIABLE_1231231) BOUND_VARIABLE_1231232))))) (let ((_let_3121 (forall ((BOUND_VARIABLE_1231222 tptp.nat) (BOUND_VARIABLE_1231223 tptp.nat)) (= (ho_4216 (ho_4215 k_5570 BOUND_VARIABLE_1231222) BOUND_VARIABLE_1231223) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231223) BOUND_VARIABLE_1231222))))) (let ((_let_3122 (forall ((BOUND_VARIABLE_1231202 tptp.nat) (BOUND_VARIABLE_1231203 tptp.nat) (BOUND_VARIABLE_1231204 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5571 BOUND_VARIABLE_1231202) BOUND_VARIABLE_1231203) BOUND_VARIABLE_1231204) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1231202) BOUND_VARIABLE_1231203))) (or (not (= BOUND_VARIABLE_1231204 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3123 (forall ((BOUND_VARIABLE_1231177 tptp.nat) (BOUND_VARIABLE_1231178 tptp.nat) (BOUND_VARIABLE_1231179 tptp.nat) (BOUND_VARIABLE_1231180 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_5572 BOUND_VARIABLE_1231177) BOUND_VARIABLE_1231178) BOUND_VARIABLE_1231179) BOUND_VARIABLE_1231180) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231177) BOUND_VARIABLE_1231179)) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231178) BOUND_VARIABLE_1231179)))) (or (not (= BOUND_VARIABLE_1231180 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3124 (forall ((BOUND_VARIABLE_1231169 tptp.nat) (BOUND_VARIABLE_1231170 tptp.nat)) (= (ho_4216 (ho_4215 k_5573 BOUND_VARIABLE_1231169) BOUND_VARIABLE_1231170) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231170) BOUND_VARIABLE_1231169))))) (let ((_let_3125 (forall ((BOUND_VARIABLE_1231161 tptp.nat) (BOUND_VARIABLE_1231162 tptp.nat)) (= (ho_4216 (ho_4215 k_5574 BOUND_VARIABLE_1231161) BOUND_VARIABLE_1231162) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1231162) BOUND_VARIABLE_1231161))))) (let ((_let_3126 (forall ((BOUND_VARIABLE_1231141 tptp.nat) (BOUND_VARIABLE_1231142 tptp.nat) (BOUND_VARIABLE_1231143 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5575 BOUND_VARIABLE_1231141) BOUND_VARIABLE_1231142) BOUND_VARIABLE_1231143) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1231141) BOUND_VARIABLE_1231142))) (or (not (= BOUND_VARIABLE_1231143 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3127 (forall ((BOUND_VARIABLE_1231134 tptp.num)) (= (ho_4191 k_5576 BOUND_VARIABLE_1231134) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1231134)))))) (let ((_let_3128 (forall ((BOUND_VARIABLE_1231127 tptp.num)) (= (ho_4191 k_5577 BOUND_VARIABLE_1231127) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1231127)))))) (let ((_let_3129 (forall ((BOUND_VARIABLE_1231120 tptp.num)) (= (ho_4191 k_5578 BOUND_VARIABLE_1231120) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1231120)))))) (let ((_let_3130 (forall ((BOUND_VARIABLE_1231113 tptp.num)) (= (ho_4191 k_5579 BOUND_VARIABLE_1231113) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1231113)))))) (let ((_let_3131 (forall ((BOUND_VARIABLE_1231106 tptp.num)) (= (ho_4191 k_5580 BOUND_VARIABLE_1231106) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1231106)))))) (let ((_let_3132 (forall ((BOUND_VARIABLE_1231071 tptp.real)) (= (not (forall ((I3 tptp.int) (J3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (or (not (= BOUND_VARIABLE_1231071 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275) (ho_4251 k_4250 (ho_4315 k_4522 I3))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4251 k_4250 (ho_4315 k_4523 J3)))))) (= J3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))))))) (ho_4351 k_5581 BOUND_VARIABLE_1231071))))) (let ((_let_3133 (forall ((BOUND_VARIABLE_1231042 tptp.real)) (= (not (forall ((I3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (or (not (= BOUND_VARIABLE_1231042 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4251 k_4250 (ho_4315 k_4524 I3))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) N2) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))))) (= N2 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))))))))) (ho_4351 k_5582 BOUND_VARIABLE_1231042))))) (let ((_let_3134 (forall ((BOUND_VARIABLE_1231000 tptp.nat) (BOUND_VARIABLE_1231001 tptp.num)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) BOUND_VARIABLE_1231000))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1231001)))) (let ((_let_7 (ho_4216 (ho_4215 k_4223 _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 _let_6) _let_4)) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2)))))) (= (ho_4231 (ho_4230 (ho_4229 k_4228 (= (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3) _let_7)) (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one)) (ho_4191 k_4194 (ho_4225 k_4224 _let_7))) (ho_4191 (ho_4236 k_5583 BOUND_VARIABLE_1231000) BOUND_VARIABLE_1231001)))))))))))) (let ((_let_3135 (forall ((BOUND_VARIABLE_1230986 tptp.nat) (BOUND_VARIABLE_1230987 tptp.num)) (= (ho_5589 (ho_5588 k_5587 k_4528) (ho_5586 (ho_5585 k_5584 BOUND_VARIABLE_1230986) BOUND_VARIABLE_1230987)) (ho_4191 (ho_4236 k_5590 BOUND_VARIABLE_1230986) BOUND_VARIABLE_1230987))))) (let ((_let_3136 (forall ((BOUND_VARIABLE_1230979 tptp.num)) (= (ho_4191 k_5591 BOUND_VARIABLE_1230979) (ho_4191 k_4194 (ho_4193 k_4237 BOUND_VARIABLE_1230979)))))) (let ((_let_3137 (forall ((BOUND_VARIABLE_1230933 tptp.num) (BOUND_VARIABLE_1230934 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) BOUND_VARIABLE_1230934))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1230933)))) (let ((_let_7 (ho_4216 (ho_4215 k_4223 _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 _let_6) _let_4)) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2)))))) (= (ho_4191 k_4194 (ho_4241 (ho_4240 (ho_4239 k_4238 tptp.one) k_4237) (ho_4231 (ho_4230 (ho_4229 k_4228 (= (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3) _let_7)) (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one)) (ho_4191 k_4194 (ho_4225 k_4224 _let_7))))) (ho_4300 (ho_4299 k_5592 BOUND_VARIABLE_1230933) BOUND_VARIABLE_1230934)))))))))))) (let ((_let_3138 (forall ((BOUND_VARIABLE_1230928 tptp.nat)) (= (ho_4191 k_4194 tptp.one) (ho_4300 k_5593 BOUND_VARIABLE_1230928))))) (let ((_let_3139 (forall ((BOUND_VARIABLE_1230882 tptp.num) (BOUND_VARIABLE_1230883 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4216 (ho_4215 k_4214 _let_3) BOUND_VARIABLE_1230883))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1230882)))) (let ((_let_7 (ho_4216 (ho_4215 k_4223 _let_6) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 _let_6) _let_4)) _let_2)) (ho_4209 (ho_4220 _let_5 _let_4) _let_2)))))) (let ((_let_8 (ho_4191 (ho_4227 k_4226 tptp.one) tptp.one))) (= (ho_4231 (ho_4234 (ho_4233 k_4232 _let_8) k_4529) (ho_4231 (ho_4230 (ho_4229 k_4228 (= (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3) _let_7)) _let_8) (ho_4191 k_4194 (ho_4225 k_4224 _let_7)))) (ho_4300 (ho_4299 k_5594 BOUND_VARIABLE_1230882) BOUND_VARIABLE_1230883))))))))))))) (let ((_let_3140 (forall ((BOUND_VARIABLE_1230875 tptp.num)) (= (ho_4191 k_5595 BOUND_VARIABLE_1230875) (ho_4191 k_4194 (ho_4193 k_4192 BOUND_VARIABLE_1230875)))))) (let ((_let_3141 (forall ((BOUND_VARIABLE_1230868 tptp.num)) (= (ho_4191 k_5596 BOUND_VARIABLE_1230868) (ho_4191 k_4194 (ho_4193 k_4192 BOUND_VARIABLE_1230868)))))) (let ((_let_3142 (forall ((BOUND_VARIABLE_1230745 tptp.num) (BOUND_VARIABLE_1230746 tptp.num)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1230745))))) (let ((_let_5 (ho_4211 k_4210 _let_4))) (let ((_let_6 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 _let_5 _let_1)) _let_3))) (ho_4209 _let_2 _let_4)) _let_4))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4219 k_4218 k_4217))) (let ((_let_9 (ho_4209 _let_5 (ho_4209 _let_2 (ho_4196 k_4195 BOUND_VARIABLE_1230746))))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_9) _let_1)) _let_3))) (ho_4209 _let_2 _let_9)) _let_9)))) (let ((_let_11 (ho_4209 (ho_4220 _let_8 (ho_4216 (ho_4215 k_4223 _let_10) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_8 (ho_4216 (ho_4215 k_4221 _let_10) _let_7)) _let_3)) (ho_4209 (ho_4220 _let_8 _let_7) _let_3))))) _let_3))) (let ((_let_12 (ho_4209 k_4594 _let_4))) (let ((_let_13 (ho_4211 k_4222 _let_12))) (= (ho_4196 (ho_5284 k_5599 BOUND_VARIABLE_1230745) BOUND_VARIABLE_1230746) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_4)) _let_9) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 _let_9))) (ho_4209 _let_13 _let_11)) (ho_4209 _let_13 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_6) (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1230745))))) (not (= (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4196 k_4195 BOUND_VARIABLE_1230746))) (ho_4209 (ho_4211 k_4222 _let_1) K3)))))))) (ho_4209 _let_2 _let_11)))))))))))))))))))))) (let ((_let_3143 (forall ((BOUND_VARIABLE_1230728 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230729 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5600 BOUND_VARIABLE_1230728) BOUND_VARIABLE_1230729) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1230729 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230728) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1230728))))))))))) (let ((_let_3144 (forall ((BOUND_VARIABLE_1230568 tptp.vEBT_VEBT) (BOUND_VARIABLE_1230569 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230570 tptp.nat) (BOUND_VARIABLE_1230571 tptp.nat) (BOUND_VARIABLE_1230572 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230570) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230572) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230572) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230569) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1230571 BOUND_VARIABLE_1230572))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1230572))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5609 BOUND_VARIABLE_1230568) BOUND_VARIABLE_1230569) BOUND_VARIABLE_1230570) BOUND_VARIABLE_1230571) BOUND_VARIABLE_1230572) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1230571)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1230570))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230570) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230570) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_477498 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230569) I3)) BOUND_VARIABLE_477498)))) (not (forall ((BOUND_VARIABLE_477504 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230569) I3)) BOUND_VARIABLE_477504))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1230568) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1230568) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_230474 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4530 BOUND_VARIABLE_1230569)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_230474)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_230474)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230570) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230569) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1230570)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1230571)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1230572))))))))))))))))))))))))))))))))) (let ((_let_3145 (forall ((BOUND_VARIABLE_1230551 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230552 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5612 BOUND_VARIABLE_1230551) BOUND_VARIABLE_1230552) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1230552 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230551) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1230551))))))))))) (let ((_let_3146 (forall ((BOUND_VARIABLE_1230391 tptp.vEBT_VEBT) (BOUND_VARIABLE_1230392 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230393 tptp.nat) (BOUND_VARIABLE_1230394 tptp.nat) (BOUND_VARIABLE_1230395 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230393) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230395) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230395) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230392) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1230394 BOUND_VARIABLE_1230395))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1230395))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5613 BOUND_VARIABLE_1230391) BOUND_VARIABLE_1230392) BOUND_VARIABLE_1230393) BOUND_VARIABLE_1230394) BOUND_VARIABLE_1230395) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1230394)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1230393))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230393) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230393) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_477148 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230392) I3)) BOUND_VARIABLE_477148)))) (not (forall ((BOUND_VARIABLE_477154 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230392) I3)) BOUND_VARIABLE_477154))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1230391) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1230391) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_230310 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4538 BOUND_VARIABLE_1230392)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_230310)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_230310)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230393) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230392) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1230393)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1230394)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1230395))))))))))))))))))))))))))))))))) (let ((_let_3147 (forall ((BOUND_VARIABLE_1230374 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230375 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5614 BOUND_VARIABLE_1230374) BOUND_VARIABLE_1230375) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1230375 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230374) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1230374))))))))))) (let ((_let_3148 (forall ((BOUND_VARIABLE_1230214 tptp.vEBT_VEBT) (BOUND_VARIABLE_1230215 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230216 tptp.nat) (BOUND_VARIABLE_1230217 tptp.nat) (BOUND_VARIABLE_1230218 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230216) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230218) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230218) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230215) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1230217 BOUND_VARIABLE_1230218))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1230218))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5615 BOUND_VARIABLE_1230214) BOUND_VARIABLE_1230215) BOUND_VARIABLE_1230216) BOUND_VARIABLE_1230217) BOUND_VARIABLE_1230218) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1230217)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1230216))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230216) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230216) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_476790 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230215) I3)) BOUND_VARIABLE_476790)))) (not (forall ((BOUND_VARIABLE_476796 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230215) I3)) BOUND_VARIABLE_476796))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1230214) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1230214) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_230175 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4539 BOUND_VARIABLE_1230215)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_230175)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_230175)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230216) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230215) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1230216)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1230217)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1230218))))))))))))))))))))))))))))))))) (let ((_let_3149 (forall ((BOUND_VARIABLE_1230197 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230198 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5616 BOUND_VARIABLE_1230197) BOUND_VARIABLE_1230198) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1230198 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230197) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1230197))))))))))) (let ((_let_3150 (forall ((BOUND_VARIABLE_1230037 tptp.vEBT_VEBT) (BOUND_VARIABLE_1230038 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230039 tptp.nat) (BOUND_VARIABLE_1230040 tptp.nat) (BOUND_VARIABLE_1230041 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230039) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230041) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230041) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230038) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1230040 BOUND_VARIABLE_1230041))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1230041))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5617 BOUND_VARIABLE_1230037) BOUND_VARIABLE_1230038) BOUND_VARIABLE_1230039) BOUND_VARIABLE_1230040) BOUND_VARIABLE_1230041) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1230040)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1230039))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1230039) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230039) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_476431 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230038) I3)) BOUND_VARIABLE_476431)))) (not (forall ((BOUND_VARIABLE_476437 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230038) I3)) BOUND_VARIABLE_476437))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1230037) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1230037) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_230015 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4540 BOUND_VARIABLE_1230038)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_230015)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_230015)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1230039) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230038) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1230039)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1230040)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1230041))))))))))))))))))))))))))))))))) (let ((_let_3151 (forall ((BOUND_VARIABLE_1230020 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1230021 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5618 BOUND_VARIABLE_1230020) BOUND_VARIABLE_1230021) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1230021 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1230020) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1230020))))))))))) (let ((_let_3152 (forall ((BOUND_VARIABLE_1229860 tptp.vEBT_VEBT) (BOUND_VARIABLE_1229861 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1229862 tptp.nat) (BOUND_VARIABLE_1229863 tptp.nat) (BOUND_VARIABLE_1229864 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229862) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229864) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229864) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229861) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1229863 BOUND_VARIABLE_1229864))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1229864))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5619 BOUND_VARIABLE_1229860) BOUND_VARIABLE_1229861) BOUND_VARIABLE_1229862) BOUND_VARIABLE_1229863) BOUND_VARIABLE_1229864) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1229863)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1229862))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229862) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229862) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_476068 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229861) I3)) BOUND_VARIABLE_476068)))) (not (forall ((BOUND_VARIABLE_476074 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229861) I3)) BOUND_VARIABLE_476074))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1229860) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1229860) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_229893 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4541 BOUND_VARIABLE_1229861)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_229893)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_229893)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229862) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229861) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1229862)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1229863)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1229864))))))))))))))))))))))))))))))))) (let ((_let_3153 (forall ((BOUND_VARIABLE_1229843 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1229844 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5620 BOUND_VARIABLE_1229843) BOUND_VARIABLE_1229844) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1229844 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229843) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1229843))))))))))) (let ((_let_3154 (forall ((BOUND_VARIABLE_1229683 tptp.vEBT_VEBT) (BOUND_VARIABLE_1229684 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1229685 tptp.nat) (BOUND_VARIABLE_1229686 tptp.nat) (BOUND_VARIABLE_1229687 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229685) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229687) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229687) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229684) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1229686 BOUND_VARIABLE_1229687))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1229687))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5621 BOUND_VARIABLE_1229683) BOUND_VARIABLE_1229684) BOUND_VARIABLE_1229685) BOUND_VARIABLE_1229686) BOUND_VARIABLE_1229687) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1229686)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1229685))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229685) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229685) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_475705 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229684) I3)) BOUND_VARIABLE_475705)))) (not (forall ((BOUND_VARIABLE_475711 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229684) I3)) BOUND_VARIABLE_475711))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1229683) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1229683) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_229814 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4542 BOUND_VARIABLE_1229684)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_229814)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_229814)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229685) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229684) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1229685)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1229686)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1229687))))))))))))))))))))))))))))))))) (let ((_let_3155 (forall ((BOUND_VARIABLE_1229666 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1229667 tptp.vEBT_VEBT)) (= (ho_4532 (ho_4531 k_5622 BOUND_VARIABLE_1229666) BOUND_VARIABLE_1229667) (not (forall ((I3 tptp.nat)) (or (not (= BOUND_VARIABLE_1229667 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229666) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4534 k_4533 BOUND_VARIABLE_1229666))))))))))) (let ((_let_3156 (forall ((BOUND_VARIABLE_1229506 tptp.vEBT_VEBT) (BOUND_VARIABLE_1229507 tptp.list_VEBT_VEBT) (BOUND_VARIABLE_1229508 tptp.nat) (BOUND_VARIABLE_1229509 tptp.nat) (BOUND_VARIABLE_1229510 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4215 k_4214 _let_3))) (let ((_let_5 (ho_4216 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229508) _let_3)))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229510) _let_5))) (let ((_let_8 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229510) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_7) _let_2)) (ho_4209 (ho_4220 _let_6 _let_5) _let_2)))))) (let ((_let_9 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229507) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1229509 BOUND_VARIABLE_1229510))) (let ((_let_11 (ho_4290 k_4289 BOUND_VARIABLE_1229510))) (= (ho_4288 (ho_4287 (ho_4303 (ho_5611 (ho_5610 k_5623 BOUND_VARIABLE_1229506) BOUND_VARIABLE_1229507) BOUND_VARIABLE_1229508) BOUND_VARIABLE_1229509) BOUND_VARIABLE_1229510) (and (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1229509)) _let_11) (ho_4293 (ho_4292 k_4291 _let_11) (ho_4290 k_4289 (ho_4216 _let_4 BOUND_VARIABLE_1229508))) (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (or (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4214 _let_1) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1229508) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229508) _let_1)))))) (= (or (not (forall ((BOUND_VARIABLE_475264 tptp.nat)) (not (ho_4288 (ho_5602 k_5603 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229507) I3)) BOUND_VARIABLE_475264)))) (not (forall ((BOUND_VARIABLE_475270 tptp.nat)) (not (ho_4288 (ho_5602 k_5601 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229507) I3)) BOUND_VARIABLE_475270))))) (or (ho_4288 (ho_5602 k_5603 BOUND_VARIABLE_1229506) I3) (ho_4288 (ho_5602 k_5601 BOUND_VARIABLE_1229506) I3)))))) (or (not _let_10) (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_229717 tptp.nat)) (or (not (ho_5608 (ho_5607 k_5606 X2) (ho_5605 k_5604 (ho_4531 k_4543 BOUND_VARIABLE_1229507)))) (and (not (ho_4288 (ho_5602 k_5603 X2) BOUND_VARIABLE_229717)) (not (ho_4288 (ho_5602 k_5601 X2) BOUND_VARIABLE_229717)))))) (or _let_10 (and (or (ho_4288 (ho_5602 k_5603 _let_9) _let_8) (ho_4288 (ho_5602 k_5601 _let_9) _let_8)) (forall ((X2 tptp.nat)) (let ((_let_1 (ho_4290 k_4289 X2))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_5 (ho_4215 k_4214 _let_4))) (let ((_let_6 (ho_4216 _let_5 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1229508) _let_4)))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 X2) _let_6))) (let ((_let_9 (ho_4216 (ho_4215 k_4223 X2) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 _let_8) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3)))))) (let ((_let_10 (ho_4537 (ho_4536 k_4535 BOUND_VARIABLE_1229507) _let_8))) (or (not (ho_4293 (ho_4292 k_4291 _let_1) (ho_4290 k_4289 (ho_4216 _let_5 BOUND_VARIABLE_1229508)))) (and (not (ho_4288 (ho_5602 k_5603 _let_10) _let_9)) (not (ho_4288 (ho_5602 k_5601 _let_10) _let_9))) (and (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1229509)) _let_1) (ho_4293 (ho_4292 k_4304 _let_1) (ho_4290 k_4289 BOUND_VARIABLE_1229510))))))))))))))))))))))))))))))))) (let ((_let_3157 (forall ((BOUND_VARIABLE_1229461 tptp.nat) (BOUND_VARIABLE_1229462 tptp.nat) (BOUND_VARIABLE_1229463 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4544 BOUND_VARIABLE_1229461) BOUND_VARIABLE_1229462)) BOUND_VARIABLE_1229463) (ho_5062 (ho_5210 (ho_5209 k_5624 BOUND_VARIABLE_1229461) BOUND_VARIABLE_1229462) BOUND_VARIABLE_1229463))))) (let ((_let_3158 (forall ((BOUND_VARIABLE_1229416 tptp.nat) (BOUND_VARIABLE_1229417 tptp.nat) (BOUND_VARIABLE_1229418 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4545 BOUND_VARIABLE_1229416) BOUND_VARIABLE_1229417)) BOUND_VARIABLE_1229418) (ho_5062 (ho_5210 (ho_5209 k_5625 BOUND_VARIABLE_1229416) BOUND_VARIABLE_1229417) BOUND_VARIABLE_1229418))))) (let ((_let_3159 (forall ((BOUND_VARIABLE_1229335 tptp.nat) (BOUND_VARIABLE_1229336 tptp.nat) (BOUND_VARIABLE_1229337 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4546 BOUND_VARIABLE_1229335) BOUND_VARIABLE_1229336)) BOUND_VARIABLE_1229337) (ho_5062 (ho_5210 (ho_5209 k_5626 BOUND_VARIABLE_1229335) BOUND_VARIABLE_1229336) BOUND_VARIABLE_1229337))))) (let ((_let_3160 (forall ((BOUND_VARIABLE_1229319 tptp.int) (BOUND_VARIABLE_1229320 tptp.int)) (= (ho_4549 (ho_5629 (ho_5628 k_5627 k_4550) (ho_4204 k_4203 BOUND_VARIABLE_1229319)) (ho_4204 k_4203 BOUND_VARIABLE_1229320)) (ho_4310 (ho_4309 k_5630 BOUND_VARIABLE_1229319) BOUND_VARIABLE_1229320))))) (let ((_let_3161 (forall ((BOUND_VARIABLE_1229303 tptp.int) (BOUND_VARIABLE_1229304 tptp.int)) (= (ho_4549 (ho_5629 (ho_5628 k_5627 k_4553) (ho_4204 k_4203 BOUND_VARIABLE_1229303)) (ho_4204 k_4203 BOUND_VARIABLE_1229304)) (ho_4310 (ho_4309 k_5631 BOUND_VARIABLE_1229303) BOUND_VARIABLE_1229304))))) (let ((_let_3162 (forall ((BOUND_VARIABLE_1229258 tptp.nat) (BOUND_VARIABLE_1229259 tptp.nat) (BOUND_VARIABLE_1229260 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4554 BOUND_VARIABLE_1229258) BOUND_VARIABLE_1229259)) BOUND_VARIABLE_1229260) (ho_5062 (ho_5210 (ho_5209 k_5632 BOUND_VARIABLE_1229258) BOUND_VARIABLE_1229259) BOUND_VARIABLE_1229260))))) (let ((_let_3163 (forall ((BOUND_VARIABLE_1229213 tptp.nat) (BOUND_VARIABLE_1229214 tptp.nat) (BOUND_VARIABLE_1229215 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4555 BOUND_VARIABLE_1229213) BOUND_VARIABLE_1229214)) BOUND_VARIABLE_1229215) (ho_5062 (ho_5210 (ho_5209 k_5633 BOUND_VARIABLE_1229213) BOUND_VARIABLE_1229214) BOUND_VARIABLE_1229215))))) (let ((_let_3164 (forall ((BOUND_VARIABLE_1229166 tptp.nat) (BOUND_VARIABLE_1229167 tptp.nat) (BOUND_VARIABLE_1229168 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4556 BOUND_VARIABLE_1229166) BOUND_VARIABLE_1229167)) BOUND_VARIABLE_1229168) (ho_4549 (ho_4552 (ho_4551 k_5634 BOUND_VARIABLE_1229166) BOUND_VARIABLE_1229167) BOUND_VARIABLE_1229168))))) (let ((_let_3165 (forall ((BOUND_VARIABLE_1229119 tptp.nat) (BOUND_VARIABLE_1229120 tptp.nat) (BOUND_VARIABLE_1229121 tptp.product_prod_nat_nat)) (= (ho_4549 (ho_4548 k_4547 (ho_4303 (ho_4302 k_4557 BOUND_VARIABLE_1229119) BOUND_VARIABLE_1229120)) BOUND_VARIABLE_1229121) (ho_4549 (ho_4552 (ho_4551 k_5635 BOUND_VARIABLE_1229119) BOUND_VARIABLE_1229120) BOUND_VARIABLE_1229121))))) (let ((_let_3166 (forall ((BOUND_VARIABLE_1229111 tptp.nat) (BOUND_VARIABLE_1229112 tptp.nat)) (= (ho_4406 (ho_4198 k_5636 BOUND_VARIABLE_1229111) BOUND_VARIABLE_1229112) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1229112) BOUND_VARIABLE_1229111))))) (let ((_let_3167 (forall ((BOUND_VARIABLE_1229103 tptp.nat)) (= (ho_4335 k_5637 BOUND_VARIABLE_1229103) (ho_4202 k_4201 (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1229103) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))))))) (let ((_let_3168 (forall ((BOUND_VARIABLE_1229021 tptp.nat) (BOUND_VARIABLE_1229022 tptp.nat) (BOUND_VARIABLE_1229023 tptp.product_prod_nat_nat)) (= (ho_5062 (ho_4200 k_4199 (ho_4409 (ho_4408 k_4558 BOUND_VARIABLE_1229021) BOUND_VARIABLE_1229022)) BOUND_VARIABLE_1229023) (ho_5062 (ho_5210 (ho_5209 k_5638 BOUND_VARIABLE_1229021) BOUND_VARIABLE_1229022) BOUND_VARIABLE_1229023))))) (let ((_let_3169 (forall ((BOUND_VARIABLE_1228950 tptp.code_integer) (BOUND_VARIABLE_1228951 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4560 k_4559 _let_1)))) (let ((_let_3 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1228951) _let_2)) (ho_4560 k_4559 BOUND_VARIABLE_1228951)) BOUND_VARIABLE_1228951))) (let ((_let_4 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1228950) _let_2)) (ho_4560 k_4559 BOUND_VARIABLE_1228950)) BOUND_VARIABLE_1228950))) (let ((_let_5 (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 _let_4) _let_3)) (ho_4560 (ho_4564 k_5197 _let_4) _let_3)))) (let ((_let_6 (ho_4571 k_4570 _let_2))) (= (ho_4572 (ho_4571 k_5651 BOUND_VARIABLE_1228950) BOUND_VARIABLE_1228951) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1228950 _let_2)) (ho_4572 _let_6 _let_2)) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1228951 _let_2)) (ho_4572 _let_6 BOUND_VARIABLE_1228950)) (ho_4576 (ho_5650 (ho_5649 (ho_5648 k_5647 (ho_5646 (ho_5645 k_5644 k_5642) k_4630)) k_5641) BOUND_VARIABLE_1228951) (ho_4576 (ho_4575 (ho_4574 k_4573 (= (ho_4560 k_5641 BOUND_VARIABLE_1228951) (ho_4560 k_5641 BOUND_VARIABLE_1228950))) _let_5) (ho_4576 (ho_5640 k_5639 (ho_4578 k_4577 BOUND_VARIABLE_1228951)) _let_5))))))))))))))) (let ((_let_3170 (forall ((BOUND_VARIABLE_1228940 tptp.nat) (BOUND_VARIABLE_1228941 tptp.nat)) (= (ho_4288 (ho_4287 k_5652 BOUND_VARIABLE_1228940) BOUND_VARIABLE_1228941) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1228941)) (ho_4290 k_4289 BOUND_VARIABLE_1228940)))))) (let ((_let_3171 (forall ((BOUND_VARIABLE_1228930 tptp.nat) (BOUND_VARIABLE_1228931 tptp.nat)) (= (ho_4288 (ho_4287 k_5653 BOUND_VARIABLE_1228930) BOUND_VARIABLE_1228931) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1228931)) (ho_4290 k_4289 BOUND_VARIABLE_1228930)))))) (let ((_let_3172 (forall ((BOUND_VARIABLE_1228908 tptp.nat) (BOUND_VARIABLE_1228909 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1228908) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1228909) _let_2))) (ho_4216 (ho_4215 k_5654 BOUND_VARIABLE_1228908) BOUND_VARIABLE_1228909)))))))) (let ((_let_3173 (forall ((BOUND_VARIABLE_1228863 tptp.nat) (BOUND_VARIABLE_1228864 tptp.nat) (BOUND_VARIABLE_1228865 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1228863) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1228864))) (or (not (= BOUND_VARIABLE_1228865 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5655 BOUND_VARIABLE_1228863) BOUND_VARIABLE_1228864) BOUND_VARIABLE_1228865))))) (let ((_let_3174 (forall ((BOUND_VARIABLE_1228810 tptp.nat) (BOUND_VARIABLE_1228811 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228811 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5656 BOUND_VARIABLE_1228810) BOUND_VARIABLE_1228811) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228811 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228811) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228811)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228811)) BOUND_VARIABLE_1228811)) BOUND_VARIABLE_1228810)))))))))))))) (let ((_let_3175 (forall ((BOUND_VARIABLE_1228776 tptp.complex) (BOUND_VARIABLE_1228777 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1228777 _let_2))) (= (ho_4351 (ho_5659 k_5658 BOUND_VARIABLE_1228776) BOUND_VARIABLE_1228777) (and (= (ho_4703 k_5657 BOUND_VARIABLE_1228776) (ho_4771 k_4772 BOUND_VARIABLE_1228777)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1228777)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1228777 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228777) _let_3)) (not (= BOUND_VARIABLE_1228777 _let_3))))))))))) (let ((_let_3176 (forall ((BOUND_VARIABLE_1228767 tptp.nat) (BOUND_VARIABLE_1228768 tptp.complex)) (= (ho_5127 (ho_5661 k_5660 BOUND_VARIABLE_1228767) BOUND_VARIABLE_1228768) (= (ho_4701 k_4700 tptp.one) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1228768) BOUND_VARIABLE_1228767)))))) (let ((_let_3177 (forall ((BOUND_VARIABLE_1228757 tptp.complex) (BOUND_VARIABLE_1228758 tptp.nat) (BOUND_VARIABLE_1228759 tptp.complex)) (= (ho_5127 (ho_5661 (ho_5663 k_5662 BOUND_VARIABLE_1228757) BOUND_VARIABLE_1228758) BOUND_VARIABLE_1228759) (= BOUND_VARIABLE_1228757 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1228759) BOUND_VARIABLE_1228758)))))) (let ((_let_3178 (forall ((BOUND_VARIABLE_1228704 tptp.nat) (BOUND_VARIABLE_1228705 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228705 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5664 BOUND_VARIABLE_1228704) BOUND_VARIABLE_1228705) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228705 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228705) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228705)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228705)) BOUND_VARIABLE_1228705)) BOUND_VARIABLE_1228704)))))))))))))) (let ((_let_3179 (forall ((BOUND_VARIABLE_1228651 tptp.nat) (BOUND_VARIABLE_1228652 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228652 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5665 BOUND_VARIABLE_1228651) BOUND_VARIABLE_1228652) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228652 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228652) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228652)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228652)) BOUND_VARIABLE_1228652)) BOUND_VARIABLE_1228651)))))))))))))) (let ((_let_3180 (forall ((BOUND_VARIABLE_1228598 tptp.nat) (BOUND_VARIABLE_1228599 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228599 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5666 BOUND_VARIABLE_1228598) BOUND_VARIABLE_1228599) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228599 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228599) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228599)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228599)) BOUND_VARIABLE_1228599)) BOUND_VARIABLE_1228598)))))))))))))) (let ((_let_3181 (forall ((BOUND_VARIABLE_1228545 tptp.nat) (BOUND_VARIABLE_1228546 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228546 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5667 BOUND_VARIABLE_1228545) BOUND_VARIABLE_1228546) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228546 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228546) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228546)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228546)) BOUND_VARIABLE_1228546)) BOUND_VARIABLE_1228545)))))))))))))) (let ((_let_3182 (forall ((BOUND_VARIABLE_1228492 tptp.nat) (BOUND_VARIABLE_1228493 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228493 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5668 BOUND_VARIABLE_1228492) BOUND_VARIABLE_1228493) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228493 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228493) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228493)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228493)) BOUND_VARIABLE_1228493)) BOUND_VARIABLE_1228492)))))))))))))) (let ((_let_3183 (forall ((BOUND_VARIABLE_1228439 tptp.nat) (BOUND_VARIABLE_1228440 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228440 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5669 BOUND_VARIABLE_1228439) BOUND_VARIABLE_1228440) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228440 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228440) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228440)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228440)) BOUND_VARIABLE_1228440)) BOUND_VARIABLE_1228439)))))))))))))) (let ((_let_3184 (forall ((BOUND_VARIABLE_1228386 tptp.nat) (BOUND_VARIABLE_1228387 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228387 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5670 BOUND_VARIABLE_1228386) BOUND_VARIABLE_1228387) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228387 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228387) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228387)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228387)) BOUND_VARIABLE_1228387)) BOUND_VARIABLE_1228386)))))))))))))) (let ((_let_3185 (forall ((BOUND_VARIABLE_1228333 tptp.nat) (BOUND_VARIABLE_1228334 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228334 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5671 BOUND_VARIABLE_1228333) BOUND_VARIABLE_1228334) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228334 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228334) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228334)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228334)) BOUND_VARIABLE_1228334)) BOUND_VARIABLE_1228333)))))))))))))) (let ((_let_3186 (forall ((BOUND_VARIABLE_1228280 tptp.nat) (BOUND_VARIABLE_1228281 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228281 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5672 BOUND_VARIABLE_1228280) BOUND_VARIABLE_1228281) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228281 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228281) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228281)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228281)) BOUND_VARIABLE_1228281)) BOUND_VARIABLE_1228280)))))))))))))) (let ((_let_3187 (forall ((BOUND_VARIABLE_1228227 tptp.nat) (BOUND_VARIABLE_1228228 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228228 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5673 BOUND_VARIABLE_1228227) BOUND_VARIABLE_1228228) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228228 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228228) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228228)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228228)) BOUND_VARIABLE_1228228)) BOUND_VARIABLE_1228227)))))))))))))) (let ((_let_3188 (forall ((BOUND_VARIABLE_1228174 tptp.nat) (BOUND_VARIABLE_1228175 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228175 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5674 BOUND_VARIABLE_1228174) BOUND_VARIABLE_1228175) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228175 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228175) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228175)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228175)) BOUND_VARIABLE_1228175)) BOUND_VARIABLE_1228174)))))))))))))) (let ((_let_3189 (forall ((BOUND_VARIABLE_1228121 tptp.nat) (BOUND_VARIABLE_1228122 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228122 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5675 BOUND_VARIABLE_1228121) BOUND_VARIABLE_1228122) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228122 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228122) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228122)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228122)) BOUND_VARIABLE_1228122)) BOUND_VARIABLE_1228121)))))))))))))) (let ((_let_3190 (forall ((BOUND_VARIABLE_1228068 tptp.nat) (BOUND_VARIABLE_1228069 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228069 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5676 BOUND_VARIABLE_1228068) BOUND_VARIABLE_1228069) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228069 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228069) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228069)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228069)) BOUND_VARIABLE_1228069)) BOUND_VARIABLE_1228068)))))))))))))) (let ((_let_3191 (forall ((BOUND_VARIABLE_1228015 tptp.nat) (BOUND_VARIABLE_1228016 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1228016 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5677 BOUND_VARIABLE_1228015) BOUND_VARIABLE_1228016) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1228016 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1228016) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1228016)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1228016)) BOUND_VARIABLE_1228016)) BOUND_VARIABLE_1228015)))))))))))))) (let ((_let_3192 (forall ((BOUND_VARIABLE_1227962 tptp.nat) (BOUND_VARIABLE_1227963 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227963 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5678 BOUND_VARIABLE_1227962) BOUND_VARIABLE_1227963) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227963 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227963) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227963)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227963)) BOUND_VARIABLE_1227963)) BOUND_VARIABLE_1227962)))))))))))))) (let ((_let_3193 (forall ((BOUND_VARIABLE_1227909 tptp.nat) (BOUND_VARIABLE_1227910 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227910 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5679 BOUND_VARIABLE_1227909) BOUND_VARIABLE_1227910) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227910 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227910) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 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(ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227857)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227857)) BOUND_VARIABLE_1227857)) BOUND_VARIABLE_1227856)))))))))))))) (let ((_let_3195 (forall ((BOUND_VARIABLE_1227803 tptp.nat) (BOUND_VARIABLE_1227804 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227804 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5681 BOUND_VARIABLE_1227803) BOUND_VARIABLE_1227804) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227804 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227804) _let_6)) _let_8)) 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BOUND_VARIABLE_1227539) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227539 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227539) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227539)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227539)) BOUND_VARIABLE_1227539)) BOUND_VARIABLE_1227538)))))))))))))) (let ((_let_3201 (forall ((BOUND_VARIABLE_1227485 tptp.nat) (BOUND_VARIABLE_1227486 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227486 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5687 BOUND_VARIABLE_1227485) BOUND_VARIABLE_1227486) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227486 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227486) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227486)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227486)) BOUND_VARIABLE_1227486)) BOUND_VARIABLE_1227485)))))))))))))) (let ((_let_3202 (forall ((BOUND_VARIABLE_1227432 tptp.nat) (BOUND_VARIABLE_1227433 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= 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_let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227327 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5690 BOUND_VARIABLE_1227326) BOUND_VARIABLE_1227327) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227327 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227327) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227327)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227327)) BOUND_VARIABLE_1227327)) BOUND_VARIABLE_1227326)))))))))))))) (let ((_let_3205 (forall ((BOUND_VARIABLE_1227273 tptp.nat) (BOUND_VARIABLE_1227274 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227274 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5691 BOUND_VARIABLE_1227273) BOUND_VARIABLE_1227274) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227274 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227274) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227274)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227274)) BOUND_VARIABLE_1227274)) BOUND_VARIABLE_1227273)))))))))))))) (let ((_let_3206 (forall ((BOUND_VARIABLE_1227220 tptp.nat) (BOUND_VARIABLE_1227221 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227221 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5692 BOUND_VARIABLE_1227220) BOUND_VARIABLE_1227221) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227221 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227221) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227221)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227221)) BOUND_VARIABLE_1227221)) BOUND_VARIABLE_1227220)))))))))))))) (let ((_let_3207 (forall ((BOUND_VARIABLE_1227167 tptp.nat) (BOUND_VARIABLE_1227168 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227168 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5693 BOUND_VARIABLE_1227167) BOUND_VARIABLE_1227168) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227168 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227168) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227168)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227168)) BOUND_VARIABLE_1227168)) BOUND_VARIABLE_1227167)))))))))))))) (let ((_let_3208 (forall ((BOUND_VARIABLE_1227114 tptp.nat) (BOUND_VARIABLE_1227115 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227115 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5694 BOUND_VARIABLE_1227114) BOUND_VARIABLE_1227115) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227115 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227115) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227115)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227115)) BOUND_VARIABLE_1227115)) BOUND_VARIABLE_1227114)))))))))))))) (let ((_let_3209 (forall ((BOUND_VARIABLE_1227061 tptp.nat) (BOUND_VARIABLE_1227062 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227062 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5695 BOUND_VARIABLE_1227061) BOUND_VARIABLE_1227062) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227062 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227062) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227062)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227062)) BOUND_VARIABLE_1227062)) BOUND_VARIABLE_1227061)))))))))))))) (let ((_let_3210 (forall ((BOUND_VARIABLE_1227008 tptp.nat) (BOUND_VARIABLE_1227009 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1227009 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5696 BOUND_VARIABLE_1227008) BOUND_VARIABLE_1227009) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1227009 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1227009) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1227009)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1227009)) BOUND_VARIABLE_1227009)) BOUND_VARIABLE_1227008)))))))))))))) (let ((_let_3211 (forall ((BOUND_VARIABLE_1226940 tptp.nat) (BOUND_VARIABLE_1226941 tptp.nat) (BOUND_VARIABLE_1226942 tptp.real)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_5 (ho_4257 _let_4 k_4248))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4258 _let_5 _let_6))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_4))) (let ((_let_9 (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) _let_6) _let_7))) (let ((_let_10 (= BOUND_VARIABLE_1226942 _let_9))) (let ((_let_11 (not _let_10))) (= (ho_4258 (ho_4273 (ho_4715 k_5697 BOUND_VARIABLE_1226940) BOUND_VARIABLE_1226941) BOUND_VARIABLE_1226942) (ho_4258 (ho_4265 (ho_4264 _let_8 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 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_let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5698 BOUND_VARIABLE_1226887) BOUND_VARIABLE_1226888) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226888 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226888) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226888)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226888)) BOUND_VARIABLE_1226888)) BOUND_VARIABLE_1226887)))))))))))))) (let ((_let_3213 (forall ((BOUND_VARIABLE_1226834 tptp.nat) (BOUND_VARIABLE_1226835 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226835 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5699 BOUND_VARIABLE_1226834) BOUND_VARIABLE_1226835) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226835 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226835) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226835)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226835)) BOUND_VARIABLE_1226835)) BOUND_VARIABLE_1226834)))))))))))))) (let ((_let_3214 (forall ((BOUND_VARIABLE_1226781 tptp.nat) (BOUND_VARIABLE_1226782 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226782 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5700 BOUND_VARIABLE_1226781) BOUND_VARIABLE_1226782) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226782 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226782) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226782)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226782)) BOUND_VARIABLE_1226782)) BOUND_VARIABLE_1226781)))))))))))))) (let ((_let_3215 (forall ((BOUND_VARIABLE_1226728 tptp.nat) (BOUND_VARIABLE_1226729 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226729 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5701 BOUND_VARIABLE_1226728) BOUND_VARIABLE_1226729) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226729 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226729) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226729)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226729)) BOUND_VARIABLE_1226729)) BOUND_VARIABLE_1226728)))))))))))))) (let ((_let_3216 (forall ((BOUND_VARIABLE_1226675 tptp.nat) (BOUND_VARIABLE_1226676 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226676 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5702 BOUND_VARIABLE_1226675) BOUND_VARIABLE_1226676) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226676 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226676) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226676)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226676)) BOUND_VARIABLE_1226676)) BOUND_VARIABLE_1226675)))))))))))))) (let ((_let_3217 (forall ((BOUND_VARIABLE_1226622 tptp.nat) (BOUND_VARIABLE_1226623 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226623 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5703 BOUND_VARIABLE_1226622) BOUND_VARIABLE_1226623) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226623 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226623) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226623)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226623)) BOUND_VARIABLE_1226623)) BOUND_VARIABLE_1226622)))))))))))))) (let ((_let_3218 (forall ((BOUND_VARIABLE_1226569 tptp.nat) (BOUND_VARIABLE_1226570 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226570 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5704 BOUND_VARIABLE_1226569) BOUND_VARIABLE_1226570) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226570 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226570) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226570)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226570)) BOUND_VARIABLE_1226570)) BOUND_VARIABLE_1226569)))))))))))))) (let ((_let_3219 (forall ((BOUND_VARIABLE_1226516 tptp.nat) (BOUND_VARIABLE_1226517 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226517 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5705 BOUND_VARIABLE_1226516) BOUND_VARIABLE_1226517) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226517 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226517) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226517)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226517)) BOUND_VARIABLE_1226517)) BOUND_VARIABLE_1226516)))))))))))))) (let ((_let_3220 (forall ((BOUND_VARIABLE_1226463 tptp.nat) (BOUND_VARIABLE_1226464 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226464 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5706 BOUND_VARIABLE_1226463) BOUND_VARIABLE_1226464) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226464 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226464) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226464)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226464)) BOUND_VARIABLE_1226464)) BOUND_VARIABLE_1226463)))))))))))))) (let ((_let_3221 (forall ((BOUND_VARIABLE_1226410 tptp.nat) (BOUND_VARIABLE_1226411 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226411 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5707 BOUND_VARIABLE_1226410) BOUND_VARIABLE_1226411) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226411 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226411) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226411)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226411)) BOUND_VARIABLE_1226411)) BOUND_VARIABLE_1226410)))))))))))))) (let ((_let_3222 (forall ((BOUND_VARIABLE_1226357 tptp.nat) (BOUND_VARIABLE_1226358 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226358 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5708 BOUND_VARIABLE_1226357) BOUND_VARIABLE_1226358) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226358 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226358) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226358)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226358)) BOUND_VARIABLE_1226358)) BOUND_VARIABLE_1226357)))))))))))))) (let ((_let_3223 (forall ((BOUND_VARIABLE_1226304 tptp.nat) (BOUND_VARIABLE_1226305 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226305 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5709 BOUND_VARIABLE_1226304) BOUND_VARIABLE_1226305) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226305 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226305) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226305)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226305)) BOUND_VARIABLE_1226305)) BOUND_VARIABLE_1226304)))))))))))))) (let ((_let_3224 (forall ((BOUND_VARIABLE_1226251 tptp.nat) (BOUND_VARIABLE_1226252 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226252 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5710 BOUND_VARIABLE_1226251) BOUND_VARIABLE_1226252) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226252 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226252) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226252)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226252)) BOUND_VARIABLE_1226252)) BOUND_VARIABLE_1226251)))))))))))))) (let ((_let_3225 (forall ((BOUND_VARIABLE_1226198 tptp.nat) (BOUND_VARIABLE_1226199 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226199 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5711 BOUND_VARIABLE_1226198) BOUND_VARIABLE_1226199) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226199 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226199) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226199)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226199)) BOUND_VARIABLE_1226199)) BOUND_VARIABLE_1226198)))))))))))))) (let ((_let_3226 (forall ((BOUND_VARIABLE_1226145 tptp.nat) (BOUND_VARIABLE_1226146 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226146 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5712 BOUND_VARIABLE_1226145) BOUND_VARIABLE_1226146) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226146 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226146) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226146)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226146)) BOUND_VARIABLE_1226146)) BOUND_VARIABLE_1226145)))))))))))))) (let ((_let_3227 (forall ((BOUND_VARIABLE_1226092 tptp.nat) (BOUND_VARIABLE_1226093 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226093 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5713 BOUND_VARIABLE_1226092) BOUND_VARIABLE_1226093) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226093 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226093) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226093)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226093)) BOUND_VARIABLE_1226093)) BOUND_VARIABLE_1226092)))))))))))))) (let ((_let_3228 (forall ((BOUND_VARIABLE_1226039 tptp.nat) (BOUND_VARIABLE_1226040 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1226040 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5714 BOUND_VARIABLE_1226039) BOUND_VARIABLE_1226040) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1226040 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1226040) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1226040)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1226040)) BOUND_VARIABLE_1226040)) BOUND_VARIABLE_1226039)))))))))))))) (let ((_let_3229 (forall ((BOUND_VARIABLE_1225986 tptp.nat) (BOUND_VARIABLE_1225987 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1225987 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5715 BOUND_VARIABLE_1225986) BOUND_VARIABLE_1225987) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225987 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225987) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1225987)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1225987)) BOUND_VARIABLE_1225987)) BOUND_VARIABLE_1225986)))))))))))))) (let ((_let_3230 (forall ((BOUND_VARIABLE_1225933 tptp.nat) (BOUND_VARIABLE_1225934 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1225934 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5716 BOUND_VARIABLE_1225933) BOUND_VARIABLE_1225934) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225934 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225934) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1225934)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1225934)) BOUND_VARIABLE_1225934)) BOUND_VARIABLE_1225933)))))))))))))) (let ((_let_3231 (forall ((BOUND_VARIABLE_1225881 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1225881 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 k_5717 BOUND_VARIABLE_1225881) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225881 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225881) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1225881)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1225881)) BOUND_VARIABLE_1225881)) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))))))))))))))) (let ((_let_3232 (forall ((BOUND_VARIABLE_1225829 tptp.real)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_6 (ho_4257 _let_5 k_4248))) (let ((_let_7 (ho_4247 k_4246 tptp.one))) (let ((_let_8 (ho_4258 _let_6 _let_7))) (let ((_let_9 (ho_4263 (ho_4262 k_4261 k_4252) _let_5))) (let ((_let_10 (ho_4258 (ho_4265 (ho_4264 _let_9 k_4259) _let_7) _let_8))) (let ((_let_11 (= BOUND_VARIABLE_1225829 _let_10))) (let ((_let_12 (not _let_11))) (= (ho_4258 k_5718 BOUND_VARIABLE_1225829) (ho_4258 (ho_4265 (ho_4264 _let_9 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_11) _let_10) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225829 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225829) _let_10)) _let_12)) _let_7) _let_8))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_10 (ho_4258 (ho_4265 k_4349 _let_10) BOUND_VARIABLE_1225829)) _let_12)) (ho_4258 _let_6 BOUND_VARIABLE_1225829)) BOUND_VARIABLE_1225829)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))))))))))))))))) (let ((_let_3233 (forall ((BOUND_VARIABLE_1225776 tptp.nat) (BOUND_VARIABLE_1225777 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1225777 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5719 BOUND_VARIABLE_1225776) BOUND_VARIABLE_1225777) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225777 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225777) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1225777)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1225777)) BOUND_VARIABLE_1225777)) BOUND_VARIABLE_1225776)))))))))))))) (let ((_let_3234 (forall ((BOUND_VARIABLE_1225737 tptp.int) (BOUND_VARIABLE_1225738 tptp.int) (BOUND_VARIABLE_1225739 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4636 (ho_4635 k_4634 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1225737) _let_1)) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1225738) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) (or (not (= BOUND_VARIABLE_1225739 (ho_4335 (ho_4640 k_4639 _let_2) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_2))))))))) (ho_4310 (ho_4309 (ho_4308 k_5720 BOUND_VARIABLE_1225737) BOUND_VARIABLE_1225738) BOUND_VARIABLE_1225739))))) (let ((_let_3235 (forall ((BOUND_VARIABLE_1225684 tptp.nat) (BOUND_VARIABLE_1225685 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (= BOUND_VARIABLE_1225685 _let_6))) (let ((_let_8 (not _let_7))) (= (ho_4258 (ho_4273 k_5721 BOUND_VARIABLE_1225684) BOUND_VARIABLE_1225685) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 _let_7) _let_6) (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= BOUND_VARIABLE_1225685 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1225685) _let_6)) _let_8)) _let_3) _let_4))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (and (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) BOUND_VARIABLE_1225685)) _let_8)) (ho_4258 _let_2 BOUND_VARIABLE_1225685)) BOUND_VARIABLE_1225685)) BOUND_VARIABLE_1225684)))))))))))))) (let ((_let_3236 (forall ((BOUND_VARIABLE_1225673 tptp.set_nat) (BOUND_VARIABLE_1225674 tptp.nat)) (= (ho_4288 (ho_5139 k_5722 BOUND_VARIABLE_1225673) BOUND_VARIABLE_1225674) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1225674)) (ho_4290 k_4289 (ho_5346 k_5723 BOUND_VARIABLE_1225673))))))) (let ((_let_3237 (forall ((BOUND_VARIABLE_1225619 tptp.nat) (BOUND_VARIABLE_1225620 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1225619) BOUND_VARIABLE_1225620)) _let_3))) (let ((_let_6 (ho_5726 (ho_5725 k_5724 BOUND_VARIABLE_1225620) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1225619) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_5) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1225620) _let_3))))))) (let ((_let_7 (ho_4587 k_4586 _let_6))) (= (ho_5726 (ho_5725 k_5727 BOUND_VARIABLE_1225619) BOUND_VARIABLE_1225620) (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1225620 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4428 (ho_4427 k_4426 _let_1) _let_3)) (ho_4428 (ho_4427 k_4426 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4587 k_4588 _let_6)) (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 _let_7) _let_5)))))))))))))))) (let ((_let_3238 (forall ((BOUND_VARIABLE_1225596 tptp.rat) (BOUND_VARIABLE_1225597 tptp.rat)) (= (ho_4582 (ho_4581 k_4580 (ho_4584 k_4583 BOUND_VARIABLE_1225597)) (ho_4437 k_4579 BOUND_VARIABLE_1225596)) (ho_5243 (ho_5729 k_5728 BOUND_VARIABLE_1225596) BOUND_VARIABLE_1225597))))) (let ((_let_3239 (forall ((BOUND_VARIABLE_1225572 tptp.rat) (BOUND_VARIABLE_1225573 tptp.rat)) (= (ho_4582 (ho_4581 k_4580 (ho_4584 k_4585 BOUND_VARIABLE_1225573)) (ho_4437 k_4579 BOUND_VARIABLE_1225572)) (ho_5243 (ho_5729 k_5730 BOUND_VARIABLE_1225572) BOUND_VARIABLE_1225573))))) (let ((_let_3240 (forall ((BOUND_VARIABLE_1225545 tptp.int) (BOUND_VARIABLE_1225546 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_1 _let_2)))) (= (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1225545) _let_2)) _let_3))) (ho_4209 _let_1 BOUND_VARIABLE_1225545)) BOUND_VARIABLE_1225545)) BOUND_VARIABLE_1225546) (ho_4428 (ho_4427 k_5731 BOUND_VARIABLE_1225545) BOUND_VARIABLE_1225546)))))))) (let ((_let_3241 (forall ((BOUND_VARIABLE_1225531 tptp.int) (BOUND_VARIABLE_1225532 tptp.int)) (= (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) BOUND_VARIABLE_1225531)) BOUND_VARIABLE_1225532) (ho_4428 (ho_4427 k_5732 BOUND_VARIABLE_1225531) BOUND_VARIABLE_1225532))))) (let ((_let_3242 (forall ((BOUND_VARIABLE_1225183 tptp.rat) (BOUND_VARIABLE_1225184 tptp.int) (BOUND_VARIABLE_1225185 tptp.int)) (= (ho_4432 (ho_5734 k_5733 (ho_4597 (ho_4596 k_4595 BOUND_VARIABLE_1225184) BOUND_VARIABLE_1225185)) (ho_4437 k_4579 BOUND_VARIABLE_1225183)) (ho_4428 (ho_4427 (ho_5736 k_5735 BOUND_VARIABLE_1225183) BOUND_VARIABLE_1225184) BOUND_VARIABLE_1225185))))) (let ((_let_3243 (forall ((BOUND_VARIABLE_1224837 tptp.rat) (BOUND_VARIABLE_1224838 tptp.int) (BOUND_VARIABLE_1224839 tptp.int)) (= (ho_4432 (ho_5734 k_5733 (ho_4597 (ho_4596 k_4598 BOUND_VARIABLE_1224838) BOUND_VARIABLE_1224839)) (ho_4437 k_4579 BOUND_VARIABLE_1224837)) (ho_4428 (ho_4427 (ho_5736 k_5737 BOUND_VARIABLE_1224837) BOUND_VARIABLE_1224838) BOUND_VARIABLE_1224839))))) (let ((_let_3244 (forall ((BOUND_VARIABLE_1224497 tptp.rat) (BOUND_VARIABLE_1224498 tptp.int) (BOUND_VARIABLE_1224499 tptp.int)) (= (ho_4432 (ho_5734 k_5733 (ho_4597 (ho_4596 k_4599 BOUND_VARIABLE_1224498) BOUND_VARIABLE_1224499)) (ho_4437 k_4579 BOUND_VARIABLE_1224497)) (ho_4428 (ho_4427 (ho_5736 k_5738 BOUND_VARIABLE_1224497) BOUND_VARIABLE_1224498) BOUND_VARIABLE_1224499))))) (let ((_let_3245 (forall ((BOUND_VARIABLE_1224156 tptp.rat) (BOUND_VARIABLE_1224157 tptp.int) (BOUND_VARIABLE_1224158 tptp.int)) (= (ho_4432 (ho_5734 k_5733 (ho_4597 (ho_4596 k_4600 BOUND_VARIABLE_1224157) BOUND_VARIABLE_1224158)) (ho_4437 k_4579 BOUND_VARIABLE_1224156)) (ho_4428 (ho_4427 (ho_5736 k_5739 BOUND_VARIABLE_1224156) BOUND_VARIABLE_1224157) BOUND_VARIABLE_1224158))))) (let ((_let_3246 (forall ((BOUND_VARIABLE_1224142 tptp.rat) (BOUND_VARIABLE_1224143 tptp.rat)) (let ((_let_1 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_1) k_4443) BOUND_VARIABLE_1224142) (ho_4442 (ho_4441 _let_1 k_4435) BOUND_VARIABLE_1224143)) (ho_4442 (ho_4448 k_5740 BOUND_VARIABLE_1224142) BOUND_VARIABLE_1224143)))))) (let ((_let_3247 (forall ((BOUND_VARIABLE_1224105 tptp.int) (BOUND_VARIABLE_1224106 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_1 _let_2)))) (= (ho_4428 (ho_4427 k_5741 BOUND_VARIABLE_1224105) BOUND_VARIABLE_1224106) (ho_4432 (ho_4431 (ho_4430 k_4429 (= BOUND_VARIABLE_1224105 _let_3)) (ho_4428 (ho_4427 k_4426 _let_3) _let_2)) (ho_4428 (ho_4427 k_4426 (ho_4209 (ho_4211 k_4222 (ho_4209 k_4594 BOUND_VARIABLE_1224105)) BOUND_VARIABLE_1224106)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1224105) _let_2)) _let_3))) (ho_4209 _let_1 BOUND_VARIABLE_1224105)) BOUND_VARIABLE_1224105)))))))))) (let ((_let_3248 (forall ((BOUND_VARIABLE_1224092 tptp.rat) (BOUND_VARIABLE_1224093 tptp.rat)) (let ((_let_1 (= BOUND_VARIABLE_1224092 BOUND_VARIABLE_1224093))) (= (ho_5243 (ho_5729 k_5742 BOUND_VARIABLE_1224092) BOUND_VARIABLE_1224093) (or (and (= BOUND_VARIABLE_1224093 (ho_4442 (ho_4448 k_5252 BOUND_VARIABLE_1224093) BOUND_VARIABLE_1224092)) (not _let_1)) _let_1)))))) (let ((_let_3249 (forall ((BOUND_VARIABLE_1224055 tptp.nat) (BOUND_VARIABLE_1224056 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1224055) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (= (ho_5062 (ho_5061 (ho_5060 k_5059 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1224056)) (ho_4290 k_4289 BOUND_VARIABLE_1224055))) (ho_4406 (ho_4198 k_4405 BOUND_VARIABLE_1224056) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1224055) BOUND_VARIABLE_1224056))) (ho_4406 (ho_4198 k_5743 _let_4) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1224056) _let_4))) (ho_4406 (ho_4198 k_5744 BOUND_VARIABLE_1224055) BOUND_VARIABLE_1224056))))))))) (let ((_let_3250 (forall ((BOUND_VARIABLE_1224050 tptp.nat)) (= BOUND_VARIABLE_1224050 (ho_4216 k_5745 BOUND_VARIABLE_1224050))))) (let ((_let_3251 (forall ((BOUND_VARIABLE_1224025 tptp.nat) (BOUND_VARIABLE_1224026 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1224026)) (ho_4290 k_4289 BOUND_VARIABLE_1224025))) BOUND_VARIABLE_1224025) BOUND_VARIABLE_1224026)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (ho_4216 (ho_4215 k_5746 BOUND_VARIABLE_1224025) BOUND_VARIABLE_1224026)))))))) (let ((_let_3252 (forall ((BOUND_VARIABLE_1224000 tptp.nat) (BOUND_VARIABLE_1224001 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1224000)) (ho_4290 k_4289 BOUND_VARIABLE_1224001))) BOUND_VARIABLE_1224001) BOUND_VARIABLE_1224000)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (ho_4216 (ho_4215 k_5747 BOUND_VARIABLE_1224000) BOUND_VARIABLE_1224001)))))))) (let ((_let_3253 (forall ((BOUND_VARIABLE_1223990 tptp.nat) (BOUND_VARIABLE_1223991 tptp.nat)) (= (ho_4288 (ho_4287 k_5748 BOUND_VARIABLE_1223990) BOUND_VARIABLE_1223991) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1223990)) (ho_4290 k_4289 BOUND_VARIABLE_1223991)))))) (let ((_let_3254 (forall ((BOUND_VARIABLE_1223985 tptp.nat)) (not (ho_4288 k_5749 BOUND_VARIABLE_1223985))))) (let ((_let_3255 (forall ((BOUND_VARIABLE_1223980 tptp.nat)) (ho_4288 k_5750 BOUND_VARIABLE_1223980)))) (let ((_let_3256 (forall ((BOUND_VARIABLE_1223959 tptp.complex)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (let ((_let_4 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_3 _let_4) (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_3 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 BOUND_VARIABLE_1223959)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 BOUND_VARIABLE_1223959)) _let_1)))) (ho_4769 k_5751 BOUND_VARIABLE_1223959))))))))) (let ((_let_3257 (forall ((BOUND_VARIABLE_1223944 tptp.complex)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_3 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_3))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4769 k_4773 (ho_4703 (ho_4705 k_4710 BOUND_VARIABLE_1223944) (ho_4703 k_5752 BOUND_VARIABLE_1223944))))) (ho_4769 k_5753 BOUND_VARIABLE_1223944)))))))) (let ((_let_3258 (forall ((BOUND_VARIABLE_1223872 tptp.complex) (BOUND_VARIABLE_1223873 tptp.complex)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4257 _let_3 k_4248))) (let ((_let_8 (ho_4771 k_4770 (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_2 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_2))) (ho_4258 (ho_4265 _let_5 _let_6) (ho_4258 _let_7 _let_6))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_5 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 BOUND_VARIABLE_1223873)) _let_2)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 BOUND_VARIABLE_1223873)) _let_2))))) _let_2)))) (let ((_let_9 (ho_4769 k_4768 _let_8))) (let ((_let_10 (ho_4769 k_4773 _let_8))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4258 _let_11 (ho_4258 (ho_4265 _let_5 (ho_4245 (ho_4244 k_4243 _let_10) _let_2)) (ho_4245 (ho_4244 k_4243 _let_9) _let_2))))) (let ((_let_13 (ho_4264 _let_4 k_4275))) (let ((_let_14 (ho_4247 k_4246 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 BOUND_VARIABLE_1223872) (ho_4703 k_5752 BOUND_VARIABLE_1223873))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_13 _let_10) _let_12))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_13 (ho_4258 (ho_4265 _let_13 _let_14) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_14)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_13 (ho_4258 _let_7 _let_9)) _let_12))))) (ho_4703 (ho_4705 k_5754 BOUND_VARIABLE_1223872) BOUND_VARIABLE_1223873))))))))))))))))))) (let ((_let_3259 (forall ((BOUND_VARIABLE_1223829 tptp.complex) (BOUND_VARIABLE_1223830 tptp.complex)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4769 k_4768 BOUND_VARIABLE_1223830))) (let ((_let_4 (ho_4769 k_4773 BOUND_VARIABLE_1223830))) (let ((_let_5 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_5))) (let ((_let_7 (ho_4257 _let_5 k_4274))) (let ((_let_8 (ho_4258 _let_7 (ho_4258 (ho_4265 (ho_4264 _let_6 k_4259) (ho_4245 (ho_4244 k_4243 _let_4) _let_2)) (ho_4245 (ho_4244 k_4243 _let_3) _let_2))))) (let ((_let_9 (ho_4264 _let_6 k_4275))) (let ((_let_10 (ho_4247 k_4246 _let_1))) (= (ho_4703 (ho_4705 k_4710 BOUND_VARIABLE_1223829) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_9 _let_4) _let_8))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 _let_10) (ho_4506 k_4505 k_4504))) (ho_4258 _let_7 _let_10)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4257 _let_5 k_4248) _let_3)) _let_8))))) (ho_4703 (ho_4705 k_5755 BOUND_VARIABLE_1223829) BOUND_VARIABLE_1223830))))))))))))))) (let ((_let_3260 (forall ((BOUND_VARIABLE_1223767 tptp.complex) (BOUND_VARIABLE_1223768 tptp.complex)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4769 k_4768 BOUND_VARIABLE_1223768))) (let ((_let_4 (ho_4769 k_4773 BOUND_VARIABLE_1223768))) (let ((_let_5 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_5))) (let ((_let_7 (ho_4264 _let_6 k_4259))) (let ((_let_8 (ho_4257 _let_5 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_4) _let_2)) (ho_4245 (ho_4244 k_4243 _let_3) _let_2))))) (let ((_let_10 (ho_4264 _let_6 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4769 k_4773 BOUND_VARIABLE_1223767)))) (let ((_let_12 (ho_4265 _let_10 (ho_4769 k_4768 BOUND_VARIABLE_1223767)))) (let ((_let_13 (ho_4247 k_4246 _let_1))) (= (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_7 (ho_4258 _let_11 _let_4)) (ho_4258 _let_12 _let_3))) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_13) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_13)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_7 (ho_4258 _let_12 _let_4)) (ho_4258 (ho_4257 _let_5 k_4248) (ho_4258 _let_11 _let_3)))) _let_9)))) (ho_4703 (ho_4705 k_5756 BOUND_VARIABLE_1223767) BOUND_VARIABLE_1223768)))))))))))))))))) (let ((_let_3261 (forall ((BOUND_VARIABLE_1223723 tptp.complex) (BOUND_VARIABLE_1223724 tptp.complex)) (let ((_let_1 (ho_4769 k_4773 BOUND_VARIABLE_1223724))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4265 _let_4 (ho_4769 k_4768 BOUND_VARIABLE_1223723)))) (let ((_let_6 (ho_4769 k_4768 BOUND_VARIABLE_1223724))) (let ((_let_7 (ho_4265 _let_4 (ho_4769 k_4773 BOUND_VARIABLE_1223723)))) (let ((_let_8 (ho_4264 _let_3 k_4259))) (let ((_let_9 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (= (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_8 (ho_4258 _let_7 _let_1)) (ho_4258 (ho_4257 _let_2 k_4248) (ho_4258 _let_5 _let_6))))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_9) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_9)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_8 (ho_4258 _let_7 _let_6)) (ho_4258 _let_5 _let_1))))) (ho_4703 (ho_4705 k_5757 BOUND_VARIABLE_1223723) BOUND_VARIABLE_1223724)))))))))))))) (let ((_let_3262 (forall ((BOUND_VARIABLE_1223671 tptp.complex) (BOUND_VARIABLE_1223672 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_5759 k_5758 BOUND_VARIABLE_1223671) BOUND_VARIABLE_1223672) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1223672 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1223672) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1223672) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 BOUND_VARIABLE_1223671)) BOUND_VARIABLE_1223672))))))))))))))))) (let ((_let_3263 (forall ((BOUND_VARIABLE_1223624 tptp.complex) (BOUND_VARIABLE_1223625 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_5759 k_5760 BOUND_VARIABLE_1223624) BOUND_VARIABLE_1223625) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1223625 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1223625) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1223625) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 BOUND_VARIABLE_1223624)) BOUND_VARIABLE_1223625))))))))))))) (let ((_let_3264 (forall ((BOUND_VARIABLE_1223562 tptp.nat) (BOUND_VARIABLE_1223563 tptp.real) (BOUND_VARIABLE_1223564 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4272 k_4271 k_4270))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (let ((_let_8 (ho_4196 k_4195 tptp.one))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_11 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_8)))) (let ((_let_12 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 (ho_4492 k_5761 BOUND_VARIABLE_1223562) BOUND_VARIABLE_1223563) BOUND_VARIABLE_1223564) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1223564 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1223564) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_12 (ho_4216 (ho_4215 k_4221 _let_9) _let_10)) _let_11)) (ho_4209 (ho_4220 _let_12 _let_9) _let_11))))) _let_10))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 _let_6 (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1223564) _let_9)) _let_5))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4273 _let_6 BOUND_VARIABLE_1223562) _let_5)) BOUND_VARIABLE_1223563)) BOUND_VARIABLE_1223564)))))))))))))))))) (let ((_let_3265 (forall ((BOUND_VARIABLE_1223532 tptp.complex) (BOUND_VARIABLE_1223533 tptp.complex)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4264 _let_2 k_4259))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (ho_4264 _let_2 k_4275))) (= (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_3 (ho_4769 k_4773 BOUND_VARIABLE_1223532)) (ho_4769 k_4773 BOUND_VARIABLE_1223533)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 _let_4) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_1 k_4274) _let_4)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_3 (ho_4769 k_4768 BOUND_VARIABLE_1223532)) (ho_4769 k_4768 BOUND_VARIABLE_1223533))))) (ho_4703 (ho_4705 k_5762 BOUND_VARIABLE_1223532) BOUND_VARIABLE_1223533)))))))))) (let ((_let_3266 (forall ((BOUND_VARIABLE_1223520 tptp.code_integer) (BOUND_VARIABLE_1223521 tptp.code_integer)) (= (ho_4572 (ho_4571 k_5763 BOUND_VARIABLE_1223520) BOUND_VARIABLE_1223521) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 BOUND_VARIABLE_1223520) BOUND_VARIABLE_1223521)) (ho_4560 (ho_4564 k_5197 BOUND_VARIABLE_1223520) BOUND_VARIABLE_1223521)))))) (let ((_let_3267 (forall ((BOUND_VARIABLE_1223428 tptp.code_integer) (BOUND_VARIABLE_1223429 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4560 (ho_4564 k_4563 _let_1) (ho_4560 k_4559 _let_1)))) (let ((_let_3 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1223429) _let_2)) (ho_4560 k_4559 BOUND_VARIABLE_1223429)) BOUND_VARIABLE_1223429))) (let ((_let_4 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1223428) _let_2))) (let ((_let_5 (ho_4560 (ho_4564 (ho_4569 k_4568 _let_4) (ho_4560 k_4559 BOUND_VARIABLE_1223428)) BOUND_VARIABLE_1223428))) (let ((_let_6 (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 _let_5) _let_3)) (ho_4560 (ho_4564 k_5197 _let_5) _let_3)))) (let ((_let_7 (ho_4571 k_4570 _let_2))) (let ((_let_8 (ho_4566 k_4565 _let_2))) (= (ho_4572 (ho_4571 k_5764 BOUND_VARIABLE_1223428) BOUND_VARIABLE_1223429) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1223428 _let_2)) (ho_4572 _let_7 _let_2)) (ho_4576 (ho_4575 (ho_4574 k_4573 (ho_4567 _let_8 BOUND_VARIABLE_1223429)) (ho_4576 (ho_4575 (ho_4574 k_4573 (ho_4567 _let_8 BOUND_VARIABLE_1223428)) _let_6) (ho_4576 (ho_5640 k_5639 (ho_4578 k_4601 BOUND_VARIABLE_1223429)) _let_6))) (ho_4576 (ho_4575 (ho_4574 k_4573 (= BOUND_VARIABLE_1223429 _let_2)) (ho_4572 _let_7 BOUND_VARIABLE_1223428)) (ho_4576 (ho_5643 k_5642 k_4559) (ho_4576 (ho_4575 (ho_4574 k_4573 _let_4) _let_6) (ho_4576 (ho_5640 k_5639 (ho_4578 k_4602 BOUND_VARIABLE_1223429)) _let_6)))))))))))))))))) (let ((_let_3268 (forall ((BOUND_VARIABLE_1223371 tptp.nat) (BOUND_VARIABLE_1223372 tptp.real) (BOUND_VARIABLE_1223373 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4272 k_4271 k_4270))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (= (ho_4245 (ho_4244 (ho_4492 k_5765 BOUND_VARIABLE_1223371) BOUND_VARIABLE_1223372) BOUND_VARIABLE_1223373) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1223373 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1223373) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 _let_6 (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1223373) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4273 _let_6 BOUND_VARIABLE_1223371) _let_5)) BOUND_VARIABLE_1223372)) BOUND_VARIABLE_1223373)))))))))))))) (let ((_let_3269 (forall ((BOUND_VARIABLE_1223362 tptp.nat) (BOUND_VARIABLE_1223363 tptp.complex)) (= (ho_5127 (ho_5661 k_5766 BOUND_VARIABLE_1223362) BOUND_VARIABLE_1223363) (= (ho_4701 k_4700 tptp.one) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1223363) BOUND_VARIABLE_1223362)))))) (let ((_let_3270 (forall ((BOUND_VARIABLE_1223352 tptp.complex) (BOUND_VARIABLE_1223353 tptp.nat) (BOUND_VARIABLE_1223354 tptp.complex)) (= (ho_5127 (ho_5661 (ho_5663 k_5767 BOUND_VARIABLE_1223352) BOUND_VARIABLE_1223353) BOUND_VARIABLE_1223354) (= BOUND_VARIABLE_1223352 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1223354) BOUND_VARIABLE_1223353)))))) (let ((_let_3271 (forall ((BOUND_VARIABLE_1223347 tptp.nat)) (= BOUND_VARIABLE_1223347 (ho_4216 k_5768 BOUND_VARIABLE_1223347))))) (let ((_let_3272 (forall ((BOUND_VARIABLE_1223328 tptp.set_nat) (BOUND_VARIABLE_1223329 tptp.nat)) (= (ho_4288 (ho_5139 k_5769 BOUND_VARIABLE_1223328) BOUND_VARIABLE_1223329) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_5346 k_5723 BOUND_VARIABLE_1223328)))) (or (not (= BOUND_VARIABLE_1223329 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3273 (forall ((BOUND_VARIABLE_1223323 tptp.nat)) (= BOUND_VARIABLE_1223323 (ho_4216 k_5770 BOUND_VARIABLE_1223323))))) (let ((_let_3274 (forall ((BOUND_VARIABLE_1223305 tptp.nat) (BOUND_VARIABLE_1223306 tptp.nat)) (= (ho_4288 (ho_4287 k_5771 BOUND_VARIABLE_1223305) BOUND_VARIABLE_1223306) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1223305))) (or (not (= BOUND_VARIABLE_1223306 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3275 (forall ((BOUND_VARIABLE_1223256 tptp.nat) (BOUND_VARIABLE_1223257 tptp.set_nat) (BOUND_VARIABLE_1223258 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1223256) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223256) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_5346 k_5723 BOUND_VARIABLE_1223257)) _let_2)))))) (or (not (= BOUND_VARIABLE_1223258 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_5139 (ho_5773 k_5772 BOUND_VARIABLE_1223256) BOUND_VARIABLE_1223257) BOUND_VARIABLE_1223258))))) (let ((_let_3276 (forall ((BOUND_VARIABLE_1223227 tptp.set_nat) (BOUND_VARIABLE_1223228 tptp.nat) (BOUND_VARIABLE_1223229 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (ho_5142 (ho_5141 k_5140 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223229) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1223227) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223229)) (ho_4290 k_4289 BOUND_VARIABLE_1223228))) (ho_4288 (ho_4287 (ho_5775 k_5774 BOUND_VARIABLE_1223227) BOUND_VARIABLE_1223228) BOUND_VARIABLE_1223229)))))))) (let ((_let_3277 (forall ((BOUND_VARIABLE_1223198 tptp.set_nat) (BOUND_VARIABLE_1223199 tptp.nat) (BOUND_VARIABLE_1223200 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (ho_5142 (ho_5141 k_5140 BOUND_VARIABLE_1223200) BOUND_VARIABLE_1223198) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223200)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223199) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (ho_4288 (ho_4287 (ho_5775 k_5776 BOUND_VARIABLE_1223198) BOUND_VARIABLE_1223199) BOUND_VARIABLE_1223200)))))))) (let ((_let_3278 (forall ((BOUND_VARIABLE_1223169 tptp.set_nat) (BOUND_VARIABLE_1223170 tptp.nat) (BOUND_VARIABLE_1223171 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (ho_5142 (ho_5141 k_5140 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223171) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) BOUND_VARIABLE_1223169) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223171)) (ho_4290 k_4289 BOUND_VARIABLE_1223170))) (ho_4288 (ho_4287 (ho_5775 k_5777 BOUND_VARIABLE_1223169) BOUND_VARIABLE_1223170) BOUND_VARIABLE_1223171)))))))) (let ((_let_3279 (forall ((BOUND_VARIABLE_1223140 tptp.set_nat) (BOUND_VARIABLE_1223141 tptp.nat) (BOUND_VARIABLE_1223142 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (ho_5142 (ho_5141 k_5140 BOUND_VARIABLE_1223142) BOUND_VARIABLE_1223140) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223142)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223141) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (ho_4288 (ho_4287 (ho_5775 k_5778 BOUND_VARIABLE_1223140) BOUND_VARIABLE_1223141) BOUND_VARIABLE_1223142)))))))) (let ((_let_3280 (forall ((BOUND_VARIABLE_1223111 tptp.set_nat) (BOUND_VARIABLE_1223112 tptp.nat) (BOUND_VARIABLE_1223113 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (and (ho_5142 (ho_5141 k_5140 BOUND_VARIABLE_1223113) BOUND_VARIABLE_1223111) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223113)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223112) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (ho_4288 (ho_4287 (ho_5775 k_5779 BOUND_VARIABLE_1223111) BOUND_VARIABLE_1223112) BOUND_VARIABLE_1223113)))))))) (let ((_let_3281 (forall ((BOUND_VARIABLE_1223091 tptp.int) (BOUND_VARIABLE_1223092 tptp.int) (BOUND_VARIABLE_1223093 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_5780 BOUND_VARIABLE_1223091) BOUND_VARIABLE_1223092) BOUND_VARIABLE_1223093) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1223091) BOUND_VARIABLE_1223092))) (or (not (= BOUND_VARIABLE_1223093 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_3282 (forall ((BOUND_VARIABLE_1223047 tptp.nat) (BOUND_VARIABLE_1223048 tptp.nat) (BOUND_VARIABLE_1223049 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1223047) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1223048) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1223049 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5781 BOUND_VARIABLE_1223047) BOUND_VARIABLE_1223048) BOUND_VARIABLE_1223049))))) (let ((_let_3283 (forall ((BOUND_VARIABLE_1223037 tptp.nat) (BOUND_VARIABLE_1223038 tptp.nat)) (= (ho_4288 (ho_4287 k_5782 BOUND_VARIABLE_1223037) BOUND_VARIABLE_1223038) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1223038)) (ho_4290 k_4289 BOUND_VARIABLE_1223037)))))) (let ((_let_3284 (forall ((BOUND_VARIABLE_1223027 tptp.nat) (BOUND_VARIABLE_1223028 tptp.nat)) (= (ho_4288 (ho_4287 k_5783 BOUND_VARIABLE_1223027) BOUND_VARIABLE_1223028) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1223028)) (ho_4290 k_4289 BOUND_VARIABLE_1223027)))))) (let ((_let_3285 (forall ((BOUND_VARIABLE_1223017 tptp.nat) (BOUND_VARIABLE_1223018 tptp.nat)) (= (ho_4288 (ho_4287 k_5784 BOUND_VARIABLE_1223017) BOUND_VARIABLE_1223018) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1223018)) (ho_4290 k_4289 BOUND_VARIABLE_1223017)))))) (let ((_let_3286 (forall ((BOUND_VARIABLE_1223005 tptp.code_integer)) (= (ho_4606 k_5785 BOUND_VARIABLE_1223005) (ho_4609 (ho_4608 k_4607 (ho_4560 (ho_4564 k_5198 BOUND_VARIABLE_1223005) (ho_4562 k_4561 (ho_4193 k_4192 tptp.one)))) (forall ((K3 tptp.code_integer)) (not (= BOUND_VARIABLE_1223005 (ho_4560 (ho_4564 k_4630 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one))) K3))))))))) (let ((_let_3287 (forall ((BOUND_VARIABLE_1222958 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4562 k_4561 tptp.one))) (let ((_let_3 (ho_4560 (ho_4564 k_4563 _let_2) (ho_4560 k_4559 _let_2)))) (let ((_let_4 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 _let_1) _let_3)) (ho_4560 k_4559 _let_1)) _let_1))) (let ((_let_5 (ho_4560 (ho_4564 (ho_4569 k_4568 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1222958) _let_3)) (ho_4560 k_4559 BOUND_VARIABLE_1222958)) BOUND_VARIABLE_1222958))) (= (ho_4606 k_5793 BOUND_VARIABLE_1222958) (ho_5792 (ho_5791 (ho_5790 k_5789 (= BOUND_VARIABLE_1222958 _let_3)) (ho_4609 (ho_4608 k_4607 _let_3) false)) (ho_5788 (ho_5787 k_5786 (ho_4604 k_4603 BOUND_VARIABLE_1222958)) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 _let_5) _let_4)) (ho_4560 (ho_4564 k_5197 _let_5) _let_4))))))))))))) (let ((_let_3288 (forall ((BOUND_VARIABLE_1222933 tptp.code_integer)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4562 k_4561 _let_1))) (let ((_let_3 (ho_4562 k_4561 tptp.one))) (let ((_let_4 (ho_4625 k_4624 (ho_4560 (ho_4564 k_4563 _let_3) (ho_4560 k_4559 _let_3))))) (= (ho_4216 (ho_4215 (ho_4613 k_4612 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 BOUND_VARIABLE_1222933)) _let_4))) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (ho_5796 (ho_5795 k_5794 k_4614) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 BOUND_VARIABLE_1222933) _let_2)) (ho_4560 (ho_4564 k_5197 BOUND_VARIABLE_1222933) _let_2)))) (ho_4611 k_5797 BOUND_VARIABLE_1222933))))))))) (let ((_let_3289 (forall ((BOUND_VARIABLE_1222908 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4625 k_4624 (ho_4562 k_4561 tptp.one)))) (= (ho_4193 (ho_4619 (ho_4621 k_4620 (= _let_2 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 BOUND_VARIABLE_1222908)) _let_2))) tptp.one) (ho_5800 (ho_5799 k_5798 k_4622) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 BOUND_VARIABLE_1222908) _let_1)) (ho_4560 (ho_4564 k_5197 BOUND_VARIABLE_1222908) _let_1)))) (ho_4617 k_5801 BOUND_VARIABLE_1222908))))))) (let ((_let_3290 (forall ((BOUND_VARIABLE_1222897 tptp.code_integer) (BOUND_VARIABLE_1222898 tptp.code_integer)) (let ((_let_1 (ho_4625 k_4624 BOUND_VARIABLE_1222898))) (= (ho_4567 (ho_4566 k_5802 BOUND_VARIABLE_1222897) BOUND_VARIABLE_1222898) (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 BOUND_VARIABLE_1222897)) _let_1))))))) (let ((_let_3291 (forall ((BOUND_VARIABLE_1222886 tptp.code_integer) (BOUND_VARIABLE_1222887 tptp.code_integer)) (let ((_let_1 (ho_4625 k_4624 BOUND_VARIABLE_1222887))) (= (ho_4567 (ho_4566 k_5803 BOUND_VARIABLE_1222886) BOUND_VARIABLE_1222887) (= _let_1 (ho_4209 (ho_4211 k_4311 (ho_4625 k_4624 BOUND_VARIABLE_1222886)) _let_1))))))) (let ((_let_3292 (forall ((BOUND_VARIABLE_1222852 tptp.code_integer)) (let ((_let_1 (ho_4562 k_4561 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_4 (ho_4562 k_4561 tptp.one))) (let ((_let_5 (ho_4560 (ho_4564 k_4563 _let_4) (ho_4560 k_4559 _let_4)))) (= (ho_4625 k_5807 BOUND_VARIABLE_1222852) (ho_4209 (ho_4211 (ho_4593 k_4592 (ho_4567 (ho_4566 k_4565 BOUND_VARIABLE_1222852) _let_5)) (ho_4209 _let_3 (ho_4625 k_4624 (ho_4560 k_4559 BOUND_VARIABLE_1222852)))) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1222852 _let_5)) (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_3 _let_2))) (ho_5806 (ho_5805 k_5804 k_4626) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 BOUND_VARIABLE_1222852) _let_1)) (ho_4560 (ho_4564 k_5197 BOUND_VARIABLE_1222852) _let_1)))))))))))))) (let ((_let_3293 (forall ((BOUND_VARIABLE_1222722 tptp.int)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_3 _let_2)))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1222722 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4196 k_4195 _let_7))) (let ((_let_9 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_8) _let_2)) _let_4))) (ho_4209 _let_3 _let_8)) _let_8))) (let ((_let_10 (ho_4213 k_4212 _let_9))) (let ((_let_11 (ho_4209 _let_3 BOUND_VARIABLE_1222722))) (let ((_let_12 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1222722) _let_2)) _let_4)))) (let ((_let_13 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 _let_12) _let_11) BOUND_VARIABLE_1222722)))) (let ((_let_14 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_13) _let_10)) _let_4))) (let ((_let_15 (ho_4209 k_4594 _let_8))) (let ((_let_16 (ho_4593 k_4592 (= _let_15 (ho_4209 k_4594 BOUND_VARIABLE_1222722))))) (let ((_let_17 (ho_4593 k_4592 (= _let_4 _let_8)))) (let ((_let_18 (ho_4560 (ho_4564 k_4630 (ho_4562 k_4561 _let_7)) (ho_5809 k_5808 (ho_4209 (ho_4211 _let_17 _let_4) (ho_4209 (ho_4211 _let_16 _let_14) (ho_4209 _let_3 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_14) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))))) (let ((_let_19 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_13) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_14) (ho_4209 (ho_4220 _let_6 _let_10) _let_4))))) _let_4))) (let ((_let_20 (ho_4211 k_4222 _let_15))) (= (ho_5809 k_5810 BOUND_VARIABLE_1222722) (ho_4560 (ho_4564 (ho_4569 k_4568 _let_12) (ho_4560 k_4559 (ho_5809 k_5808 _let_11))) (ho_4560 (ho_4564 (ho_4569 k_4568 (= BOUND_VARIABLE_1222722 _let_4)) (ho_4560 (ho_4564 k_4563 _let_1) (ho_4560 k_4559 _let_1))) (ho_4560 (ho_4564 (ho_4569 k_4568 (= _let_4 (ho_4209 (ho_4211 _let_17 BOUND_VARIABLE_1222722) (ho_4209 (ho_4211 _let_16 (ho_4209 _let_20 _let_19)) (ho_4209 _let_20 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_9) (ho_5598 k_5597 _let_5))) (ho_4209 _let_3 _let_19))))))) _let_18) (ho_4560 (ho_4564 k_4563 _let_18) _let_1)))))))))))))))))))))))))))) (let ((_let_3294 (forall ((BOUND_VARIABLE_1222708 tptp.num) (BOUND_VARIABLE_1222709 tptp.num)) (let ((_let_1 (ho_4562 k_4561 BOUND_VARIABLE_1222709))) (let ((_let_2 (ho_4562 k_4561 BOUND_VARIABLE_1222708))) (= (ho_5813 (ho_5812 k_5811 BOUND_VARIABLE_1222708) BOUND_VARIABLE_1222709) (ho_4572 (ho_4571 k_4570 (ho_4560 (ho_4564 k_5198 _let_2) _let_1)) (ho_4560 (ho_4564 k_5197 _let_2) _let_1)))))))) (let ((_let_3295 (forall ((BOUND_VARIABLE_1222668 tptp.num) (BOUND_VARIABLE_1222669 tptp.produc8923325533196201883nteger)) (= (ho_4576 (ho_5640 k_5639 (ho_4629 k_4628 BOUND_VARIABLE_1222668)) BOUND_VARIABLE_1222669) (ho_4576 (ho_5815 k_5814 BOUND_VARIABLE_1222668) BOUND_VARIABLE_1222669))))) (let ((_let_3296 (forall ((BOUND_VARIABLE_1222628 tptp.num) (BOUND_VARIABLE_1222629 tptp.produc8923325533196201883nteger)) (= (ho_4576 (ho_5640 k_5639 (ho_4629 k_4631 BOUND_VARIABLE_1222628)) BOUND_VARIABLE_1222629) (ho_4576 (ho_5815 k_5816 BOUND_VARIABLE_1222628) BOUND_VARIABLE_1222629))))) (let ((_let_3297 (forall ((BOUND_VARIABLE_1222589 tptp.int) (BOUND_VARIABLE_1222590 tptp.int) (BOUND_VARIABLE_1222591 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1222589) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1222590) _let_1)) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) (or (not (= BOUND_VARIABLE_1222591 (ho_4335 (ho_4640 k_4639 _let_2) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_2))))))))) (ho_4310 (ho_4309 (ho_4308 k_5817 BOUND_VARIABLE_1222589) BOUND_VARIABLE_1222590) BOUND_VARIABLE_1222591))))) (let ((_let_3298 (forall ((BOUND_VARIABLE_1222569 tptp.int) (BOUND_VARIABLE_1222570 tptp.int) (BOUND_VARIABLE_1222571 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_5818 BOUND_VARIABLE_1222569) BOUND_VARIABLE_1222570) BOUND_VARIABLE_1222571) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1222569) BOUND_VARIABLE_1222570))) (or (not (= BOUND_VARIABLE_1222571 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_3299 (forall ((BOUND_VARIABLE_1301181 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1301177 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1222546 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1301181 BOUND_VARIABLE_1222546)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1301177 BOUND_VARIABLE_1222546)) _let_2))) (ho_4216 (ho_5088 (ho_5820 k_5819 BOUND_VARIABLE_1301181) BOUND_VARIABLE_1301177) BOUND_VARIABLE_1222546)))))))) (let ((_let_3300 (forall ((BOUND_VARIABLE_1222526 tptp.nat) (BOUND_VARIABLE_1222527 tptp.nat)) (= (ho_4288 (ho_4287 k_5821 BOUND_VARIABLE_1222526) BOUND_VARIABLE_1222527) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1222526))) (or (not (= BOUND_VARIABLE_1222527 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3301 (forall ((BOUND_VARIABLE_1222508 tptp.nat) (BOUND_VARIABLE_1222509 tptp.nat)) (= (ho_4288 (ho_4287 k_5822 BOUND_VARIABLE_1222508) BOUND_VARIABLE_1222509) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1222508))) (or (not (= BOUND_VARIABLE_1222509 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3302 (forall ((BOUND_VARIABLE_1222495 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 BOUND_VARIABLE_1222495)) (ho_4209 _let_1 (ho_4196 k_4195 tptp.one))) (ho_4209 k_5823 BOUND_VARIABLE_1222495)))))) (let ((_let_3303 (forall ((BOUND_VARIABLE_1222421 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1222421 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1222421) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1222421)) BOUND_VARIABLE_1222421))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7)))) _let_4))) (= (ho_4209 k_5824 BOUND_VARIABLE_1222421) (ho_4209 (ho_4211 k_4210 (ho_5598 k_5597 (not _let_5))) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_7)) _let_4) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_7) (ho_4209 k_4594 BOUND_VARIABLE_1222421))) _let_8) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))) _let_3))))))))))))))) (let ((_let_3304 (forall ((BOUND_VARIABLE_1222411 tptp.nat) (BOUND_VARIABLE_1222412 tptp.nat)) (= (ho_4288 (ho_4287 k_5825 BOUND_VARIABLE_1222411) BOUND_VARIABLE_1222412) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1222412)) (ho_4290 k_4289 BOUND_VARIABLE_1222411)))))) (let ((_let_3305 (forall ((BOUND_VARIABLE_1222379 tptp.nat) (BOUND_VARIABLE_1222380 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))) BOUND_VARIABLE_1222379))) (or (not (= BOUND_VARIABLE_1222380 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5826 BOUND_VARIABLE_1222379) BOUND_VARIABLE_1222380))))) (let ((_let_3306 (forall ((BOUND_VARIABLE_1222357 tptp.nat) (BOUND_VARIABLE_1222358 tptp.num) (BOUND_VARIABLE_1222359 tptp.nat)) (= (ho_4288 (ho_5829 (ho_5828 k_5827 BOUND_VARIABLE_1222357) BOUND_VARIABLE_1222358) BOUND_VARIABLE_1222359) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222357) (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1222358))))) (or (not (= BOUND_VARIABLE_1222359 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3307 (forall ((BOUND_VARIABLE_1222333 tptp.nat) (BOUND_VARIABLE_1222334 tptp.num) (BOUND_VARIABLE_1222335 tptp.nat)) (= (ho_4288 (ho_5829 (ho_5828 k_5830 BOUND_VARIABLE_1222333) BOUND_VARIABLE_1222334) BOUND_VARIABLE_1222335) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222333) (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1222334))) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))))) (or (not (= BOUND_VARIABLE_1222335 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3308 (forall ((BOUND_VARIABLE_1222311 tptp.nat) (BOUND_VARIABLE_1222312 tptp.num) (BOUND_VARIABLE_1222313 tptp.nat)) (= (ho_4288 (ho_5829 (ho_5828 k_5831 BOUND_VARIABLE_1222311) BOUND_VARIABLE_1222312) BOUND_VARIABLE_1222313) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222311) (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1222312))))) (or (not (= BOUND_VARIABLE_1222313 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3309 (forall ((BOUND_VARIABLE_1222293 tptp.nat) (BOUND_VARIABLE_1222294 tptp.nat)) (= (ho_4288 (ho_4287 k_5832 BOUND_VARIABLE_1222293) BOUND_VARIABLE_1222294) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1222293))) (or (not (= BOUND_VARIABLE_1222294 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3310 (forall ((BOUND_VARIABLE_1222261 tptp.nat) (BOUND_VARIABLE_1222262 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))) BOUND_VARIABLE_1222261))) (or (not (= BOUND_VARIABLE_1222262 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5833 BOUND_VARIABLE_1222261) BOUND_VARIABLE_1222262))))) (let ((_let_3311 (forall ((BOUND_VARIABLE_1222217 tptp.nat) (BOUND_VARIABLE_1222218 tptp.nat) (BOUND_VARIABLE_1222219 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222217) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1222218) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1222219 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5834 BOUND_VARIABLE_1222217) BOUND_VARIABLE_1222218) BOUND_VARIABLE_1222219))))) (let ((_let_3312 (forall ((BOUND_VARIABLE_1222197 tptp.nat) (BOUND_VARIABLE_1222198 tptp.nat) (BOUND_VARIABLE_1222199 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5835 BOUND_VARIABLE_1222197) BOUND_VARIABLE_1222198) BOUND_VARIABLE_1222199) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222197) BOUND_VARIABLE_1222198))) (or (not (= BOUND_VARIABLE_1222199 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3313 (forall ((BOUND_VARIABLE_1222153 tptp.nat) (BOUND_VARIABLE_1222154 tptp.nat) (BOUND_VARIABLE_1222155 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1222153) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1222154) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1222155 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5836 BOUND_VARIABLE_1222153) BOUND_VARIABLE_1222154) BOUND_VARIABLE_1222155))))) (let ((_let_3314 (forall ((BOUND_VARIABLE_1222135 tptp.nat) (BOUND_VARIABLE_1222136 tptp.nat)) (= (ho_4288 (ho_4287 k_5837 BOUND_VARIABLE_1222135) BOUND_VARIABLE_1222136) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1222135))) (or (not (= BOUND_VARIABLE_1222136 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3315 (forall ((BOUND_VARIABLE_1222030 tptp.nat) (BOUND_VARIABLE_1222031 tptp.int)) (= (ho_4209 (ho_4220 k_5838 BOUND_VARIABLE_1222030) BOUND_VARIABLE_1222031) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1222031) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) (ho_4209 (ho_4211 k_4222 (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1222030))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1222031) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1222031)) BOUND_VARIABLE_1222031))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 BOUND_VARIABLE_1222031))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_459508 tptp.int)) (not (= BOUND_VARIABLE_1222031 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1222030)) BOUND_VARIABLE_459508)))))) _let_3)))) _let_3)))))))))))))))) (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1222030)))))))) (let ((_let_3316 (forall ((BOUND_VARIABLE_1222011 tptp.nat) (BOUND_VARIABLE_1222012 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4209 (ho_4211 k_5839 BOUND_VARIABLE_1222012) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 _let_1) (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1222011)))) (ho_4209 _let_2 _let_1))) (ho_4209 (ho_4220 k_5840 BOUND_VARIABLE_1222011) BOUND_VARIABLE_1222012))))))) (let ((_let_3317 (forall ((BOUND_VARIABLE_1221969 tptp.nat) (BOUND_VARIABLE_1221970 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1221969) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1221970 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5841 BOUND_VARIABLE_1221969) BOUND_VARIABLE_1221970))))) (let ((_let_3318 (forall ((BOUND_VARIABLE_1221951 tptp.nat) (BOUND_VARIABLE_1221952 tptp.nat)) (= (ho_4288 (ho_4287 k_5842 BOUND_VARIABLE_1221951) BOUND_VARIABLE_1221952) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1221951))) (or (not (= BOUND_VARIABLE_1221952 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3319 (forall ((BOUND_VARIABLE_1221933 tptp.nat) (BOUND_VARIABLE_1221934 tptp.nat)) (= (ho_4288 (ho_4287 k_5843 BOUND_VARIABLE_1221933) BOUND_VARIABLE_1221934) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1221933))) (or (not (= BOUND_VARIABLE_1221934 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3320 (forall ((BOUND_VARIABLE_1221915 tptp.nat) (BOUND_VARIABLE_1221916 tptp.nat)) (= (ho_4288 (ho_4287 k_5844 BOUND_VARIABLE_1221915) BOUND_VARIABLE_1221916) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) BOUND_VARIABLE_1221915))) (or (not (= BOUND_VARIABLE_1221916 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3321 (forall ((BOUND_VARIABLE_1221872 tptp.nat) (BOUND_VARIABLE_1221873 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1221872) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1221872) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1221873 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 k_5845 BOUND_VARIABLE_1221872) BOUND_VARIABLE_1221873))))) (let ((_let_3322 (forall ((BOUND_VARIABLE_1221867 tptp.nat)) (= BOUND_VARIABLE_1221867 (ho_4216 k_5846 BOUND_VARIABLE_1221867))))) (let ((_let_3323 (forall ((BOUND_VARIABLE_1221847 tptp.nat) (BOUND_VARIABLE_1221848 tptp.nat) (BOUND_VARIABLE_1221849 tptp.nat)) (= (ho_4288 (ho_4287 (ho_4303 k_5847 BOUND_VARIABLE_1221847) BOUND_VARIABLE_1221848) BOUND_VARIABLE_1221849) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1221847) BOUND_VARIABLE_1221848))) (or (not (= BOUND_VARIABLE_1221849 (ho_4216 (ho_4468 k_4467 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_1)))))))))))) (let ((_let_3324 (forall ((BOUND_VARIABLE_1221549 tptp.int) (BOUND_VARIABLE_1221550 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1221550 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4209 _let_2 BOUND_VARIABLE_1221550))) (let ((_let_11 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221550) _let_1)) _let_4))) _let_10) BOUND_VARIABLE_1221550)))) (let ((_let_12 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_11) _let_9)) _let_4))) (let ((_let_13 (ho_4209 k_4594 _let_7))) (let ((_let_14 (ho_4593 k_4592 (= _let_13 (ho_4209 k_4594 BOUND_VARIABLE_1221550))))) (let ((_let_15 (ho_4593 k_4592 (= _let_4 _let_7)))) (let ((_let_16 (ho_4211 _let_15 _let_4))) (let ((_let_17 (ho_4209 _let_16 (ho_4209 (ho_4211 _let_14 _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))) (let ((_let_18 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1221549 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_19 (ho_4209 _let_2 BOUND_VARIABLE_1221549))) (let ((_let_20 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221549) _let_1)) _let_4))) _let_19) BOUND_VARIABLE_1221549)))) (let ((_let_21 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_20) _let_9)) _let_4))) (let ((_let_22 (ho_4593 k_4592 (= _let_13 (ho_4209 k_4594 BOUND_VARIABLE_1221549))))) (let ((_let_23 (ho_4209 _let_16 (ho_4209 (ho_4211 _let_22 _let_21) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_21) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_18)) _let_4)))) _let_4)))))) (let ((_let_24 (ho_4209 (ho_4220 _let_6 _let_9) _let_4))) (let ((_let_25 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_11) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_12) _let_24)))) _let_4))) (let ((_let_26 (ho_4211 k_4222 _let_8))) (let ((_let_27 (ho_4211 k_4222 _let_13))) (let ((_let_28 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_20) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_21) _let_24)))) _let_4))) (let ((_let_29 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 _let_15 BOUND_VARIABLE_1221549) (ho_4209 (ho_4211 _let_22 (ho_4209 _let_27 _let_28)) (ho_4209 _let_27 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_26 (ho_5598 k_5597 _let_18))) (ho_4209 _let_2 _let_28)))))) (ho_4209 _let_2 (ho_4209 (ho_4211 _let_15 BOUND_VARIABLE_1221550) (ho_4209 (ho_4211 _let_14 (ho_4209 _let_27 _let_25)) (ho_4209 _let_27 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_26 (ho_5598 k_5597 _let_5))) (ho_4209 _let_2 _let_25))))))))) (= (ho_4209 (ho_4211 k_5848 BOUND_VARIABLE_1221549) BOUND_VARIABLE_1221550) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1221549 _let_3)) (ho_4209 (ho_4211 k_4210 _let_10) _let_3)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1221550 _let_3)) (ho_4209 (ho_4211 k_4210 _let_19) _let_3)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1221549 _let_4)) BOUND_VARIABLE_1221550) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1221550 _let_4)) BOUND_VARIABLE_1221549) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_29) _let_1)) _let_4))) (ho_4209 _let_2 _let_29)) _let_29)) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 _let_23) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_17)) _let_3)))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_23)) _let_3)) _let_17))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))))))))) (let ((_let_3325 (forall ((BOUND_VARIABLE_1221500 tptp.int) (BOUND_VARIABLE_1221501 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4209 _let_1 (ho_4196 k_4195 tptp.one)))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 (ho_4209 (ho_4211 k_5839 BOUND_VARIABLE_1221500) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 BOUND_VARIABLE_1221501)) _let_2)))) _let_2)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 BOUND_VARIABLE_1221500)) _let_2)) BOUND_VARIABLE_1221501))) _let_2)))) _let_2) (ho_4209 (ho_4211 k_5849 BOUND_VARIABLE_1221500) BOUND_VARIABLE_1221501))))))) (let ((_let_3326 (forall ((BOUND_VARIABLE_1221334 tptp.int) (BOUND_VARIABLE_1221335 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1221335 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221335) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1221335)) BOUND_VARIABLE_1221335))) _let_8)) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_7))) (let ((_let_11 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_7)) _let_4))) (let ((_let_12 (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1221335))) _let_9) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_9) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))) (let ((_let_13 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1221334 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_14 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221334) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1221334)) BOUND_VARIABLE_1221334))) _let_8)) _let_4))) (let ((_let_15 (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1221334))) _let_14) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_14) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_13)) _let_4)))) _let_4)))))) (= (ho_4209 (ho_4211 k_5850 BOUND_VARIABLE_1221334) BOUND_VARIABLE_1221335) (ho_4209 (ho_4211 k_4210 (ho_5598 k_5597 (not (= _let_5 _let_13)))) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 _let_15) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_12)) _let_3)))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_15)) _let_3)) _let_12))) _let_3)))) _let_3)))))))))))))))))))))) (let ((_let_3327 (forall ((BOUND_VARIABLE_1221229 tptp.nat) (BOUND_VARIABLE_1221230 tptp.int)) (= (ho_4209 (ho_4220 k_5851 BOUND_VARIABLE_1221229) BOUND_VARIABLE_1221230) (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221230) (ho_4209 (ho_4211 k_4222 (ho_5598 k_5597 (not (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1221229))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221230) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1221230)) BOUND_VARIABLE_1221230))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 BOUND_VARIABLE_1221230))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_459508 tptp.int)) (not (= BOUND_VARIABLE_1221230 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1221229)) BOUND_VARIABLE_459508)))))) _let_3)))) _let_3))))))))))))))))) (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1221229))))))) (let ((_let_3328 (forall ((BOUND_VARIABLE_1221197 tptp.nat) (BOUND_VARIABLE_1221198 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 BOUND_VARIABLE_1221198)) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 _let_1) (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1221197)))) _let_3)))) _let_3) (ho_4209 (ho_4220 k_5852 BOUND_VARIABLE_1221197) BOUND_VARIABLE_1221198)))))))) (let ((_let_3329 (forall ((BOUND_VARIABLE_1221084 tptp.nat) (BOUND_VARIABLE_1221085 tptp.int) (BOUND_VARIABLE_1221086 tptp.int)) (let ((_let_1 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1221084))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_3 _let_2)))) (let ((_let_5 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) _let_2)) _let_4))) (ho_4209 _let_3 _let_1)) _let_1))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1221085) _let_2)) _let_4))) (ho_4209 _let_3 BOUND_VARIABLE_1221085)) BOUND_VARIABLE_1221085)))) (let ((_let_9 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_8) _let_6)) _let_4)) (ho_4209 (ho_4220 _let_7 _let_6) _let_4))))) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_1))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_1)) BOUND_VARIABLE_1221085) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1221085))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_5) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1221085 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1221084)) K3))))))) (ho_4209 _let_3 _let_9)))))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1221086) _let_1)) (ho_4209 (ho_4211 (ho_5854 k_5853 BOUND_VARIABLE_1221084) BOUND_VARIABLE_1221085) BOUND_VARIABLE_1221086)))))))))))))))) (let ((_let_3330 (forall ((BOUND_VARIABLE_1220953 tptp.nat) (BOUND_VARIABLE_1220954 tptp.int) (BOUND_VARIABLE_1220955 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1220953))) (let ((_let_5 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_6 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_5 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_4) _let_1)) _let_5))) (ho_4209 _let_2 _let_4)) _let_4))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4219 k_4218 k_4217))) (let ((_let_9 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_5 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1220954) _let_1)) _let_5))) (ho_4209 _let_2 BOUND_VARIABLE_1220954)) BOUND_VARIABLE_1220954)))) (let ((_let_10 (ho_4209 (ho_4220 _let_8 (ho_4216 (ho_4215 k_4223 _let_9) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_8 (ho_4216 (ho_4215 k_4221 _let_9) _let_7)) _let_5)) (ho_4209 (ho_4220 _let_8 _let_7) _let_5))))) _let_5))) (let ((_let_11 (ho_4209 k_4594 _let_4))) (let ((_let_12 (ho_4211 k_4222 _let_11))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_5 _let_4)) BOUND_VARIABLE_1220954) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_11 (ho_4209 k_4594 BOUND_VARIABLE_1220954))) (ho_4209 _let_12 _let_10)) (ho_4209 _let_12 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_6) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1220954 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1220953)) K3))))))) (ho_4209 _let_2 _let_10))))))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1220955) _let_4))) _let_3)))) _let_3) (ho_4209 (ho_4211 (ho_5854 k_5855 BOUND_VARIABLE_1220953) BOUND_VARIABLE_1220954) BOUND_VARIABLE_1220955))))))))))))))))) (let ((_let_3331 (forall ((BOUND_VARIABLE_1220845 tptp.nat) (BOUND_VARIABLE_1220846 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220846) _let_5)) _let_4))) (let ((_let_8 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220845) _let_5)) _let_4))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 _let_5) _let_4))) (let ((_let_10 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1220845) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_8) _let_9))))) (let ((_let_11 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1220846) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_7) _let_9))))) (let ((_let_12 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_5))) (= (ho_4216 (ho_4215 k_5856 BOUND_VARIABLE_1220845) BOUND_VARIABLE_1220846) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1220845 _let_12)) BOUND_VARIABLE_1220846) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1220846 _let_12)) BOUND_VARIABLE_1220845) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 _let_10)) (ho_4290 k_4289 _let_11))) _let_11) _let_10)) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_9) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_8)) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_7)) _let_3)))) _let_3))) _let_4)))) _let_4))))))))))))))))))))) (let ((_let_3332 (forall ((BOUND_VARIABLE_1220741 tptp.nat) (BOUND_VARIABLE_1220742 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220742) _let_5)) _let_4))) (let ((_let_8 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220741) _let_5)) _let_4))) (= (ho_4216 (ho_4215 k_5857 BOUND_VARIABLE_1220741) BOUND_VARIABLE_1220742) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 (not (= (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220742 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220741 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))))) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_5) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 _let_8) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_7)) _let_3)))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_8)) _let_3)) _let_7))) _let_3)))) _let_3))) _let_4)))) _let_4))))))))))))))) (let ((_let_3333 (forall ((BOUND_VARIABLE_1220681 tptp.nat) (BOUND_VARIABLE_1220682 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1220682) _let_4))) (let ((_let_7 (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1220681) _let_4))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_6)) _let_3)))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_7)) _let_3)) _let_6))) _let_3)))) _let_3)) (ho_4216 (ho_4215 k_5858 BOUND_VARIABLE_1220681) BOUND_VARIABLE_1220682)))))))))))) (let ((_let_3334 (forall ((BOUND_VARIABLE_1220535 tptp.nat) (BOUND_VARIABLE_1220536 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220536) _let_5)) _let_4))) (let ((_let_8 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220535) _let_5)) _let_4))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 _let_5) _let_4))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1220535) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_8) _let_9)))) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1220536) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_7) _let_9)))) _let_4))))) (let ((_let_11 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_5))) (= (ho_4216 (ho_4215 k_5859 BOUND_VARIABLE_1220535) BOUND_VARIABLE_1220536) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1220535 _let_11)) BOUND_VARIABLE_1220536) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1220536 _let_11)) BOUND_VARIABLE_1220535) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_10) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_10) _let_5)) _let_4)) _let_9)))) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_9) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 _let_8) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_7)) _let_3)))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 _let_8)) _let_3)) _let_7))) _let_3)))) _let_3))) _let_4)))) _let_4)))))))))))))))))))) (let ((_let_3335 (forall ((BOUND_VARIABLE_1220495 tptp.nat) (BOUND_VARIABLE_1220496 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1220495) _let_4))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1220496) _let_4))) _let_3)))) _let_3)) (ho_4216 (ho_4215 k_5860 BOUND_VARIABLE_1220495) BOUND_VARIABLE_1220496)))))))))) (let ((_let_3336 (forall ((BOUND_VARIABLE_1220413 tptp.nat) (BOUND_VARIABLE_1220414 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (= (ho_4216 (ho_4215 k_5861 BOUND_VARIABLE_1220413) BOUND_VARIABLE_1220414) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 (or (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220413 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220414 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))))) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 _let_5) _let_4)) (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220413) _let_5)) _let_4))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220414) _let_5)) _let_4))) _let_3)))) _let_3))) _let_4)))) _let_4))))))))))))) (let ((_let_3337 (forall ((BOUND_VARIABLE_1220268 tptp.int) (BOUND_VARIABLE_1220269 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1220269 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1220269) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1220269)) BOUND_VARIABLE_1220269))) _let_8)) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_7))) (let ((_let_11 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_7)) _let_4))) (let ((_let_12 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1220268 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_13 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1220268) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1220268)) BOUND_VARIABLE_1220268))) _let_8)) _let_4))) (= (ho_4209 (ho_4211 k_5862 BOUND_VARIABLE_1220268) BOUND_VARIABLE_1220269) (ho_4209 (ho_4211 k_4210 (ho_5598 k_5597 (or _let_12 _let_5))) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1220268))) _let_13) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_13) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_12)) _let_4)))) _let_4)))))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1220269))) _let_9) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_9) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))) _let_3)))) _let_3)))))))))))))))))))) (let ((_let_3338 (forall ((BOUND_VARIABLE_1220213 tptp.real) (BOUND_VARIABLE_1220214 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4265 _let_4 (ho_4247 k_4246 _let_1)))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4258 (ho_4257 _let_2 k_4248) _let_6))) (let ((_let_8 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_6) _let_7))) (let ((_let_9 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (= (ho_4245 (ho_4244 k_5863 BOUND_VARIABLE_1220213) BOUND_VARIABLE_1220214) (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220214 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 _let_7) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1220214) _let_9))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_9) BOUND_VARIABLE_1220214) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_8)))) _let_8)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 (ho_4258 _let_5 (ho_4258 _let_5 (ho_4506 k_4505 k_4632)))) BOUND_VARIABLE_1220213)) BOUND_VARIABLE_1220214))))))))))))))) (let ((_let_3339 (forall ((BOUND_VARIABLE_1220158 tptp.real) (BOUND_VARIABLE_1220159 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4265 _let_4 (ho_4247 k_4246 _let_1)))) (let ((_let_6 (ho_4247 k_4246 tptp.one))) (let ((_let_7 (ho_4258 (ho_4257 _let_2 k_4248) _let_6))) (let ((_let_8 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_6) _let_7))) (let ((_let_9 (ho_4196 k_4195 tptp.one))) (let ((_let_10 (ho_4213 k_4212 _let_9))) (let ((_let_11 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_9) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_9)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_5864 BOUND_VARIABLE_1220158) BOUND_VARIABLE_1220159) (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1220159 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_8) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 _let_7) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1220159) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_10) _let_11)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_10) _let_12))))) _let_11))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_11) BOUND_VARIABLE_1220159) _let_10)) _let_8))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 (ho_4258 _let_5 (ho_4258 _let_5 (ho_4506 k_4505 k_4504)))) BOUND_VARIABLE_1220158)) BOUND_VARIABLE_1220159))))))))))))))))))) (let ((_let_3340 (forall ((BOUND_VARIABLE_1220063 tptp.int) (BOUND_VARIABLE_1220064 tptp.nat)) (= (ho_4288 (ho_5533 k_5865 BOUND_VARIABLE_1220063) BOUND_VARIABLE_1220064) (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1220064))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1220063) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1220063)) BOUND_VARIABLE_1220063))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 BOUND_VARIABLE_1220063))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_459508 tptp.int)) (not (= BOUND_VARIABLE_1220063 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1220064)) BOUND_VARIABLE_459508)))))) _let_3)))) _let_3)))))))))))))))))) (let ((_let_3341 (forall ((BOUND_VARIABLE_1219968 tptp.int) (BOUND_VARIABLE_1219969 tptp.nat)) (= (ho_4288 (ho_5533 k_5866 BOUND_VARIABLE_1219968) BOUND_VARIABLE_1219969) (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1219969))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219968) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1219968)) BOUND_VARIABLE_1219968))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 BOUND_VARIABLE_1219968))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_901227 tptp.int)) (not (= BOUND_VARIABLE_1219968 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1219969)) BOUND_VARIABLE_901227)))))) _let_3)))) _let_3)))))))))))))))))) (let ((_let_3342 (forall ((BOUND_VARIABLE_1219815 tptp.nat) (BOUND_VARIABLE_1219816 tptp.int)) (let ((_let_1 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1219815))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 _let_2 _let_3)))) (let ((_let_5 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) _let_3)) _let_4))) (ho_4209 _let_2 _let_1)) _let_1))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219816) _let_3)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1219816)) BOUND_VARIABLE_1219816)))) (let ((_let_9 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_8) _let_6)) _let_4)) (ho_4209 (ho_4220 _let_7 _let_6) _let_4))))) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_1))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4220 k_5867 BOUND_VARIABLE_1219815) BOUND_VARIABLE_1219816) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_1)) BOUND_VARIABLE_1219816) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 BOUND_VARIABLE_1219816) _let_10)) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_5) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1219816 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1219815)) K3))))))) (ho_4209 _let_2 _let_9)))))) (ho_4209 (ho_4211 k_4222 (ho_4209 _let_2 (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1219815))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219816) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1219816)) BOUND_VARIABLE_1219816))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 BOUND_VARIABLE_1219816) (ho_4209 k_4594 _let_6))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_459508 tptp.int)) (not (= BOUND_VARIABLE_1219816 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1219815)) BOUND_VARIABLE_459508)))))) _let_3)))) _let_3))))))))))))))))) _let_1))))))))))))))))) (let ((_let_3343 (forall ((BOUND_VARIABLE_1219758 tptp.real) (BOUND_VARIABLE_1219759 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (let ((_let_7 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_5) _let_6))) (let ((_let_8 (ho_4196 k_4195 tptp.one))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_11 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_8)))) (let ((_let_12 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_5868 BOUND_VARIABLE_1219758) BOUND_VARIABLE_1219759) (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1219759 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_7) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1219759) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_12 (ho_4216 (ho_4215 k_4221 _let_9) _let_10)) _let_11)) (ho_4209 (ho_4220 _let_12 _let_9) _let_11))))) _let_10))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1219759) _let_9)) _let_7))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1219758) (ho_4258 (ho_4265 _let_4 (ho_4247 k_4246 _let_1)) (ho_4506 k_4505 k_4504)))) BOUND_VARIABLE_1219759)))))))))))))))))) (let ((_let_3344 (forall ((BOUND_VARIABLE_1219728 tptp.int) (BOUND_VARIABLE_1219729 tptp.int)) (let ((_let_1 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_2 (ho_4209 _let_1 (ho_4196 k_4195 tptp.one)))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 BOUND_VARIABLE_1219728)) _let_2)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_1 BOUND_VARIABLE_1219729)) _let_2)))) _let_2) (ho_4209 (ho_4211 k_5869 BOUND_VARIABLE_1219728) BOUND_VARIABLE_1219729))))))) (let ((_let_3345 (forall ((BOUND_VARIABLE_1219482 tptp.int) (BOUND_VARIABLE_1219483 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1219483 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219483) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1219483)) BOUND_VARIABLE_1219483)))) (let ((_let_11 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_10) _let_9)) _let_4))) (let ((_let_12 (ho_4209 k_4594 _let_7))) (let ((_let_13 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 BOUND_VARIABLE_1219483))))) (let ((_let_14 (ho_4593 k_4592 (= _let_4 _let_7)))) (let ((_let_15 (ho_4211 _let_14 _let_4))) (let ((_let_16 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1219482 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_17 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219482) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1219482)) BOUND_VARIABLE_1219482)))) (let ((_let_18 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_17) _let_9)) _let_4))) (let ((_let_19 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 BOUND_VARIABLE_1219482))))) (let ((_let_20 (ho_4209 (ho_4220 _let_6 _let_9) _let_4))) (let ((_let_21 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_10) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_11) _let_20)))) _let_4))) (let ((_let_22 (ho_4211 k_4222 _let_8))) (let ((_let_23 (ho_4211 k_4222 _let_12))) (let ((_let_24 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_17) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_18) _let_20)))) _let_4))) (= (ho_4209 (ho_4211 k_5870 BOUND_VARIABLE_1219482) BOUND_VARIABLE_1219483) (ho_4209 (ho_4211 (ho_4593 k_4592 (or (= BOUND_VARIABLE_1219482 _let_3) (= BOUND_VARIABLE_1219483 _let_3))) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1219482 _let_4)) BOUND_VARIABLE_1219483) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1219483 _let_4)) BOUND_VARIABLE_1219482) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 _let_14 BOUND_VARIABLE_1219482) (ho_4209 (ho_4211 _let_19 (ho_4209 _let_23 _let_24)) (ho_4209 _let_23 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_22 (ho_5598 k_5597 _let_16))) (ho_4209 _let_2 _let_24)))))) (ho_4209 (ho_4211 _let_14 BOUND_VARIABLE_1219483) (ho_4209 (ho_4211 _let_13 (ho_4209 _let_23 _let_21)) (ho_4209 _let_23 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_22 (ho_5598 k_5597 _let_5))) (ho_4209 _let_2 _let_21))))))) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 _let_15 (ho_4209 (ho_4211 _let_19 _let_18) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_18) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_16)) _let_4)))) _let_4)))))) _let_3)) (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 (ho_4209 _let_15 (ho_4209 (ho_4211 _let_13 _let_11) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_11) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))) _let_3)))) _let_3)))))))))))))))))))))))))))))))))) (let ((_let_3346 (forall ((BOUND_VARIABLE_1219275 tptp.nat) (BOUND_VARIABLE_1219276 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1219275) _let_3)) (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 _let_1)) _let_3)))))) (let ((_let_6 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_5) _let_1)) _let_3))) (ho_4209 _let_2 _let_5)) _let_5))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219276) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1219276)) BOUND_VARIABLE_1219276)))) (let ((_let_9 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_8) _let_7)) _let_3)) (ho_4209 (ho_4220 _let_4 _let_7) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 _let_5))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4220 k_5871 BOUND_VARIABLE_1219275) BOUND_VARIABLE_1219276) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_5)) BOUND_VARIABLE_1219276) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 BOUND_VARIABLE_1219276) _let_10)) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_6) (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1219276 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1219275) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) K3)))))))))) (ho_4209 _let_2 _let_9)))))) (ho_4209 _let_2 (ho_4209 (ho_4211 k_4222 _let_5) (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_6 (ho_4335 (ho_4334 k_4333 _let_5) BOUND_VARIABLE_1219275))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1219276) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1219276)) BOUND_VARIABLE_1219276))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) _let_3))) (not (= (ho_4209 (ho_4211 k_4222 _let_5) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 BOUND_VARIABLE_1219276))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((BOUND_VARIABLE_459508 tptp.int)) (not (= BOUND_VARIABLE_1219276 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1219275)) BOUND_VARIABLE_459508)))))) _let_3)))) _let_3))))))))))))))))))))))))))))))))) (let ((_let_3347 (forall ((BOUND_VARIABLE_1219240 tptp.nat) (BOUND_VARIABLE_1219241 tptp.nat) (BOUND_VARIABLE_1219242 tptp.nat)) (= (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4215 k_4214 _let_1))) (let ((_let_3 (ho_4196 k_4195 tptp.one))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_3) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_3)))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (not (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_5 _let_1) _let_4)) (ho_4209 (ho_4220 _let_5 K3) _let_4))) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_5 (ho_4216 _let_2 BOUND_VARIABLE_1219240)) _let_4)) (ho_4209 (ho_4220 _let_5 BOUND_VARIABLE_1219241) _let_4)))) (ho_4216 _let_2 BOUND_VARIABLE_1219242)))))))))) (ho_4288 (ho_4287 (ho_4303 k_5872 BOUND_VARIABLE_1219240) BOUND_VARIABLE_1219241) BOUND_VARIABLE_1219242))))) (let ((_let_3348 (forall ((BOUND_VARIABLE_1219223 tptp.nat) (BOUND_VARIABLE_1219224 tptp.nat)) (= (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_2)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (not (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_1) _let_3)) (ho_4209 (ho_4220 _let_4 K3) _let_3))) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1219223) (ho_4216 (ho_4215 k_4214 _let_1) BOUND_VARIABLE_1219224))))))))) (ho_4288 (ho_4287 k_5873 BOUND_VARIABLE_1219223) BOUND_VARIABLE_1219224))))) (let ((_let_3349 (forall ((BOUND_VARIABLE_1219213 tptp.nat) (BOUND_VARIABLE_1219214 tptp.nat)) (= (ho_4288 (ho_4287 k_5874 BOUND_VARIABLE_1219213) BOUND_VARIABLE_1219214) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1219214)) (ho_4290 k_4289 BOUND_VARIABLE_1219213)))))) (let ((_let_3350 (forall ((BOUND_VARIABLE_1219171 tptp.nat) (BOUND_VARIABLE_1219172 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) _let_5))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1219171) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1219172 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_5875 BOUND_VARIABLE_1219171) BOUND_VARIABLE_1219172))))) (let ((_let_3351 (forall ((BOUND_VARIABLE_1219159 tptp.num) (BOUND_VARIABLE_1219160 tptp.nat)) (= (ho_4288 (ho_5829 k_5876 BOUND_VARIABLE_1219159) BOUND_VARIABLE_1219160) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1219160)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1219159)))))))) (let ((_let_3352 (forall ((BOUND_VARIABLE_1219145 tptp.num) (BOUND_VARIABLE_1219146 tptp.nat)) (= (ho_4288 (ho_5829 k_5877 BOUND_VARIABLE_1219145) BOUND_VARIABLE_1219146) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1219146)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1219145))) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))))))) (let ((_let_3353 (forall ((BOUND_VARIABLE_1219133 tptp.num) (BOUND_VARIABLE_1219134 tptp.nat)) (= (ho_4288 (ho_5829 k_5878 BOUND_VARIABLE_1219133) BOUND_VARIABLE_1219134) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1219134)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1219133)))))))) (let ((_let_3354 (forall ((BOUND_VARIABLE_1219119 tptp.num) (BOUND_VARIABLE_1219120 tptp.nat)) (= (ho_4288 (ho_5829 k_5879 BOUND_VARIABLE_1219119) BOUND_VARIABLE_1219120) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1219120)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4196 k_4195 BOUND_VARIABLE_1219119))) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))))))))) (let ((_let_3355 (forall ((BOUND_VARIABLE_1219075 tptp.nat) (BOUND_VARIABLE_1219076 tptp.nat) (BOUND_VARIABLE_1219077 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1219075) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1219076) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1219077 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5880 BOUND_VARIABLE_1219075) BOUND_VARIABLE_1219076) BOUND_VARIABLE_1219077))))) (let ((_let_3356 (forall ((BOUND_VARIABLE_1219020 tptp.nat) (BOUND_VARIABLE_1219021 tptp.nat) (BOUND_VARIABLE_1219022 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1219020) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1219021) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1219022 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5881 BOUND_VARIABLE_1219020) BOUND_VARIABLE_1219021) BOUND_VARIABLE_1219022))))) (let ((_let_3357 (forall ((BOUND_VARIABLE_1218966 tptp.nat) (BOUND_VARIABLE_1218967 tptp.nat) (BOUND_VARIABLE_1218968 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1218966) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218967) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1218968 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5882 BOUND_VARIABLE_1218966) BOUND_VARIABLE_1218967) BOUND_VARIABLE_1218968))))) (let ((_let_3358 (forall ((BOUND_VARIABLE_1218922 tptp.nat) (BOUND_VARIABLE_1218923 tptp.nat) (BOUND_VARIABLE_1218924 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1218922) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218923) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1218924 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5883 BOUND_VARIABLE_1218922) BOUND_VARIABLE_1218923) BOUND_VARIABLE_1218924))))) (let ((_let_3359 (forall ((BOUND_VARIABLE_1218867 tptp.nat) (BOUND_VARIABLE_1218868 tptp.nat) (BOUND_VARIABLE_1218869 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218867) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218868) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1218869 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5884 BOUND_VARIABLE_1218867) BOUND_VARIABLE_1218868) BOUND_VARIABLE_1218869))))) (let ((_let_3360 (forall ((BOUND_VARIABLE_1218823 tptp.nat) (BOUND_VARIABLE_1218824 tptp.nat) (BOUND_VARIABLE_1218825 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1218823) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218824) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1218825 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5885 BOUND_VARIABLE_1218823) BOUND_VARIABLE_1218824) BOUND_VARIABLE_1218825))))) (let ((_let_3361 (forall ((BOUND_VARIABLE_1218771 tptp.nat) (BOUND_VARIABLE_1218772 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1218771) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1218772 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_5886 BOUND_VARIABLE_1218771) BOUND_VARIABLE_1218772))))) (let ((_let_3362 (forall ((BOUND_VARIABLE_1218729 tptp.nat) (BOUND_VARIABLE_1218730 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1218729) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1218730 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_5887 BOUND_VARIABLE_1218729) BOUND_VARIABLE_1218730))))) (let ((_let_3363 (forall ((BOUND_VARIABLE_1218705 tptp.nat) (BOUND_VARIABLE_1218706 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1218706)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218705) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5888 BOUND_VARIABLE_1218705) BOUND_VARIABLE_1218706)))))))) (let ((_let_3364 (forall ((BOUND_VARIABLE_1218695 tptp.nat) (BOUND_VARIABLE_1218696 tptp.nat)) (= (ho_4288 (ho_4287 k_5889 BOUND_VARIABLE_1218695) BOUND_VARIABLE_1218696) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1218696)) (ho_4290 k_4289 BOUND_VARIABLE_1218695)))))) (let ((_let_3365 (forall ((BOUND_VARIABLE_1218685 tptp.nat) (BOUND_VARIABLE_1218686 tptp.nat)) (= (ho_4288 (ho_4287 k_5890 BOUND_VARIABLE_1218685) BOUND_VARIABLE_1218686) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1218686)) (ho_4290 k_4289 BOUND_VARIABLE_1218685)))))) (let ((_let_3366 (forall ((BOUND_VARIABLE_1218661 tptp.nat) (BOUND_VARIABLE_1218662 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1218662)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218661) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_5891 BOUND_VARIABLE_1218661) BOUND_VARIABLE_1218662)))))))) (let ((_let_3367 (forall ((BOUND_VARIABLE_1218597 tptp.nat) (BOUND_VARIABLE_1218598 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4216 (ho_4215 k_5892 BOUND_VARIABLE_1218597) BOUND_VARIABLE_1218598) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (and (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1218597 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1218598 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2)))))))))))) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_3) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1218597) _let_3)) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1218598) _let_3)) _let_2)))) _let_2)))) _let_2))))))))))) (let ((_let_3368 (forall ((BOUND_VARIABLE_1218575 tptp.nat) (BOUND_VARIABLE_1218576 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_5839 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218575) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1218576) _let_2))) (ho_4216 (ho_4215 k_5893 BOUND_VARIABLE_1218575) BOUND_VARIABLE_1218576)))))))) (let ((_let_3369 (forall ((BOUND_VARIABLE_1218488 tptp.nat) (BOUND_VARIABLE_1218489 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1218489) _let_3)) _let_2))) (let ((_let_6 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1218488) _let_3)) _let_2))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) _let_3))) (= (ho_4216 (ho_4215 k_5894 BOUND_VARIABLE_1218488) BOUND_VARIABLE_1218489) (ho_4216 (ho_4215 (ho_4613 k_4612 (or (= BOUND_VARIABLE_1218488 _let_8) (= BOUND_VARIABLE_1218489 _let_8))) _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1218488) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_6) _let_7)))) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1218489) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_5) _let_7)))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_5839 _let_6) _let_5))) _let_2)))) _let_2)))))))))))))))) (let ((_let_3370 (forall ((BOUND_VARIABLE_1218444 tptp.int) (BOUND_VARIABLE_1218445 tptp.int)) (= (ho_5547 k_5546 (ho_4309 (ho_4308 k_4633 BOUND_VARIABLE_1218444) BOUND_VARIABLE_1218445)) (ho_5897 (ho_5896 k_5895 BOUND_VARIABLE_1218444) BOUND_VARIABLE_1218445))))) (let ((_let_3371 (forall ((BOUND_VARIABLE_1218384 tptp.int) (BOUND_VARIABLE_1218385 tptp.int)) (= (ho_5551 (ho_5902 (ho_5901 k_5900 (= BOUND_VARIABLE_1218384 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1218385) (ho_4196 k_4195 tptp.one))) BOUND_VARIABLE_1218384))) tptp.bot_bot_set_int) (ho_5551 (ho_5899 k_5898 BOUND_VARIABLE_1218384) (ho_5547 k_5546 (ho_4309 (ho_4308 k_4641 BOUND_VARIABLE_1218384) BOUND_VARIABLE_1218385)))) (ho_5897 (ho_5896 k_5903 BOUND_VARIABLE_1218384) BOUND_VARIABLE_1218385))))) (let ((_let_3372 (forall ((BOUND_VARIABLE_1218363 tptp.int) (BOUND_VARIABLE_1218364 tptp.int) (BOUND_VARIABLE_1218365 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_5904 BOUND_VARIABLE_1218363) BOUND_VARIABLE_1218364) BOUND_VARIABLE_1218365) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1218363) (ho_4209 (ho_4211 k_4210 (ho_4196 k_4195 tptp.one)) BOUND_VARIABLE_1218364)))) (or (not (= BOUND_VARIABLE_1218365 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_3373 (forall ((BOUND_VARIABLE_1218343 tptp.int) (BOUND_VARIABLE_1218344 tptp.int) (BOUND_VARIABLE_1218345 tptp.int)) (= (ho_4310 (ho_4309 (ho_4308 k_5905 BOUND_VARIABLE_1218343) BOUND_VARIABLE_1218344) BOUND_VARIABLE_1218345) (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4636 (ho_4635 k_4634 BOUND_VARIABLE_1218343) BOUND_VARIABLE_1218344))) (or (not (= BOUND_VARIABLE_1218345 (ho_4335 (ho_4640 k_4639 _let_1) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_1)))))))))))) (let ((_let_3374 (forall ((BOUND_VARIABLE_1218200 tptp.int) (BOUND_VARIABLE_1218201 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1218201 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1218201) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1218201)) BOUND_VARIABLE_1218201))) _let_8)) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_7))) (let ((_let_11 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_7)) _let_4))) (let ((_let_12 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1218200 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_13 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1218200) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1218200)) BOUND_VARIABLE_1218200))) _let_8)) _let_4))) (let ((_let_14 (ho_5598 k_5597 (and _let_12 _let_5)))) (let ((_let_15 (ho_5551 (ho_5899 k_5898 _let_4) (ho_5551 (ho_5899 k_5898 _let_3) tptp.bot_bot_set_int)))) (= (ho_4209 (ho_4211 k_5906 BOUND_VARIABLE_1218200) BOUND_VARIABLE_1218201) (ho_4209 (ho_4211 (ho_4593 k_4592 (and (ho_5117 (ho_5116 k_5115 BOUND_VARIABLE_1218200) _let_15) (ho_5117 (ho_5116 k_5115 BOUND_VARIABLE_1218201) _let_15))) (ho_4209 _let_2 _let_14)) (ho_4209 (ho_4211 k_4210 _let_14) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_5839 (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1218200))) _let_13) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_13) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_12)) _let_4)))) _let_4))))) (ho_4209 _let_11 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1218201))) _let_9) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_9) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4))))))))))))))))))))))))))) (let ((_let_3375 (forall ((BOUND_VARIABLE_1218073 tptp.int) (BOUND_VARIABLE_1218074 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1218074 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_5 (ho_4219 k_4218 k_4217))) (let ((_let_6 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_7 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6)))) (let ((_let_8 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1218074) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1218074)) BOUND_VARIABLE_1218074))) _let_7)) _let_3))) (let ((_let_9 (ho_4209 k_4594 _let_6))) (let ((_let_10 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_6)) _let_3))) (let ((_let_11 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1218073 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_12 (ho_4209 (ho_4220 _let_5 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1218073) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1218073)) BOUND_VARIABLE_1218073))) _let_7)) _let_3))) (= (ho_4209 (ho_4211 k_5907 BOUND_VARIABLE_1218073) BOUND_VARIABLE_1218074) (ho_4209 (ho_4211 k_4210 (ho_5598 k_5597 (and _let_11 _let_4))) (ho_4209 (ho_4211 k_4222 _let_6) (ho_4209 (ho_4211 k_5839 (ho_4209 _let_10 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_9 (ho_4209 k_4594 BOUND_VARIABLE_1218073))) _let_12) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_5 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4220 _let_5 (ho_4591 k_4590 _let_11)) _let_3)))) _let_3))))) (ho_4209 _let_10 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_9 (ho_4209 k_4594 BOUND_VARIABLE_1218074))) _let_8) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_5 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_8) (ho_4209 (ho_4220 _let_5 (ho_4591 k_4590 _let_4)) _let_3)))) _let_3))))))))))))))))))))))) (let ((_let_3376 (forall ((BOUND_VARIABLE_1217867 tptp.int) (BOUND_VARIABLE_1217868 tptp.nat) (BOUND_VARIABLE_1217869 tptp.int)) (let ((_let_1 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217868))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_3 _let_2)))) (let ((_let_5 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) _let_2)) _let_4))) (ho_4209 _let_3 _let_1)) _let_1))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4209 (ho_4220 _let_7 _let_6) _let_4))) (let ((_let_9 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1217867) _let_2)) _let_4))) (ho_4209 _let_3 BOUND_VARIABLE_1217867)) BOUND_VARIABLE_1217867)))) (let ((_let_10 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_9) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_9) _let_6)) _let_4)) _let_8)))) _let_4))) (let ((_let_11 (ho_4211 k_4222 _let_5))) (let ((_let_12 (ho_4209 k_4594 _let_1))) (let ((_let_13 (ho_4211 k_4222 _let_12))) (let ((_let_14 (ho_4593 k_4592 (= _let_4 _let_1)))) (let ((_let_15 (ho_4209 (ho_4211 _let_14 BOUND_VARIABLE_1217867) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 BOUND_VARIABLE_1217867))) (ho_4209 _let_13 _let_10)) (ho_4209 _let_13 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_11 (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1217867 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217868)) K3))))))) (ho_4209 _let_3 _let_10))))))) (let ((_let_16 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_15) _let_2)) _let_4))) (ho_4209 _let_3 _let_15)) _let_15)))) (let ((_let_17 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_16) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_16) _let_6)) _let_4)) _let_8)))) _let_4))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 _let_14 _let_15) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 _let_15))) (ho_4209 _let_13 _let_17)) (ho_4209 _let_13 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_11 (ho_5598 k_5597 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217868))) (let ((_let_5 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_4) _let_1)) _let_3))) (ho_4209 _let_2 _let_4)) _let_4))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1217867) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1217867)) BOUND_VARIABLE_1217867)))) (let ((_let_9 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_8) _let_6)) _let_3)) (ho_4209 (ho_4220 _let_7 _let_6) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 _let_4))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (not (= (ho_4209 (ho_4211 k_4222 _let_4) K3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_4)) BOUND_VARIABLE_1217867) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1217867))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_5) (ho_5598 k_5597 (forall ((BOUND_VARIABLE_891698 tptp.int)) (not (= BOUND_VARIABLE_1217867 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217868)) BOUND_VARIABLE_891698))))))) (ho_4209 _let_2 _let_9)))))))))))))))))))))) (ho_4209 _let_3 _let_17)))))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1217869) _let_1)) (ho_4209 (ho_4220 (ho_4723 k_5908 BOUND_VARIABLE_1217867) BOUND_VARIABLE_1217868) BOUND_VARIABLE_1217869)))))))))))))))))))))) (let ((_let_3377 (forall ((BOUND_VARIABLE_1217754 tptp.int) (BOUND_VARIABLE_1217755 tptp.nat) (BOUND_VARIABLE_1217756 tptp.int)) (let ((_let_1 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217755))) (let ((_let_2 (ho_4196 k_4195 tptp.one))) (let ((_let_3 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_2) (ho_4209 _let_3 _let_2)))) (let ((_let_5 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) _let_2)) _let_4))) (ho_4209 _let_3 _let_1)) _let_1))) (let ((_let_6 (ho_4213 k_4212 _let_5))) (let ((_let_7 (ho_4219 k_4218 k_4217))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1217754) _let_2)) _let_4))) (ho_4209 _let_3 BOUND_VARIABLE_1217754)) BOUND_VARIABLE_1217754)))) (let ((_let_9 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_7 (ho_4216 (ho_4215 k_4221 _let_8) _let_6)) _let_4)) (ho_4209 (ho_4220 _let_7 _let_6) _let_4))))) _let_4))) (let ((_let_10 (ho_4209 k_4594 _let_1))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 _let_1)) BOUND_VARIABLE_1217754) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 BOUND_VARIABLE_1217754))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_5) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1217754 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) BOUND_VARIABLE_1217755)) K3))))))) (ho_4209 _let_3 _let_9)))))) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1217756) _let_1)) (ho_4209 (ho_4220 (ho_4723 k_5909 BOUND_VARIABLE_1217754) BOUND_VARIABLE_1217755) BOUND_VARIABLE_1217756)))))))))))))))) (let ((_let_3378 (forall ((BOUND_VARIABLE_1217526 tptp.int) (BOUND_VARIABLE_1217527 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 _let_2 _let_1))) (let ((_let_4 (ho_4209 (ho_4211 k_4210 _let_1) _let_3))) (let ((_let_5 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1217527 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_8 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_4))) (ho_4209 _let_2 _let_7)) _let_7))) (let ((_let_9 (ho_4213 k_4212 _let_8))) (let ((_let_10 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1217527) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1217527)) BOUND_VARIABLE_1217527)))) (let ((_let_11 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_10) _let_9)) _let_4))) (let ((_let_12 (ho_4209 k_4594 _let_7))) (let ((_let_13 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 BOUND_VARIABLE_1217527))))) (let ((_let_14 (ho_4593 k_4592 (= _let_4 _let_7)))) (let ((_let_15 (ho_4211 _let_14 _let_4))) (let ((_let_16 (forall ((K3 tptp.int)) (not (= BOUND_VARIABLE_1217526 (ho_4209 (ho_4211 k_4222 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) K3)))))) (let ((_let_17 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_4 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1217526) _let_1)) _let_4))) (ho_4209 _let_2 BOUND_VARIABLE_1217526)) BOUND_VARIABLE_1217526)))) (let ((_let_18 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_17) _let_9)) _let_4))) (let ((_let_19 (ho_4593 k_4592 (= _let_12 (ho_4209 k_4594 BOUND_VARIABLE_1217526))))) (let ((_let_20 (ho_4209 (ho_4220 _let_6 _let_9) _let_4))) (let ((_let_21 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_10) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_11) _let_20)))) _let_4))) (let ((_let_22 (ho_4211 k_4222 _let_8))) (let ((_let_23 (ho_4211 k_4222 _let_12))) (let ((_let_24 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_17) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 _let_18) _let_20)))) _let_4))) (= (ho_4209 (ho_4211 k_5910 BOUND_VARIABLE_1217526) BOUND_VARIABLE_1217527) (ho_4209 (ho_4211 (ho_4593 k_4592 (or (= BOUND_VARIABLE_1217526 _let_4) (= BOUND_VARIABLE_1217527 _let_4))) _let_4) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1217526 _let_3)) BOUND_VARIABLE_1217527) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1217527 _let_3)) BOUND_VARIABLE_1217526) (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 _let_14 BOUND_VARIABLE_1217526) (ho_4209 (ho_4211 _let_19 (ho_4209 _let_23 _let_24)) (ho_4209 _let_23 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_22 (ho_5598 k_5597 _let_16))) (ho_4209 _let_2 _let_24)))))) (ho_4209 (ho_4211 _let_14 BOUND_VARIABLE_1217527) (ho_4209 (ho_4211 _let_13 (ho_4209 _let_23 _let_21)) (ho_4209 _let_23 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_22 (ho_5598 k_5597 _let_5))) (ho_4209 _let_2 _let_21))))))) (ho_4209 (ho_4211 k_4222 _let_7) (ho_4209 (ho_4211 k_5839 (ho_4209 _let_15 (ho_4209 (ho_4211 _let_19 _let_18) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_18) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_16)) _let_4)))) _let_4))))) (ho_4209 _let_15 (ho_4209 (ho_4211 _let_13 _let_11) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_6 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_11) (ho_4209 (ho_4220 _let_6 (ho_4591 k_4590 _let_5)) _let_4)))) _let_4)))))))))))))))))))))))))))))))))))))) (let ((_let_3379 (forall ((BOUND_VARIABLE_1217519 tptp.int) (BOUND_VARIABLE_1217520 tptp.nat)) (= (ho_4316 (ho_4315 k_5911 BOUND_VARIABLE_1217519) BOUND_VARIABLE_1217520) (ho_4318 k_4317 BOUND_VARIABLE_1217519))))) (let ((_let_3380 (forall ((BOUND_VARIABLE_1217453 tptp.real) (BOUND_VARIABLE_1217454 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (ho_4351 (ho_4508 k_5912 BOUND_VARIABLE_1217453) BOUND_VARIABLE_1217454) (and (= (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4642 BOUND_VARIABLE_1217454))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4643 BOUND_VARIABLE_1217454)))) (ho_4258 (ho_4265 _let_4 (ho_4247 k_4246 tptp.one)) (ho_4258 _let_3 BOUND_VARIABLE_1217453))) (= BOUND_VARIABLE_1217454 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217454) _let_6)) (not (= BOUND_VARIABLE_1217454 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1217454)) (not (= BOUND_VARIABLE_1217454 _let_5))))))))))))) (let ((_let_3381 (forall ((BOUND_VARIABLE_1217391 tptp.real) (BOUND_VARIABLE_1217392 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4274))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 _let_3 _let_1)))) (let ((_let_6 (ho_4258 (ho_4257 _let_2 k_4248) _let_5))) (= (ho_4351 (ho_4508 k_5913 BOUND_VARIABLE_1217391) BOUND_VARIABLE_1217392) (and (= BOUND_VARIABLE_1217391 (ho_4258 (ho_4265 _let_4 (ho_4348 k_4347 (ho_4244 k_4644 BOUND_VARIABLE_1217392))) (ho_4258 _let_3 (ho_4348 k_4347 (ho_4244 k_4645 BOUND_VARIABLE_1217392))))) (= BOUND_VARIABLE_1217392 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217392) _let_6)) (not (= BOUND_VARIABLE_1217392 _let_6)) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) BOUND_VARIABLE_1217392)) (not (= BOUND_VARIABLE_1217392 _let_5))))))))))))) (let ((_let_3382 (forall ((BOUND_VARIABLE_1217384 tptp.int) (BOUND_VARIABLE_1217385 tptp.nat)) (= (ho_4316 (ho_4315 k_5914 BOUND_VARIABLE_1217384) BOUND_VARIABLE_1217385) (ho_4318 k_4317 BOUND_VARIABLE_1217384))))) (let ((_let_3383 (forall ((BOUND_VARIABLE_1217350 tptp.complex) (BOUND_VARIABLE_1217351 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1217351 _let_2))) (= (ho_4351 (ho_5659 k_5915 BOUND_VARIABLE_1217350) BOUND_VARIABLE_1217351) (and (= (ho_4771 k_4772 BOUND_VARIABLE_1217351) (ho_4703 k_5657 BOUND_VARIABLE_1217350)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1217351)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1217351 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217351) _let_3)) (not (= BOUND_VARIABLE_1217351 _let_3))))))))))) (let ((_let_3384 (forall ((BOUND_VARIABLE_1217316 tptp.complex) (BOUND_VARIABLE_1217317 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1217317 _let_2))) (= (ho_4351 (ho_5659 k_5916 BOUND_VARIABLE_1217316) BOUND_VARIABLE_1217317) (and (= (ho_4771 k_4772 BOUND_VARIABLE_1217317) (ho_4703 k_5657 BOUND_VARIABLE_1217316)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1217317)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1217317 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217317) _let_3)) (not (= BOUND_VARIABLE_1217317 _let_3))))))))))) (let ((_let_3385 (forall ((BOUND_VARIABLE_1217259 tptp.real) (BOUND_VARIABLE_1217260 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4647 BOUND_VARIABLE_1217260)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4646 BOUND_VARIABLE_1217260)))) (let ((_let_3 (= BOUND_VARIABLE_1217259 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1217259 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217259) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1217259)) (not (= BOUND_VARIABLE_1217259 _let_1))) (ho_4310 (ho_4673 k_5917 BOUND_VARIABLE_1217259) BOUND_VARIABLE_1217260)))))))) (let ((_let_3386 (forall ((BOUND_VARIABLE_1217202 tptp.real) (BOUND_VARIABLE_1217203 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4649 BOUND_VARIABLE_1217203)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4648 BOUND_VARIABLE_1217203)))) (let ((_let_3 (= BOUND_VARIABLE_1217202 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1217202 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217202) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1217202)) (not (= BOUND_VARIABLE_1217202 _let_1))) (ho_4310 (ho_4673 k_5918 BOUND_VARIABLE_1217202) BOUND_VARIABLE_1217203)))))))) (let ((_let_3387 (forall ((BOUND_VARIABLE_1217140 tptp.nat) (BOUND_VARIABLE_1217141 tptp.int)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1217140) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4651 BOUND_VARIABLE_1217141)))) (let ((_let_5 (ho_4251 k_4250 (ho_4315 k_4650 BOUND_VARIABLE_1217141)))) (let ((_let_6 (= _let_3 _let_5))) (= (ho_4310 (ho_5920 k_5919 BOUND_VARIABLE_1217140) BOUND_VARIABLE_1217141) (and (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_5)) (not _let_6)) _let_6) (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) _let_3)) (not (= _let_4 _let_3))))))))))))) (let ((_let_3388 (forall ((BOUND_VARIABLE_1217083 tptp.real) (BOUND_VARIABLE_1217084 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4653 BOUND_VARIABLE_1217084)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4652 BOUND_VARIABLE_1217084)))) (let ((_let_3 (= BOUND_VARIABLE_1217083 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1217083 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217083) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1217083)) (not (= BOUND_VARIABLE_1217083 _let_1))) (ho_4310 (ho_4673 k_5921 BOUND_VARIABLE_1217083) BOUND_VARIABLE_1217084)))))))) (let ((_let_3389 (forall ((BOUND_VARIABLE_1217026 tptp.real) (BOUND_VARIABLE_1217027 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4655 BOUND_VARIABLE_1217027)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4654 BOUND_VARIABLE_1217027)))) (let ((_let_3 (= BOUND_VARIABLE_1217026 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1217026 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1217026) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1217026)) (not (= BOUND_VARIABLE_1217026 _let_1))) (ho_4310 (ho_4673 k_5922 BOUND_VARIABLE_1217026) BOUND_VARIABLE_1217027)))))))) (let ((_let_3390 (forall ((BOUND_VARIABLE_1216971 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4657 BOUND_VARIABLE_1216971)))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259) _let_2) (ho_4258 (ho_4257 _let_3 k_4248) _let_2)))) (let ((_let_5 (ho_4251 k_4250 (ho_4315 k_4656 BOUND_VARIABLE_1216971)))) (let ((_let_6 (= _let_4 _let_5))) (= (and (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) _let_5)) (not _let_6)) _let_6) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) _let_4)) (not (= _let_4 _let_1))) (ho_4310 k_5923 BOUND_VARIABLE_1216971))))))))))) (let ((_let_3391 (forall ((BOUND_VARIABLE_1216954 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1216954) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) _let_1)) (ho_4216 k_5924 BOUND_VARIABLE_1216954)))))) (let ((_let_3392 (forall ((BOUND_VARIABLE_1216840 tptp.nat) (BOUND_VARIABLE_1216841 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1216841) _let_3))) (let ((_let_6 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1216840) _let_3))) (let ((_let_7 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_6) _let_1)) _let_3))) (ho_4209 _let_2 _let_6)) _let_6))) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_5) _let_1)) _let_3))) (ho_4209 _let_2 _let_5)) _let_5)))) _let_3))) (= (ho_4216 (ho_4215 k_5925 BOUND_VARIABLE_1216840) BOUND_VARIABLE_1216841) (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 _let_5)) _let_3) (ho_4209 (ho_4211 (ho_4593 k_4592 (= (ho_4209 k_4594 _let_6) (ho_4209 k_4594 _let_5))) _let_7) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4220 _let_4 (ho_4591 k_4590 (forall ((K3 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1216840) _let_2) (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1216841) _let_2)) K3))))))))) _let_3)))) _let_3)))))))))))))))) (let ((_let_3393 (forall ((BOUND_VARIABLE_1304667 |u_(-> tptp.nat Bool)|)) (= (ho_5927 k_5926 BOUND_VARIABLE_1304667) (forall ((X4 tptp.nat)) (ho_4288 BOUND_VARIABLE_1304667 X4)))))) (let ((_let_3394 (forall ((BOUND_VARIABLE_1304680 |u_(-> tptp.nat Bool)|)) (= (forall ((X2 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (or (not (= X2 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) X2))) (ho_4288 BOUND_VARIABLE_1304680 (ho_4213 k_4212 X2))))) (ho_5927 k_5928 BOUND_VARIABLE_1304680))))) (let ((_let_3395 (forall ((BOUND_VARIABLE_1304695 |u_(-> tptp.nat Bool)|)) (= (ho_5927 k_5929 BOUND_VARIABLE_1304695) (not (forall ((X4 tptp.nat)) (not (ho_4288 BOUND_VARIABLE_1304695 X4)))))))) (let ((_let_3396 (forall ((BOUND_VARIABLE_1304706 |u_(-> tptp.nat Bool)|)) (= (not (forall ((X2 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (or (not (= X2 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) X2))) (not (ho_4288 BOUND_VARIABLE_1304706 (ho_4213 k_4212 X2))))))) (ho_5927 k_5930 BOUND_VARIABLE_1304706))))) (let ((_let_3397 (forall ((BOUND_VARIABLE_1216747 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_5 (= BOUND_VARIABLE_1216747 _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1216747 _let_3))) (= (ho_4351 k_5931 BOUND_VARIABLE_1216747) (and (or (and (= BOUND_VARIABLE_1216747 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1216747) _let_3)) (not _let_6)) _let_6) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1216747)) (not _let_5)) _let_5) (= _let_3 (ho_4348 k_4347 (ho_4244 k_4658 BOUND_VARIABLE_1216747)))))))))))))) (let ((_let_3398 (forall ((BOUND_VARIABLE_1216742 tptp.real)) (not (ho_4351 k_5932 BOUND_VARIABLE_1216742))))) (let ((_let_3399 (forall ((BOUND_VARIABLE_1216696 tptp.real) (BOUND_VARIABLE_1216697 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5933 BOUND_VARIABLE_1216696) BOUND_VARIABLE_1216697) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216697 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1216697) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1216697) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216696) BOUND_VARIABLE_1216697))))))))))))) (let ((_let_3400 (forall ((BOUND_VARIABLE_1216645 tptp.real) (BOUND_VARIABLE_1216646 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5934 BOUND_VARIABLE_1216645) BOUND_VARIABLE_1216646) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216646 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1216646) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1216646) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216645) BOUND_VARIABLE_1216646))))))))))))))))) (let ((_let_3401 (forall ((BOUND_VARIABLE_1216599 tptp.real) (BOUND_VARIABLE_1216600 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5935 BOUND_VARIABLE_1216599) BOUND_VARIABLE_1216600) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216600 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1216600) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1216600) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216599) BOUND_VARIABLE_1216600))))))))))))) (let ((_let_3402 (forall ((BOUND_VARIABLE_1216548 tptp.real) (BOUND_VARIABLE_1216549 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5936 BOUND_VARIABLE_1216548) BOUND_VARIABLE_1216549) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216549 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1216549) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1216549) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216548) BOUND_VARIABLE_1216549))))))))))))))))) (let ((_let_3403 (forall ((BOUND_VARIABLE_1216502 tptp.real) (BOUND_VARIABLE_1216503 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5937 BOUND_VARIABLE_1216502) BOUND_VARIABLE_1216503) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216503 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1216503) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1216503) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216502) BOUND_VARIABLE_1216503))))))))))))) (let ((_let_3404 (forall ((BOUND_VARIABLE_1216451 tptp.real) (BOUND_VARIABLE_1216452 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5938 BOUND_VARIABLE_1216451) BOUND_VARIABLE_1216452) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1216452 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1216452) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1216452) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1216451) BOUND_VARIABLE_1216452))))))))))))))))) (let ((_let_3405 (forall ((BOUND_VARIABLE_1216427 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_3 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504))) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (ho_4771 k_4770 BOUND_VARIABLE_1216427)))) (= (ho_4703 (ho_4705 k_4710 (ho_4771 k_4770 (ho_4258 k_5410 (ho_4769 k_4773 _let_4)))) (ho_4771 k_4772 (ho_4769 k_4768 _let_4))) (ho_4771 k_5939 BOUND_VARIABLE_1216427))))))))) (let ((_let_3406 (forall ((BOUND_VARIABLE_1216401 tptp.nat) (BOUND_VARIABLE_1216402 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_5 (ho_4272 k_4271 k_4270))) (let ((_let_6 (ho_4264 _let_3 k_4275))) (let ((_let_7 (ho_4265 _let_6 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))))) (= (ho_4771 k_4772 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 (ho_4258 _let_7 (ho_4258 _let_7 (ho_4506 k_4505 k_4504)))) (ho_4258 (ho_4273 _let_5 BOUND_VARIABLE_1216402) _let_4))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 _let_5 BOUND_VARIABLE_1216401) _let_4)))) (ho_4767 (ho_4779 k_5940 BOUND_VARIABLE_1216401) BOUND_VARIABLE_1216402)))))))))))) (let ((_let_3407 (forall ((BOUND_VARIABLE_1216391 tptp.nat) (BOUND_VARIABLE_1216392 tptp.nat)) (= (ho_4288 (ho_4287 k_5941 BOUND_VARIABLE_1216391) BOUND_VARIABLE_1216392) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1216392)) (ho_4290 k_4289 BOUND_VARIABLE_1216391)))))) (let ((_let_3408 (forall ((BOUND_VARIABLE_1216382 tptp.nat) (BOUND_VARIABLE_1216383 tptp.complex)) (= (ho_5127 (ho_5661 k_5942 BOUND_VARIABLE_1216382) BOUND_VARIABLE_1216383) (= (ho_4701 k_4700 tptp.one) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1216383) BOUND_VARIABLE_1216382)))))) (let ((_let_3409 (forall ((BOUND_VARIABLE_1216311 tptp.nat) (BOUND_VARIABLE_1216312 tptp.nat) (BOUND_VARIABLE_1216313 tptp.int)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4272 k_4271 k_4270))) (let ((_let_5 (ho_4258 (ho_4265 k_5943 (ho_4258 (ho_4273 _let_4 BOUND_VARIABLE_1216311) _let_3)) (ho_4258 (ho_4273 _let_4 BOUND_VARIABLE_1216312) _let_3)))) (let ((_let_6 (ho_4251 k_4250 (ho_4315 k_4660 BOUND_VARIABLE_1216313)))) (let ((_let_7 (ho_4251 k_4250 (ho_4315 k_4659 BOUND_VARIABLE_1216313)))) (let ((_let_8 (= _let_5 _let_7))) (= (ho_4310 (ho_5920 (ho_5945 k_5944 BOUND_VARIABLE_1216311) BOUND_VARIABLE_1216312) BOUND_VARIABLE_1216313) (and (or (and (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) _let_7)) (not _let_8)) _let_8) (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) _let_5)) (not (= _let_6 _let_5))))))))))))))) (let ((_let_3410 (forall ((BOUND_VARIABLE_1216247 tptp.nat) (BOUND_VARIABLE_1216248 tptp.int)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 k_5943 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1216247) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4662 BOUND_VARIABLE_1216248)))) (let ((_let_5 (ho_4251 k_4250 (ho_4315 k_4661 BOUND_VARIABLE_1216248)))) (let ((_let_6 (= _let_3 _let_5))) (= (ho_4310 (ho_5920 k_5946 BOUND_VARIABLE_1216247) BOUND_VARIABLE_1216248) (and (or (and (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_5)) (not _let_6)) _let_6) (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) _let_3)) (not (= _let_4 _let_3))))))))))))) (let ((_let_3411 (forall ((BOUND_VARIABLE_1216181 tptp.nat) (BOUND_VARIABLE_1216182 tptp.int)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4258 (ho_4265 k_5943 (ho_4247 k_4246 _let_3)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1216181) (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))))) (let ((_let_5 (ho_4251 k_4250 (ho_4315 k_4664 BOUND_VARIABLE_1216182)))) (let ((_let_6 (ho_4251 k_4250 (ho_4315 k_4663 BOUND_VARIABLE_1216182)))) (let ((_let_7 (= _let_4 _let_6))) (= (ho_4310 (ho_5920 k_5947 BOUND_VARIABLE_1216181) BOUND_VARIABLE_1216182) (and (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) _let_6)) (not _let_7)) _let_7) (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) _let_4)) (not (= _let_5 _let_4)))))))))))))) (let ((_let_3412 (forall ((BOUND_VARIABLE_1216106 tptp.real) (BOUND_VARIABLE_1216107 tptp.int) (BOUND_VARIABLE_1216108 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) BOUND_VARIABLE_1216106) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4251 k_4250 (ho_4315 k_4667 BOUND_VARIABLE_1216107)))))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4666 BOUND_VARIABLE_1216108)))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4665 BOUND_VARIABLE_1216108)))) (let ((_let_5 (= _let_2 _let_4))) (= (ho_4310 (ho_4309 (ho_5949 k_5948 BOUND_VARIABLE_1216106) BOUND_VARIABLE_1216107) BOUND_VARIABLE_1216108) (and (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_4)) (not _let_5)) _let_5) (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_2)) (not (= _let_3 _let_2)))))))))))) (let ((_let_3413 (forall ((BOUND_VARIABLE_1216049 tptp.real) (BOUND_VARIABLE_1216050 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4669 BOUND_VARIABLE_1216050)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4668 BOUND_VARIABLE_1216050)))) (let ((_let_3 (= BOUND_VARIABLE_1216049 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1216049 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1216049) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1216049)) (not (= BOUND_VARIABLE_1216049 _let_1))) (ho_4310 (ho_4673 k_5950 BOUND_VARIABLE_1216049) BOUND_VARIABLE_1216050)))))))) (let ((_let_3414 (forall ((BOUND_VARIABLE_1216042 tptp.int) (BOUND_VARIABLE_1216043 tptp.nat)) (= (ho_4316 (ho_4315 k_5951 BOUND_VARIABLE_1216042) BOUND_VARIABLE_1216043) (ho_4318 k_4317 BOUND_VARIABLE_1216042))))) (let ((_let_3415 (forall ((BOUND_VARIABLE_1215985 tptp.real) (BOUND_VARIABLE_1215986 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4671 BOUND_VARIABLE_1215986)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4670 BOUND_VARIABLE_1215986)))) (let ((_let_3 (= BOUND_VARIABLE_1215985 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1215985 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215985) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1215985)) (not (= BOUND_VARIABLE_1215985 _let_1))) (ho_4310 (ho_4673 k_5952 BOUND_VARIABLE_1215985) BOUND_VARIABLE_1215986)))))))) (let ((_let_3416 (forall ((BOUND_VARIABLE_1215943 tptp.real) (BOUND_VARIABLE_1215944 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4672 BOUND_VARIABLE_1215943))) (ho_4316 (ho_4253 k_5955 BOUND_VARIABLE_1215943) BOUND_VARIABLE_1215944))))) (let ((_let_3417 (forall ((BOUND_VARIABLE_1215901 tptp.real) (BOUND_VARIABLE_1215902 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4674 BOUND_VARIABLE_1215901))) (ho_4316 (ho_4253 k_5956 BOUND_VARIABLE_1215901) BOUND_VARIABLE_1215902))))) (let ((_let_3418 (forall ((BOUND_VARIABLE_1215859 tptp.real) (BOUND_VARIABLE_1215860 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4675 BOUND_VARIABLE_1215859))) (ho_4316 (ho_4253 k_5957 BOUND_VARIABLE_1215859) BOUND_VARIABLE_1215860))))) (let ((_let_3419 (forall ((BOUND_VARIABLE_1215817 tptp.real) (BOUND_VARIABLE_1215818 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4676 BOUND_VARIABLE_1215817))) (ho_4316 (ho_4253 k_5958 BOUND_VARIABLE_1215817) BOUND_VARIABLE_1215818))))) (let ((_let_3420 (forall ((BOUND_VARIABLE_1215775 tptp.real) (BOUND_VARIABLE_1215776 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4677 BOUND_VARIABLE_1215775))) (ho_4316 (ho_4253 k_5959 BOUND_VARIABLE_1215775) BOUND_VARIABLE_1215776))))) (let ((_let_3421 (forall ((BOUND_VARIABLE_1215733 tptp.real) (BOUND_VARIABLE_1215734 tptp.nat)) (= (ho_4318 k_4317 (ho_5954 k_5953 (ho_4673 k_4678 BOUND_VARIABLE_1215733))) (ho_4316 (ho_4253 k_5960 BOUND_VARIABLE_1215733) BOUND_VARIABLE_1215734))))) (let ((_let_3422 (forall ((BOUND_VARIABLE_1215726 tptp.int) (BOUND_VARIABLE_1215727 tptp.nat)) (= (ho_4316 (ho_4315 k_5961 BOUND_VARIABLE_1215726) BOUND_VARIABLE_1215727) (ho_4318 k_4317 BOUND_VARIABLE_1215726))))) (let ((_let_3423 (forall ((BOUND_VARIABLE_1215669 tptp.real) (BOUND_VARIABLE_1215670 tptp.int)) (let ((_let_1 (ho_4251 k_4250 (ho_4315 k_4680 BOUND_VARIABLE_1215670)))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4679 BOUND_VARIABLE_1215670)))) (let ((_let_3 (= BOUND_VARIABLE_1215669 _let_2))) (= (and (or (and (= BOUND_VARIABLE_1215669 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215669) _let_2)) (not _let_3)) _let_3) (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) BOUND_VARIABLE_1215669)) (not (= BOUND_VARIABLE_1215669 _let_1))) (ho_4310 (ho_4673 k_5962 BOUND_VARIABLE_1215669) BOUND_VARIABLE_1215670)))))))) (let ((_let_3424 (forall ((BOUND_VARIABLE_1215609 tptp.real) (BOUND_VARIABLE_1215610 tptp.real) (BOUND_VARIABLE_1215611 tptp.int)) (let ((_let_1 (ho_4258 (ho_4265 k_5943 BOUND_VARIABLE_1215609) BOUND_VARIABLE_1215610))) (let ((_let_2 (ho_4251 k_4250 (ho_4315 k_4682 BOUND_VARIABLE_1215611)))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4681 BOUND_VARIABLE_1215611)))) (let ((_let_4 (= _let_1 _let_3))) (= (ho_4310 (ho_4673 (ho_5964 k_5963 BOUND_VARIABLE_1215609) BOUND_VARIABLE_1215610) BOUND_VARIABLE_1215611) (and (or (and (= _let_1 (ho_4258 (ho_4265 k_4349 _let_1) _let_3)) (not _let_4)) _let_4) (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_1)) (not (= _let_2 _let_1))))))))))) (let ((_let_3425 (forall ((BOUND_VARIABLE_1215602 tptp.int) (BOUND_VARIABLE_1215603 tptp.nat)) (= (ho_4316 (ho_4315 k_5965 BOUND_VARIABLE_1215602) BOUND_VARIABLE_1215603) (ho_4318 k_4317 BOUND_VARIABLE_1215602))))) (let ((_let_3426 (forall ((BOUND_VARIABLE_1215593 tptp.int) (BOUND_VARIABLE_1215594 tptp.nat)) (= (ho_4316 (ho_4315 k_5966 BOUND_VARIABLE_1215593) BOUND_VARIABLE_1215594) (ho_4318 k_4317 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1215593) (ho_4196 k_4195 tptp.one))))))) (let ((_let_3427 (forall ((BOUND_VARIABLE_1215528 tptp.num) (BOUND_VARIABLE_1215529 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 tptp.one)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4247 k_4246 BOUND_VARIABLE_1215528)))))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4684 BOUND_VARIABLE_1215529)))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4683 BOUND_VARIABLE_1215529)))) (let ((_let_5 (= _let_2 _let_4))) (= (ho_4310 (ho_5968 k_5967 BOUND_VARIABLE_1215528) BOUND_VARIABLE_1215529) (and (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_4)) (not _let_5)) _let_5) (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_2)) (not (= _let_3 _let_2)))))))))))) (let ((_let_3428 (forall ((BOUND_VARIABLE_1215459 tptp.num) (BOUND_VARIABLE_1215460 tptp.num) (BOUND_VARIABLE_1215461 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4257 _let_1 k_4248) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 BOUND_VARIABLE_1215459)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4247 k_4246 BOUND_VARIABLE_1215460)))))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4686 BOUND_VARIABLE_1215461)))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4685 BOUND_VARIABLE_1215461)))) (let ((_let_5 (= _let_2 _let_4))) (= (ho_4310 (ho_5968 (ho_5970 k_5969 BOUND_VARIABLE_1215459) BOUND_VARIABLE_1215460) BOUND_VARIABLE_1215461) (and (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_4)) (not _let_5)) _let_5) (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_2)) (not (= _let_3 _let_2)))))))))))) (let ((_let_3429 (forall ((BOUND_VARIABLE_1215396 tptp.num) (BOUND_VARIABLE_1215397 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 tptp.one)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4247 k_4246 BOUND_VARIABLE_1215396))))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4688 BOUND_VARIABLE_1215397)))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4687 BOUND_VARIABLE_1215397)))) (let ((_let_5 (= _let_2 _let_4))) (= (ho_4310 (ho_5968 k_5971 BOUND_VARIABLE_1215396) BOUND_VARIABLE_1215397) (and (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_4)) (not _let_5)) _let_5) (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_2)) (not (= _let_3 _let_2)))))))))))) (let ((_let_3430 (forall ((BOUND_VARIABLE_1215329 tptp.num) (BOUND_VARIABLE_1215330 tptp.num) (BOUND_VARIABLE_1215331 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 BOUND_VARIABLE_1215329)) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4247 k_4246 BOUND_VARIABLE_1215330))))) (let ((_let_3 (ho_4251 k_4250 (ho_4315 k_4690 BOUND_VARIABLE_1215331)))) (let ((_let_4 (ho_4251 k_4250 (ho_4315 k_4689 BOUND_VARIABLE_1215331)))) (let ((_let_5 (= _let_2 _let_4))) (= (ho_4310 (ho_5968 (ho_5970 k_5972 BOUND_VARIABLE_1215329) BOUND_VARIABLE_1215330) BOUND_VARIABLE_1215331) (and (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) _let_4)) (not _let_5)) _let_5) (= _let_3 (ho_4258 (ho_4265 k_4349 _let_3) _let_2)) (not (= _let_3 _let_2)))))))))))) (let ((_let_3431 (forall ((BOUND_VARIABLE_1215258 tptp.nat) (BOUND_VARIABLE_1215259 tptp.nat) (BOUND_VARIABLE_1215260 tptp.int)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (let ((_let_4 (ho_4272 k_4271 k_4270))) (let ((_let_5 (ho_4258 (ho_4265 k_5943 (ho_4258 (ho_4273 _let_4 BOUND_VARIABLE_1215258) _let_3)) (ho_4258 (ho_4273 _let_4 BOUND_VARIABLE_1215259) _let_3)))) (let ((_let_6 (ho_4251 k_4250 (ho_4315 k_4692 BOUND_VARIABLE_1215260)))) (let ((_let_7 (ho_4251 k_4250 (ho_4315 k_4691 BOUND_VARIABLE_1215260)))) (let ((_let_8 (= _let_5 _let_7))) (= (ho_4310 (ho_5920 (ho_5945 k_5973 BOUND_VARIABLE_1215258) BOUND_VARIABLE_1215259) BOUND_VARIABLE_1215260) (and (or (and (= _let_5 (ho_4258 (ho_4265 k_4349 _let_5) _let_7)) (not _let_8)) _let_8) (= _let_6 (ho_4258 (ho_4265 k_4349 _let_6) _let_5)) (not (= _let_6 _let_5))))))))))))))) (let ((_let_3432 (forall ((BOUND_VARIABLE_1215224 tptp.complex) (BOUND_VARIABLE_1215225 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1215225 _let_2))) (= (ho_4351 (ho_5659 k_5974 BOUND_VARIABLE_1215224) BOUND_VARIABLE_1215225) (and (= (ho_4703 k_5657 BOUND_VARIABLE_1215224) (ho_4771 k_4772 BOUND_VARIABLE_1215225)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1215225)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1215225 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215225) _let_3)) (not (= BOUND_VARIABLE_1215225 _let_3))))))))))) (let ((_let_3433 (forall ((BOUND_VARIABLE_1215190 tptp.complex) (BOUND_VARIABLE_1215191 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1215191 _let_2))) (= (ho_4351 (ho_5659 k_5975 BOUND_VARIABLE_1215190) BOUND_VARIABLE_1215191) (and (= (ho_4703 k_5657 BOUND_VARIABLE_1215190) (ho_4771 k_4772 BOUND_VARIABLE_1215191)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1215191)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1215191 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215191) _let_3)) (not (= BOUND_VARIABLE_1215191 _let_3))))))))))) (let ((_let_3434 (forall ((BOUND_VARIABLE_1215156 tptp.complex) (BOUND_VARIABLE_1215157 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4275) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))) (ho_4506 k_4505 k_4504)))) (let ((_let_3 (ho_4258 (ho_4257 _let_1 k_4248) _let_2))) (let ((_let_4 (= BOUND_VARIABLE_1215157 _let_2))) (= (ho_4351 (ho_5659 k_5976 BOUND_VARIABLE_1215156) BOUND_VARIABLE_1215157) (and (= (ho_4703 k_5657 BOUND_VARIABLE_1215156) (ho_4771 k_4772 BOUND_VARIABLE_1215157)) (or (and (= _let_2 (ho_4258 (ho_4265 k_4349 _let_2) BOUND_VARIABLE_1215157)) (not _let_4)) _let_4) (= BOUND_VARIABLE_1215157 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215157) _let_3)) (not (= BOUND_VARIABLE_1215157 _let_3))))))))))) (let ((_let_3435 (forall ((BOUND_VARIABLE_1215122 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504)))) (let ((_let_5 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1215122 _let_4))) (= (ho_4351 k_5977 BOUND_VARIABLE_1215122) (and (= (ho_4703 k_5657 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_3 _let_4) (ho_4258 (ho_4257 _let_2 k_4274) _let_1)))) (ho_4771 k_4772 BOUND_VARIABLE_1215122)) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1215122)) (not _let_6)) _let_6) (= BOUND_VARIABLE_1215122 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215122) _let_5)) (not (= BOUND_VARIABLE_1215122 _let_5))))))))))))) (let ((_let_3436 (forall ((BOUND_VARIABLE_1215088 tptp.real)) (let ((_let_1 (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4275))) (let ((_let_4 (ho_4258 (ho_4265 _let_3 _let_1) (ho_4506 k_4505 k_4504)))) (let ((_let_5 (ho_4258 (ho_4257 _let_2 k_4248) _let_4))) (let ((_let_6 (= BOUND_VARIABLE_1215088 _let_4))) (= (ho_4351 k_5978 BOUND_VARIABLE_1215088) (and (= (ho_4703 k_5657 (ho_4703 k_4702 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_3 _let_4) (ho_4258 (ho_4257 _let_2 k_4274) _let_1))))) (ho_4771 k_4772 BOUND_VARIABLE_1215088)) (or (and (= _let_4 (ho_4258 (ho_4265 k_4349 _let_4) BOUND_VARIABLE_1215088)) (not _let_6)) _let_6) (= BOUND_VARIABLE_1215088 (ho_4258 (ho_4265 k_4349 BOUND_VARIABLE_1215088) _let_5)) (not (= BOUND_VARIABLE_1215088 _let_5))))))))))))) (let ((_let_3437 (forall ((BOUND_VARIABLE_1215031 tptp.real) (BOUND_VARIABLE_1215032 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4247 k_4246 _let_3))) (let ((_let_5 (ho_4257 _let_1 k_4274))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_7 (ho_4264 _let_6 k_4275))) (let ((_let_8 (ho_4264 _let_6 k_4259))) (let ((_let_9 (ho_4247 k_4246 tptp.one))) (let ((_let_10 (ho_4258 _let_2 _let_9))) (let ((_let_11 (ho_4258 (ho_4265 _let_8 _let_9) _let_10))) (let ((_let_12 (ho_4196 k_4195 tptp.one))) (let ((_let_13 (ho_4213 k_4212 _let_12))) (let ((_let_14 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (let ((_let_15 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_12)))) (let ((_let_16 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_5979 BOUND_VARIABLE_1215031) BOUND_VARIABLE_1215032) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1215032 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_11) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_10) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1215032) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_16 (ho_4216 (ho_4215 k_4221 _let_13) _let_14)) _let_15)) (ho_4209 (ho_4220 _let_16 _let_13) _let_15))))) _let_14))) (ho_4258 _let_5 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_14) BOUND_VARIABLE_1215032) _let_13)) _let_11))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 _let_4) (ho_4506 k_4505 k_4504))) (ho_4258 _let_5 _let_4))) (ho_4258 _let_2 BOUND_VARIABLE_1215031))) BOUND_VARIABLE_1215032)))))))))))))))))))))) (let ((_let_3438 (forall ((BOUND_VARIABLE_1214973 tptp.real) (BOUND_VARIABLE_1214974 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4247 k_4246 _let_3))) (let ((_let_5 (ho_4257 _let_1 k_4274))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_7 (ho_4264 _let_6 k_4275))) (let ((_let_8 (ho_4264 _let_6 k_4259))) (let ((_let_9 (ho_4247 k_4246 tptp.one))) (let ((_let_10 (ho_4258 _let_2 _let_9))) (let ((_let_11 (ho_4258 (ho_4265 _let_8 _let_9) _let_10))) (let ((_let_12 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (= (ho_4245 (ho_4244 k_5980 BOUND_VARIABLE_1214973) BOUND_VARIABLE_1214974) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214974 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_10) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1214974) _let_12))) (ho_4258 _let_5 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_12) BOUND_VARIABLE_1214974) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_11)))) _let_11)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 _let_4) (ho_4506 k_4505 k_4693))) (ho_4258 _let_5 _let_4))) (ho_4258 _let_2 BOUND_VARIABLE_1214973))) BOUND_VARIABLE_1214974)))))))))))))))))) (let ((_let_3439 (forall ((BOUND_VARIABLE_1214916 tptp.real) (BOUND_VARIABLE_1214917 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4247 k_4246 _let_3))) (let ((_let_5 (ho_4257 _let_1 k_4274))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_7 (ho_4264 _let_6 k_4275))) (let ((_let_8 (ho_4264 _let_6 k_4259))) (let ((_let_9 (ho_4247 k_4246 tptp.one))) (let ((_let_10 (ho_4258 _let_2 _let_9))) (let ((_let_11 (ho_4258 (ho_4265 _let_8 _let_9) _let_10))) (let ((_let_12 (ho_4196 k_4195 tptp.one))) (let ((_let_13 (ho_4213 k_4212 _let_12))) (let ((_let_14 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (let ((_let_15 (ho_4209 (ho_4211 k_4210 _let_12) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_12)))) (let ((_let_16 (ho_4219 k_4218 k_4217))) (= (ho_4245 (ho_4244 k_5981 BOUND_VARIABLE_1214916) BOUND_VARIABLE_1214917) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214917 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_11) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_10) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214917) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_16 (ho_4216 (ho_4215 k_4221 _let_13) _let_14)) _let_15)) (ho_4209 (ho_4220 _let_16 _let_13) _let_15))))) _let_14))) (ho_4258 _let_5 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_14) BOUND_VARIABLE_1214917) _let_13)) _let_11))))) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 _let_4) (ho_4506 k_4505 k_4504))) (ho_4258 _let_5 _let_4))) (ho_4258 _let_2 BOUND_VARIABLE_1214916))) BOUND_VARIABLE_1214917)))))))))))))))))))))) (let ((_let_3440 (forall ((BOUND_VARIABLE_1214858 tptp.real) (BOUND_VARIABLE_1214859 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4247 k_4246 _let_3))) (let ((_let_5 (ho_4257 _let_1 k_4274))) (let ((_let_6 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_7 (ho_4264 _let_6 k_4275))) (let ((_let_8 (ho_4264 _let_6 k_4259))) (let ((_let_9 (ho_4247 k_4246 tptp.one))) (let ((_let_10 (ho_4258 _let_2 _let_9))) (let ((_let_11 (ho_4258 (ho_4265 _let_8 _let_9) _let_10))) (let ((_let_12 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (= (ho_4245 (ho_4244 k_5982 BOUND_VARIABLE_1214858) BOUND_VARIABLE_1214859) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214859 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_10) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1214859) _let_12))) (ho_4258 _let_5 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_12) BOUND_VARIABLE_1214859) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_11)))) _let_11)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 _let_4) (ho_4506 k_4505 k_4694))) (ho_4258 _let_5 _let_4))) (ho_4258 _let_2 BOUND_VARIABLE_1214858))) BOUND_VARIABLE_1214859)))))))))))))))))) (let ((_let_3441 (forall ((BOUND_VARIABLE_1214807 tptp.real) (BOUND_VARIABLE_1214808 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5983 BOUND_VARIABLE_1214807) BOUND_VARIABLE_1214808) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214808 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214808) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1214808) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1214807) BOUND_VARIABLE_1214808))))))))))))))))) (let ((_let_3442 (forall ((BOUND_VARIABLE_1214761 tptp.real) (BOUND_VARIABLE_1214762 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5984 BOUND_VARIABLE_1214761) BOUND_VARIABLE_1214762) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214762 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1214762) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1214762) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1214761) BOUND_VARIABLE_1214762))))))))))))) (let ((_let_3443 (forall ((BOUND_VARIABLE_1214703 tptp.nat) (BOUND_VARIABLE_1214704 tptp.nat) (BOUND_VARIABLE_1214705 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1214703) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1214703) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1214704) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1214705 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_5985 BOUND_VARIABLE_1214703) BOUND_VARIABLE_1214704) BOUND_VARIABLE_1214705))))) (let ((_let_3444 (forall ((BOUND_VARIABLE_1214698 tptp.int)) (= BOUND_VARIABLE_1214698 (ho_4209 k_5986 BOUND_VARIABLE_1214698))))) (let ((_let_3445 (forall ((BOUND_VARIABLE_1214645 tptp.nat) (BOUND_VARIABLE_1214646 tptp.nat) (BOUND_VARIABLE_1214647 tptp.int)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1214645) _let_2))) (let ((_let_5 (ho_4636 (ho_4635 k_4634 _let_4) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 _let_4) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1214646) _let_2)))) _let_2)))) (or (not (= BOUND_VARIABLE_1214647 (ho_4335 (ho_4640 k_4639 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4638 k_4637 _let_5)))))))))))) (ho_4310 (ho_5920 (ho_5945 k_5987 BOUND_VARIABLE_1214645) BOUND_VARIABLE_1214646) BOUND_VARIABLE_1214647))))) (let ((_let_3446 (forall ((BOUND_VARIABLE_1214594 tptp.real) (BOUND_VARIABLE_1214595 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5988 BOUND_VARIABLE_1214594) BOUND_VARIABLE_1214595) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214595 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214595) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1214595) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1214594) BOUND_VARIABLE_1214595))))))))))))))))) (let ((_let_3447 (forall ((BOUND_VARIABLE_1214543 tptp.real) (BOUND_VARIABLE_1214544 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_5989 BOUND_VARIABLE_1214543) BOUND_VARIABLE_1214544) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1214544 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214544) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1214544) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1214543) BOUND_VARIABLE_1214544))))))))))))))))) (let ((_let_3448 (forall ((BOUND_VARIABLE_1214533 tptp.nat) (BOUND_VARIABLE_1214534 tptp.nat)) (= (ho_4288 (ho_4287 k_5990 BOUND_VARIABLE_1214533) BOUND_VARIABLE_1214534) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1214534)) (ho_4290 k_4289 BOUND_VARIABLE_1214533)))))) (let ((_let_3449 (forall ((BOUND_VARIABLE_1214516 tptp.nat) (BOUND_VARIABLE_1305904 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1305903 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1214519 tptp.nat)) (= (ho_4335 (ho_5994 (ho_5993 (ho_5992 k_5991 BOUND_VARIABLE_1214516) BOUND_VARIABLE_1305904) BOUND_VARIABLE_1305903) BOUND_VARIABLE_1214519) (ho_4209 (ho_4211 (ho_4593 k_4592 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1214519)) (ho_4290 k_4289 BOUND_VARIABLE_1214516))) (ho_4335 BOUND_VARIABLE_1305904 BOUND_VARIABLE_1214519)) (ho_4335 BOUND_VARIABLE_1305903 BOUND_VARIABLE_1214519)))))) (let ((_let_3450 (forall ((BOUND_VARIABLE_1214499 tptp.nat) (BOUND_VARIABLE_1214500 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214500)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214499) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_5995 BOUND_VARIABLE_1214499) BOUND_VARIABLE_1214500))))))))) (let ((_let_3451 (forall ((BOUND_VARIABLE_1305953 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1214471 tptp.nat) (BOUND_VARIABLE_1305948 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1214473 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 (ho_4593 k_4592 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1214473)) (ho_4290 k_4289 BOUND_VARIABLE_1214471))) (ho_4335 BOUND_VARIABLE_1305953 BOUND_VARIABLE_1214473)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1214471 BOUND_VARIABLE_1214473)) _let_1) (ho_4335 BOUND_VARIABLE_1305948 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214473) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4335 (ho_5994 (ho_5998 (ho_5997 k_5996 BOUND_VARIABLE_1305953) BOUND_VARIABLE_1214471) BOUND_VARIABLE_1305948) BOUND_VARIABLE_1214473))))))))) (let ((_let_3452 (forall ((BOUND_VARIABLE_1214460 tptp.nat) (BOUND_VARIABLE_1214461 tptp.nat)) (= (ho_4288 (ho_4287 k_5999 BOUND_VARIABLE_1214460) BOUND_VARIABLE_1214461) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214461)) (ho_4290 k_4289 BOUND_VARIABLE_1214460)))))) (let ((_let_3453 (forall ((BOUND_VARIABLE_1214443 tptp.nat) (BOUND_VARIABLE_1305998 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1305997 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1214446 tptp.nat)) (= (ho_4216 (ho_5088 (ho_5820 (ho_6001 k_6000 BOUND_VARIABLE_1214443) BOUND_VARIABLE_1305998) BOUND_VARIABLE_1305997) BOUND_VARIABLE_1214446) (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1214446)) (ho_4290 k_4289 BOUND_VARIABLE_1214443))) (ho_4216 BOUND_VARIABLE_1305998 BOUND_VARIABLE_1214446)) (ho_4216 BOUND_VARIABLE_1305997 BOUND_VARIABLE_1214446)))))) (let ((_let_3454 (forall ((BOUND_VARIABLE_1214426 tptp.nat) (BOUND_VARIABLE_1214427 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214427)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214426) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6002 BOUND_VARIABLE_1214426) BOUND_VARIABLE_1214427))))))))) (let ((_let_3455 (forall ((BOUND_VARIABLE_1306040 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1214398 tptp.nat) (BOUND_VARIABLE_1306035 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1214400 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1214400)) (ho_4290 k_4289 BOUND_VARIABLE_1214398))) (ho_4216 BOUND_VARIABLE_1306040 BOUND_VARIABLE_1214400)) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1214398 BOUND_VARIABLE_1214400)) _let_3) (ho_4216 BOUND_VARIABLE_1306035 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214400) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4216 (ho_5088 (ho_5087 (ho_5086 k_6003 BOUND_VARIABLE_1306040) BOUND_VARIABLE_1214398) BOUND_VARIABLE_1306035) BOUND_VARIABLE_1214400))))))))) (let ((_let_3456 (forall ((BOUND_VARIABLE_1214387 tptp.nat) (BOUND_VARIABLE_1214388 tptp.nat)) (= (ho_4288 (ho_4287 k_6004 BOUND_VARIABLE_1214387) BOUND_VARIABLE_1214388) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214388)) (ho_4290 k_4289 BOUND_VARIABLE_1214387)))))) (let ((_let_3457 (forall ((BOUND_VARIABLE_1214324 tptp.real) (BOUND_VARIABLE_1214325 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1214325))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_7 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 _let_6) _let_7))) (let ((_let_9 (ho_4264 _let_5 k_4275))) (= (ho_4245 (ho_4244 k_6007 BOUND_VARIABLE_1214324) BOUND_VARIABLE_1214325) (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 (ho_4258 (ho_4265 _let_9 _let_4) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1214325 _let_8)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4696 k_4695 BOUND_VARIABLE_1214324)) _let_8) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214325) _let_6)) _let_1)))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_7) BOUND_VARIABLE_1214325) _let_6)) (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_1) _let_3))))) _let_4)))))))))))))) (let ((_let_3458 (forall ((BOUND_VARIABLE_1214314 tptp.nat) (BOUND_VARIABLE_1214315 tptp.nat)) (= (ho_4288 (ho_4287 k_6008 BOUND_VARIABLE_1214314) BOUND_VARIABLE_1214315) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214315)) (ho_4290 k_4289 BOUND_VARIABLE_1214314)))))) (let ((_let_3459 (forall ((BOUND_VARIABLE_1214287 tptp.real) (BOUND_VARIABLE_1214288 tptp.nat) (BOUND_VARIABLE_1214289 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1214287) _let_4))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1214288) (ho_4258 (ho_4265 _let_6 _let_1) _let_4)))) BOUND_VARIABLE_1214289) (ho_4258 (ho_4273 (ho_4696 k_6009 BOUND_VARIABLE_1214287) BOUND_VARIABLE_1214288) BOUND_VARIABLE_1214289))))))))))) (let ((_let_3460 (forall ((BOUND_VARIABLE_1214223 tptp.rat) (BOUND_VARIABLE_1214224 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1214224))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4213 k_4212 _let_1))) (let ((_let_9 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_10 (ho_4216 (ho_4215 k_4221 _let_8) _let_9))) (let ((_let_11 (ho_4447 _let_7 k_4697))) (= (ho_4316 (ho_4799 k_6012 BOUND_VARIABLE_1214223) BOUND_VARIABLE_1214224) (ho_4442 (ho_4448 _let_11 (ho_4442 (ho_4448 _let_11 (ho_4442 (ho_4448 _let_11 _let_6) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1214224 _let_10)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4699 k_4698 BOUND_VARIABLE_1214223)) _let_10) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214224) _let_8)) _let_3)))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_9) BOUND_VARIABLE_1214224) _let_8)) (ho_4442 (ho_4448 (ho_4447 _let_7 k_4443) _let_3) _let_5))))) _let_6)))))))))))))))) (let ((_let_3461 (forall ((BOUND_VARIABLE_1214213 tptp.nat) (BOUND_VARIABLE_1214214 tptp.nat)) (= (ho_4288 (ho_4287 k_6013 BOUND_VARIABLE_1214213) BOUND_VARIABLE_1214214) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214214)) (ho_4290 k_4289 BOUND_VARIABLE_1214213)))))) (let ((_let_3462 (forall ((BOUND_VARIABLE_1214186 tptp.rat) (BOUND_VARIABLE_1214187 tptp.nat) (BOUND_VARIABLE_1214188 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1214186) _let_6))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1214187) (ho_4442 (ho_4448 _let_8 _let_3) _let_6)))) BOUND_VARIABLE_1214188) (ho_4442 (ho_4458 (ho_4699 k_6014 BOUND_VARIABLE_1214186) BOUND_VARIABLE_1214187) BOUND_VARIABLE_1214188))))))))))))) (let ((_let_3463 (forall ((BOUND_VARIABLE_1214102 tptp.complex) (BOUND_VARIABLE_1214103 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 _let_1)) BOUND_VARIABLE_1214103))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (let ((_let_5 (ho_4767 k_6015 BOUND_VARIABLE_1214103))) (let ((_let_6 (ho_4769 k_4768 _let_5))) (let ((_let_7 (ho_4769 k_4773 _let_5))) (let ((_let_8 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_9 (ho_4263 (ho_4262 k_4261 k_4252) _let_8))) (let ((_let_10 (ho_4257 _let_8 k_4274))) (let ((_let_11 (ho_4258 _let_10 (ho_4258 (ho_4265 (ho_4264 _let_9 k_4259) (ho_4245 (ho_4244 k_4243 _let_7) _let_4)) (ho_4245 (ho_4244 k_4243 _let_6) _let_4))))) (let ((_let_12 (ho_4264 _let_9 k_4275))) (let ((_let_13 (ho_4247 k_4246 _let_3))) (let ((_let_14 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_15 (ho_4216 (ho_4215 k_4221 _let_14) _let_4))) (= (ho_4767 (ho_4766 k_6018 BOUND_VARIABLE_1214102) BOUND_VARIABLE_1214103) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 _let_2) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1214103 _let_15)) _let_1) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4712 k_4711 BOUND_VARIABLE_1214102)) _let_15) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214103) _let_14)) _let_1)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_12 _let_7) _let_11))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_12 (ho_4258 (ho_4265 _let_12 _let_13) (ho_4506 k_4505 k_4504))) (ho_4258 _let_10 _let_13)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_12 (ho_4258 (ho_4257 _let_8 k_4248) _let_6)) _let_11)))))) _let_2)))))))))))))))))))) (let ((_let_3464 (forall ((BOUND_VARIABLE_1214092 tptp.nat) (BOUND_VARIABLE_1214093 tptp.nat)) (= (ho_4288 (ho_4287 k_6019 BOUND_VARIABLE_1214092) BOUND_VARIABLE_1214093) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1214093)) (ho_4290 k_4289 BOUND_VARIABLE_1214092)))))) (let ((_let_3465 (forall ((BOUND_VARIABLE_1214069 tptp.complex) (BOUND_VARIABLE_1214070 tptp.nat) (BOUND_VARIABLE_1214071 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1214069) _let_2))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1214070) (ho_4703 (ho_4705 k_4704 _let_1) _let_2)))) BOUND_VARIABLE_1214071) (ho_4703 (ho_4709 (ho_4712 k_6020 BOUND_VARIABLE_1214069) BOUND_VARIABLE_1214070) BOUND_VARIABLE_1214071))))))) (let ((_let_3466 (forall ((BOUND_VARIABLE_1214002 tptp.real) (BOUND_VARIABLE_1214003 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_6 (ho_4216 (ho_4215 k_4221 _let_4) _let_5))) (= (ho_4245 (ho_4244 k_6021 BOUND_VARIABLE_1214002) BOUND_VARIABLE_1214003) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1214003 _let_6)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4715 (ho_4714 k_4713 BOUND_VARIABLE_1214002) BOUND_VARIABLE_1214003)) _let_6) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1214003) _let_4)) _let_1))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_5) BOUND_VARIABLE_1214003) _let_4)) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))))))))))))) (let ((_let_3467 (forall ((BOUND_VARIABLE_1213934 tptp.rat) (BOUND_VARIABLE_1213935 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4213 k_4212 _let_1))) (let ((_let_7 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_8 (ho_4216 (ho_4215 k_4221 _let_6) _let_7))) (= (ho_4316 (ho_4799 k_6022 BOUND_VARIABLE_1213934) BOUND_VARIABLE_1213935) (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1213935 _let_8)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4718 (ho_4717 k_4716 BOUND_VARIABLE_1213934) BOUND_VARIABLE_1213935)) _let_8) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213935) _let_6)) _let_3))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_7) BOUND_VARIABLE_1213935) _let_6)) (ho_4442 (ho_4448 (ho_4447 _let_5 k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))))))))))))))) (let ((_let_3468 (forall ((BOUND_VARIABLE_1213844 tptp.complex) (BOUND_VARIABLE_1213845 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 k_6015 BOUND_VARIABLE_1213845))) (let ((_let_4 (ho_4769 k_4768 _let_3))) (let ((_let_5 (ho_4769 k_4773 _let_3))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4257 _let_6 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) (ho_4245 (ho_4244 k_4243 _let_5) _let_2)) (ho_4245 (ho_4244 k_4243 _let_4) _let_2))))) (let ((_let_10 (ho_4264 _let_7 k_4275))) (let ((_let_11 (ho_4247 k_4246 _let_1))) (let ((_let_12 (ho_4701 k_4700 tptp.one))) (let ((_let_13 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_14 (ho_4216 (ho_4215 k_4221 _let_13) _let_2))) (= (ho_4767 (ho_4766 k_6023 BOUND_VARIABLE_1213844) BOUND_VARIABLE_1213845) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1213845 _let_14)) _let_12) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4721 (ho_4720 k_4719 BOUND_VARIABLE_1213844) BOUND_VARIABLE_1213845)) _let_14) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213845) _let_13)) _let_12))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 _let_5) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4257 _let_6 k_4248) _let_4)) _let_9))))))))))))))))))))))) (let ((_let_3469 (forall ((BOUND_VARIABLE_1213824 tptp.int) (BOUND_VARIABLE_1213825 tptp.nat) (BOUND_VARIABLE_1213826 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1213824) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1213825) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) BOUND_VARIABLE_1213826) (ho_4209 (ho_4220 (ho_4723 k_6024 BOUND_VARIABLE_1213824) BOUND_VARIABLE_1213825) BOUND_VARIABLE_1213826)))))) (let ((_let_3470 (forall ((BOUND_VARIABLE_1213806 tptp.int) (BOUND_VARIABLE_1213807 tptp.nat) (BOUND_VARIABLE_1213808 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1213806) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213807) BOUND_VARIABLE_1213808)) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (ho_4335 (ho_4726 (ho_4725 k_6025 BOUND_VARIABLE_1213806) BOUND_VARIABLE_1213807) BOUND_VARIABLE_1213808)))))) (let ((_let_3471 (forall ((BOUND_VARIABLE_1213764 tptp.nat) (BOUND_VARIABLE_1213765 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1213764) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1213765 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6026 BOUND_VARIABLE_1213764) BOUND_VARIABLE_1213765))))) (let ((_let_3472 (forall ((BOUND_VARIABLE_1213723 tptp.nat) (BOUND_VARIABLE_1213724 tptp.nat) (BOUND_VARIABLE_1213725 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213723) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1213724) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213725) _let_2))) (ho_4216 (ho_4215 (ho_4269 k_6027 BOUND_VARIABLE_1213723) BOUND_VARIABLE_1213724) BOUND_VARIABLE_1213725)))))))) (let ((_let_3473 (forall ((BOUND_VARIABLE_1213694 tptp.nat) (BOUND_VARIABLE_1213695 tptp.nat) (BOUND_VARIABLE_1213696 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213694) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213695) BOUND_VARIABLE_1213696)) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2))) (ho_4216 (ho_4215 (ho_4269 k_6028 BOUND_VARIABLE_1213694) BOUND_VARIABLE_1213695) BOUND_VARIABLE_1213696)))))))) (let ((_let_3474 (forall ((BOUND_VARIABLE_1213652 tptp.nat) (BOUND_VARIABLE_1213653 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1213652) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1213653 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6029 BOUND_VARIABLE_1213652) BOUND_VARIABLE_1213653))))) (let ((_let_3475 (forall ((BOUND_VARIABLE_1213631 tptp.rat) (BOUND_VARIABLE_1213632 tptp.nat) (BOUND_VARIABLE_1213633 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1213631) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1213632) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1213633) (ho_4442 (ho_4458 (ho_4699 k_6030 BOUND_VARIABLE_1213631) BOUND_VARIABLE_1213632) BOUND_VARIABLE_1213633))))))))))) (let ((_let_3476 (forall ((BOUND_VARIABLE_1213612 tptp.rat) (BOUND_VARIABLE_1213613 tptp.nat) (BOUND_VARIABLE_1213614 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443))) (= (ho_4442 (ho_4448 _let_5 BOUND_VARIABLE_1213612) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213613) BOUND_VARIABLE_1213614)) (ho_4442 (ho_4448 _let_5 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (ho_4316 (ho_4338 (ho_4736 k_6031 BOUND_VARIABLE_1213612) BOUND_VARIABLE_1213613) BOUND_VARIABLE_1213614)))))))))) (let ((_let_3477 (forall ((BOUND_VARIABLE_1213570 tptp.nat) (BOUND_VARIABLE_1213571 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1213570) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1213571 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6032 BOUND_VARIABLE_1213570) BOUND_VARIABLE_1213571))))) (let ((_let_3478 (forall ((BOUND_VARIABLE_1213549 tptp.real) (BOUND_VARIABLE_1213550 tptp.nat) (BOUND_VARIABLE_1213551 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1213549) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1213550) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1213551) (ho_4258 (ho_4273 (ho_4696 k_6033 BOUND_VARIABLE_1213549) BOUND_VARIABLE_1213550) BOUND_VARIABLE_1213551))))))))) (let ((_let_3479 (forall ((BOUND_VARIABLE_1213530 tptp.real) (BOUND_VARIABLE_1213531 tptp.nat) (BOUND_VARIABLE_1213532 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (= (ho_4258 (ho_4265 _let_3 BOUND_VARIABLE_1213530) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1213531) BOUND_VARIABLE_1213532)) (ho_4258 (ho_4265 _let_3 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (ho_4245 (ho_4487 (ho_4740 k_6034 BOUND_VARIABLE_1213530) BOUND_VARIABLE_1213531) BOUND_VARIABLE_1213532)))))))) (let ((_let_3480 (forall ((BOUND_VARIABLE_1213488 tptp.nat) (BOUND_VARIABLE_1213489 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1213488) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1213489 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6035 BOUND_VARIABLE_1213488) BOUND_VARIABLE_1213489))))) (let ((_let_3481 (forall ((BOUND_VARIABLE_1213465 tptp.rat) (BOUND_VARIABLE_1213466 tptp.nat) (BOUND_VARIABLE_1213467 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1213465)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1213466) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1213467) (ho_4442 (ho_4458 (ho_4699 k_6036 BOUND_VARIABLE_1213465) BOUND_VARIABLE_1213466) BOUND_VARIABLE_1213467)))))))))))) (let ((_let_3482 (forall ((BOUND_VARIABLE_1213438 tptp.rat) (BOUND_VARIABLE_1213439 tptp.nat) (BOUND_VARIABLE_1213440 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1213438) _let_6))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1213439) (ho_4442 (ho_4448 _let_8 _let_3) _let_6)))) BOUND_VARIABLE_1213440) (ho_4442 (ho_4458 (ho_4699 k_6037 BOUND_VARIABLE_1213438) BOUND_VARIABLE_1213439) BOUND_VARIABLE_1213440))))))))))))) (let ((_let_3483 (forall ((BOUND_VARIABLE_1213415 tptp.real) (BOUND_VARIABLE_1213416 tptp.nat) (BOUND_VARIABLE_1213417 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1213415)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1213416) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1213417) (ho_4258 (ho_4273 (ho_4696 k_6038 BOUND_VARIABLE_1213415) BOUND_VARIABLE_1213416) BOUND_VARIABLE_1213417)))))))))) (let ((_let_3484 (forall ((BOUND_VARIABLE_1213388 tptp.real) (BOUND_VARIABLE_1213389 tptp.nat) (BOUND_VARIABLE_1213390 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1213388) _let_4))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1213389) (ho_4258 (ho_4265 _let_6 _let_1) _let_4)))) BOUND_VARIABLE_1213390) (ho_4258 (ho_4273 (ho_4696 k_6039 BOUND_VARIABLE_1213388) BOUND_VARIABLE_1213389) BOUND_VARIABLE_1213390))))))))))) (let ((_let_3485 (forall ((BOUND_VARIABLE_1213367 tptp.complex) (BOUND_VARIABLE_1213368 tptp.nat) (BOUND_VARIABLE_1213369 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1213367)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1213368) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1213369) (ho_4703 (ho_4709 (ho_4712 k_6040 BOUND_VARIABLE_1213367) BOUND_VARIABLE_1213368) BOUND_VARIABLE_1213369)))))) (let ((_let_3486 (forall ((BOUND_VARIABLE_1213344 tptp.complex) (BOUND_VARIABLE_1213345 tptp.nat) (BOUND_VARIABLE_1213346 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1213344) _let_2))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1213345) (ho_4703 (ho_4705 k_4704 _let_1) _let_2)))) BOUND_VARIABLE_1213346) (ho_4703 (ho_4709 (ho_4712 k_6041 BOUND_VARIABLE_1213344) BOUND_VARIABLE_1213345) BOUND_VARIABLE_1213346))))))) (let ((_let_3487 (forall ((BOUND_VARIABLE_1213312 tptp.nat) (BOUND_VARIABLE_1213313 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213313)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213312) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6042 BOUND_VARIABLE_1213312) BOUND_VARIABLE_1213313)))))))) (let ((_let_3488 (forall ((BOUND_VARIABLE_1306737 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1213279 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213279) _let_2))))) (= (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1306737 _let_4)) (ho_4335 BOUND_VARIABLE_1306737 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4335 (ho_5994 k_6043 BOUND_VARIABLE_1306737) BOUND_VARIABLE_1213279))))))))) (let ((_let_3489 (forall ((BOUND_VARIABLE_1213268 tptp.nat) (BOUND_VARIABLE_1213269 tptp.nat)) (= (ho_4288 (ho_4287 k_6044 BOUND_VARIABLE_1213268) BOUND_VARIABLE_1213269) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213269)) (ho_4290 k_4289 BOUND_VARIABLE_1213268)))))) (let ((_let_3490 (forall ((BOUND_VARIABLE_1213236 tptp.nat) (BOUND_VARIABLE_1213237 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213237)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213236) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6045 BOUND_VARIABLE_1213236) BOUND_VARIABLE_1213237)))))))) (let ((_let_3491 (forall ((BOUND_VARIABLE_1306790 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1213193 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213193) _let_2))))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1306790 _let_4)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1306790 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) _let_2))) (ho_4216 (ho_5088 k_6046 BOUND_VARIABLE_1306790) BOUND_VARIABLE_1213193))))))))) (let ((_let_3492 (forall ((BOUND_VARIABLE_1213182 tptp.nat) (BOUND_VARIABLE_1213183 tptp.nat)) (= (ho_4288 (ho_4287 k_6047 BOUND_VARIABLE_1213182) BOUND_VARIABLE_1213183) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213183)) (ho_4290 k_4289 BOUND_VARIABLE_1213182)))))) (let ((_let_3493 (forall ((BOUND_VARIABLE_1213150 tptp.nat) (BOUND_VARIABLE_1213151 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213151)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213150) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6048 BOUND_VARIABLE_1213150) BOUND_VARIABLE_1213151)))))))) (let ((_let_3494 (forall ((BOUND_VARIABLE_1306848 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1213117 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213117) _let_2))))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1306848 _let_4)) (ho_4316 BOUND_VARIABLE_1306848 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4316 (ho_4249 k_6049 BOUND_VARIABLE_1306848) BOUND_VARIABLE_1213117))))))))) (let ((_let_3495 (forall ((BOUND_VARIABLE_1213106 tptp.nat) (BOUND_VARIABLE_1213107 tptp.nat)) (= (ho_4288 (ho_4287 k_6050 BOUND_VARIABLE_1213106) BOUND_VARIABLE_1213107) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213107)) (ho_4290 k_4289 BOUND_VARIABLE_1213106)))))) (let ((_let_3496 (forall ((BOUND_VARIABLE_1213074 tptp.nat) (BOUND_VARIABLE_1213075 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213075)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213074) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6051 BOUND_VARIABLE_1213074) BOUND_VARIABLE_1213075)))))))) (let ((_let_3497 (forall ((BOUND_VARIABLE_1306901 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1213041 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1213041) _let_2))))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1306901 _let_4)) (ho_4245 BOUND_VARIABLE_1306901 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4245 (ho_4473 k_6052 BOUND_VARIABLE_1306901) BOUND_VARIABLE_1213041))))))))) (let ((_let_3498 (forall ((BOUND_VARIABLE_1213030 tptp.nat) (BOUND_VARIABLE_1213031 tptp.nat)) (= (ho_4288 (ho_4287 k_6053 BOUND_VARIABLE_1213030) BOUND_VARIABLE_1213031) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1213031)) (ho_4290 k_4289 BOUND_VARIABLE_1213030)))))) (let ((_let_3499 (forall ((BOUND_VARIABLE_1212959 tptp.nat) (BOUND_VARIABLE_1212960 tptp.nat) (BOUND_VARIABLE_1212961 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212959) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212960) _let_2)))) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1212961 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6054 BOUND_VARIABLE_1212959) BOUND_VARIABLE_1212960) BOUND_VARIABLE_1212961))))) (let ((_let_3500 (forall ((BOUND_VARIABLE_1306974 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1212926 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212926) _let_2))))) (= (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1306974 _let_4)) (ho_4335 BOUND_VARIABLE_1306974 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4335 (ho_5994 k_6055 BOUND_VARIABLE_1306974) BOUND_VARIABLE_1212926))))))))) (let ((_let_3501 (forall ((BOUND_VARIABLE_1212881 tptp.nat) (BOUND_VARIABLE_1212882 tptp.nat) (BOUND_VARIABLE_1212883 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1212881) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212882) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1212883 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6056 BOUND_VARIABLE_1212881) BOUND_VARIABLE_1212882) BOUND_VARIABLE_1212883))))) (let ((_let_3502 (forall ((BOUND_VARIABLE_1212810 tptp.nat) (BOUND_VARIABLE_1212811 tptp.nat) (BOUND_VARIABLE_1212812 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212810) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212811) _let_2)))) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1212812 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6057 BOUND_VARIABLE_1212810) BOUND_VARIABLE_1212811) BOUND_VARIABLE_1212812))))) (let ((_let_3503 (forall ((BOUND_VARIABLE_1307063 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1212767 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212767) _let_2))))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1307063 _let_4)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1307063 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) _let_2))) (ho_4216 (ho_5088 k_6058 BOUND_VARIABLE_1307063) BOUND_VARIABLE_1212767))))))))) (let ((_let_3504 (forall ((BOUND_VARIABLE_1212722 tptp.nat) (BOUND_VARIABLE_1212723 tptp.nat) (BOUND_VARIABLE_1212724 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1212722) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212723) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1212724 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6059 BOUND_VARIABLE_1212722) BOUND_VARIABLE_1212723) BOUND_VARIABLE_1212724))))) (let ((_let_3505 (forall ((BOUND_VARIABLE_1212651 tptp.nat) (BOUND_VARIABLE_1212652 tptp.nat) (BOUND_VARIABLE_1212653 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212651) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212652) _let_2)))) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1212653 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6060 BOUND_VARIABLE_1212651) BOUND_VARIABLE_1212652) BOUND_VARIABLE_1212653))))) (let ((_let_3506 (forall ((BOUND_VARIABLE_1307157 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1212618 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212618) _let_2))))) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1307157 _let_4)) (ho_4316 BOUND_VARIABLE_1307157 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4316 (ho_4249 k_6061 BOUND_VARIABLE_1307157) BOUND_VARIABLE_1212618))))))))) (let ((_let_3507 (forall ((BOUND_VARIABLE_1212573 tptp.nat) (BOUND_VARIABLE_1212574 tptp.nat) (BOUND_VARIABLE_1212575 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1212573) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212574) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1212575 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6062 BOUND_VARIABLE_1212573) BOUND_VARIABLE_1212574) BOUND_VARIABLE_1212575))))) (let ((_let_3508 (forall ((BOUND_VARIABLE_1212502 tptp.nat) (BOUND_VARIABLE_1212503 tptp.nat) (BOUND_VARIABLE_1212504 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212502) _let_2)))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212503) _let_2)))) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1212504 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6063 BOUND_VARIABLE_1212502) BOUND_VARIABLE_1212503) BOUND_VARIABLE_1212504))))) (let ((_let_3509 (forall ((BOUND_VARIABLE_1307246 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1212469 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212469) _let_2))))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1307246 _let_4)) (ho_4245 BOUND_VARIABLE_1307246 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4245 (ho_4473 k_6064 BOUND_VARIABLE_1307246) BOUND_VARIABLE_1212469))))))))) (let ((_let_3510 (forall ((BOUND_VARIABLE_1212424 tptp.nat) (BOUND_VARIABLE_1212425 tptp.nat) (BOUND_VARIABLE_1212426 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1212424) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212425) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1212426 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6065 BOUND_VARIABLE_1212424) BOUND_VARIABLE_1212425) BOUND_VARIABLE_1212426))))) (let ((_let_3511 (forall ((BOUND_VARIABLE_1212399 tptp.rat) (BOUND_VARIABLE_1212400 tptp.nat) (BOUND_VARIABLE_1212401 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 _let_5 BOUND_VARIABLE_1212399))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1212400) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1212401) (ho_4442 (ho_4458 (ho_4699 k_6066 BOUND_VARIABLE_1212399) BOUND_VARIABLE_1212400) BOUND_VARIABLE_1212401)))))))))))) (let ((_let_3512 (forall ((BOUND_VARIABLE_1212363 tptp.rat) (BOUND_VARIABLE_1212364 tptp.nat) (BOUND_VARIABLE_1212365 tptp.nat) (BOUND_VARIABLE_1212366 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (let ((_let_9 (ho_4442 (ho_4448 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1212363) (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1212364) _let_9))) _let_6))) (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1212365) _let_9))) BOUND_VARIABLE_1212366) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_6067 BOUND_VARIABLE_1212363) BOUND_VARIABLE_1212364) BOUND_VARIABLE_1212365) BOUND_VARIABLE_1212366))))))))))))))) (let ((_let_3513 (forall ((BOUND_VARIABLE_1212338 tptp.real) (BOUND_VARIABLE_1212339 tptp.nat) (BOUND_VARIABLE_1212340 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 _let_3 BOUND_VARIABLE_1212338))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1212339) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1212340) (ho_4258 (ho_4273 (ho_4696 k_6068 BOUND_VARIABLE_1212338) BOUND_VARIABLE_1212339) BOUND_VARIABLE_1212340)))))))))) (let ((_let_3514 (forall ((BOUND_VARIABLE_1212302 tptp.real) (BOUND_VARIABLE_1212303 tptp.nat) (BOUND_VARIABLE_1212304 tptp.nat) (BOUND_VARIABLE_1212305 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 _let_1) _let_4))) (let ((_let_8 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1212302) (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1212303) _let_7))) _let_4))) (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1212304) _let_7))) BOUND_VARIABLE_1212305) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_6069 BOUND_VARIABLE_1212302) BOUND_VARIABLE_1212303) BOUND_VARIABLE_1212304) BOUND_VARIABLE_1212305))))))))))))) (let ((_let_3515 (forall ((BOUND_VARIABLE_1212280 tptp.complex) (BOUND_VARIABLE_1212281 tptp.nat) (BOUND_VARIABLE_1212282 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 k_4702 BOUND_VARIABLE_1212280))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1212281) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1212282) (ho_4703 (ho_4709 (ho_4712 k_6070 BOUND_VARIABLE_1212280) BOUND_VARIABLE_1212281) BOUND_VARIABLE_1212282)))))) (let ((_let_3516 (forall ((BOUND_VARIABLE_1212245 tptp.complex) (BOUND_VARIABLE_1212246 tptp.nat) (BOUND_VARIABLE_1212247 tptp.nat) (BOUND_VARIABLE_1212248 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (let ((_let_4 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1212245) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1212246) _let_3))) _let_2))) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1212247) _let_3))) BOUND_VARIABLE_1212248) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_6071 BOUND_VARIABLE_1212245) BOUND_VARIABLE_1212246) BOUND_VARIABLE_1212247) BOUND_VARIABLE_1212248))))))))) (let ((_let_3517 (forall ((BOUND_VARIABLE_1212240 tptp.nat)) (= BOUND_VARIABLE_1212240 (ho_4216 k_6072 BOUND_VARIABLE_1212240))))) (let ((_let_3518 (forall ((BOUND_VARIABLE_1212185 tptp.nat) (BOUND_VARIABLE_1212186 tptp.nat) (BOUND_VARIABLE_1212187 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212185) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1212186) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1212187 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6073 BOUND_VARIABLE_1212185) BOUND_VARIABLE_1212186) BOUND_VARIABLE_1212187))))) (let ((_let_3519 (forall ((BOUND_VARIABLE_1212148 tptp.int) (BOUND_VARIABLE_1212149 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4213 k_4212 _let_1))) (let ((_let_3 (ho_4216 (ho_4215 k_4221 _let_2) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4335 (ho_4334 k_6077 BOUND_VARIABLE_1212148) BOUND_VARIABLE_1212149) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1212149 _let_3)) _let_1) (ho_4209 (ho_4220 (ho_6076 (ho_6075 k_6074 (ho_4723 k_4722 BOUND_VARIABLE_1212148)) _let_3) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1212149) _let_2)) _let_1))))))))) (let ((_let_3520 (forall ((BOUND_VARIABLE_1212074 tptp.int) (BOUND_VARIABLE_1212075 tptp.nat)) (= (ho_6080 (ho_6079 k_6078 (ho_4726 (ho_4725 k_4724 BOUND_VARIABLE_1212074) BOUND_VARIABLE_1212075)) (ho_4516 k_4515 (ho_4287 k_4727 BOUND_VARIABLE_1212075))) (ho_4335 (ho_4334 k_6081 BOUND_VARIABLE_1212074) BOUND_VARIABLE_1212075))))) (let ((_let_3521 (forall ((BOUND_VARIABLE_1212025 tptp.nat) (BOUND_VARIABLE_1212026 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_2 (ho_4216 (ho_4215 k_4221 _let_1) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4216 (ho_4215 k_6082 BOUND_VARIABLE_1212025) BOUND_VARIABLE_1212026) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1212026 _let_2)) _let_1) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 (ho_4269 k_4731 BOUND_VARIABLE_1212025)) _let_2) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1212026) _let_1)) _let_1)))))))) (let ((_let_3522 (forall ((BOUND_VARIABLE_1211941 tptp.nat) (BOUND_VARIABLE_1211942 tptp.nat)) (= (ho_5346 (ho_6084 k_6083 (ho_4215 (ho_4269 k_4732 BOUND_VARIABLE_1211941) BOUND_VARIABLE_1211942)) (ho_4516 k_4515 (ho_4287 k_4733 BOUND_VARIABLE_1211942))) (ho_4216 (ho_4215 k_6085 BOUND_VARIABLE_1211941) BOUND_VARIABLE_1211942))))) (let ((_let_3523 (forall ((BOUND_VARIABLE_1211903 tptp.rat) (BOUND_VARIABLE_1211904 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4213 k_4212 _let_1))) (let ((_let_5 (ho_4216 (ho_4215 k_4221 _let_4) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4316 (ho_4799 k_6086 BOUND_VARIABLE_1211903) BOUND_VARIABLE_1211904) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1211904 _let_5)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4699 k_4734 BOUND_VARIABLE_1211903)) _let_5) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1211904) _let_4)) _let_3))))))))))) (let ((_let_3524 (forall ((BOUND_VARIABLE_1211829 tptp.rat) (BOUND_VARIABLE_1211830 tptp.nat)) (= (ho_6089 (ho_6088 k_6087 (ho_4338 (ho_4736 k_4735 BOUND_VARIABLE_1211829) BOUND_VARIABLE_1211830)) (ho_4516 k_4515 (ho_4287 k_4737 BOUND_VARIABLE_1211830))) (ho_4316 (ho_4799 k_6090 BOUND_VARIABLE_1211829) BOUND_VARIABLE_1211830))))) (let ((_let_3525 (forall ((BOUND_VARIABLE_1211792 tptp.real) (BOUND_VARIABLE_1211793 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_3 (ho_4216 (ho_4215 k_4221 _let_2) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4245 (ho_4244 k_6091 BOUND_VARIABLE_1211792) BOUND_VARIABLE_1211793) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1211793 _let_3)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4696 k_4738 BOUND_VARIABLE_1211792)) _let_3) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1211793) _let_2)) _let_1))))))))) (let ((_let_3526 (forall ((BOUND_VARIABLE_1211718 tptp.real) (BOUND_VARIABLE_1211719 tptp.nat)) (= (ho_4519 (ho_4518 k_6092 (ho_4487 (ho_4740 k_4739 BOUND_VARIABLE_1211718) BOUND_VARIABLE_1211719)) (ho_4516 k_4515 (ho_4287 k_4741 BOUND_VARIABLE_1211719))) (ho_4245 (ho_4244 k_6093 BOUND_VARIABLE_1211718) BOUND_VARIABLE_1211719))))) (let ((_let_3527 (forall ((BOUND_VARIABLE_1211698 tptp.int) (BOUND_VARIABLE_1211699 tptp.nat) (BOUND_VARIABLE_1211700 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1211698) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1211699) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))))) BOUND_VARIABLE_1211700) (ho_4209 (ho_4220 (ho_4723 k_6094 BOUND_VARIABLE_1211698) BOUND_VARIABLE_1211699) BOUND_VARIABLE_1211700)))))) (let ((_let_3528 (forall ((BOUND_VARIABLE_1211683 tptp.int) (BOUND_VARIABLE_1211684 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1211683) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1211684) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (ho_4335 (ho_4334 k_6095 BOUND_VARIABLE_1211683) BOUND_VARIABLE_1211684)))))) (let ((_let_3529 (forall ((BOUND_VARIABLE_1211641 tptp.nat) (BOUND_VARIABLE_1211642 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1211641) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1211642 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6096 BOUND_VARIABLE_1211641) BOUND_VARIABLE_1211642))))) (let ((_let_3530 (forall ((BOUND_VARIABLE_1211600 tptp.nat) (BOUND_VARIABLE_1211601 tptp.nat) (BOUND_VARIABLE_1211602 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1211600) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1211601) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1211602) _let_2))) (ho_4216 (ho_4215 (ho_4269 k_6097 BOUND_VARIABLE_1211600) BOUND_VARIABLE_1211601) BOUND_VARIABLE_1211602)))))))) (let ((_let_3531 (forall ((BOUND_VARIABLE_1211574 tptp.nat) (BOUND_VARIABLE_1211575 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1211574) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1211575) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2))) (ho_4216 (ho_4215 k_6098 BOUND_VARIABLE_1211574) BOUND_VARIABLE_1211575)))))))) (let ((_let_3532 (forall ((BOUND_VARIABLE_1211532 tptp.nat) (BOUND_VARIABLE_1211533 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1211532) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1211533 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6099 BOUND_VARIABLE_1211532) BOUND_VARIABLE_1211533))))) (let ((_let_3533 (forall ((BOUND_VARIABLE_1211511 tptp.rat) (BOUND_VARIABLE_1211512 tptp.nat) (BOUND_VARIABLE_1211513 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1211511) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1211512) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1211513) (ho_4442 (ho_4458 (ho_4699 k_6100 BOUND_VARIABLE_1211511) BOUND_VARIABLE_1211512) BOUND_VARIABLE_1211513))))))))))) (let ((_let_3534 (forall ((BOUND_VARIABLE_1211495 tptp.rat) (BOUND_VARIABLE_1211496 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443))) (= (ho_4442 (ho_4448 _let_5 BOUND_VARIABLE_1211495) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1211496) (ho_4442 (ho_4448 _let_5 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (ho_4316 (ho_4799 k_6101 BOUND_VARIABLE_1211495) BOUND_VARIABLE_1211496)))))))))) (let ((_let_3535 (forall ((BOUND_VARIABLE_1211453 tptp.nat) (BOUND_VARIABLE_1211454 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1211453) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1211454 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6102 BOUND_VARIABLE_1211453) BOUND_VARIABLE_1211454))))) (let ((_let_3536 (forall ((BOUND_VARIABLE_1211432 tptp.real) (BOUND_VARIABLE_1211433 tptp.nat) (BOUND_VARIABLE_1211434 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1211432) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1211433) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1211434) (ho_4258 (ho_4273 (ho_4696 k_6103 BOUND_VARIABLE_1211432) BOUND_VARIABLE_1211433) BOUND_VARIABLE_1211434))))))))) (let ((_let_3537 (forall ((BOUND_VARIABLE_1211416 tptp.real) (BOUND_VARIABLE_1211417 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (= (ho_4258 (ho_4265 _let_3 BOUND_VARIABLE_1211416) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1211417) (ho_4258 (ho_4265 _let_3 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (ho_4245 (ho_4244 k_6104 BOUND_VARIABLE_1211416) BOUND_VARIABLE_1211417)))))))) (let ((_let_3538 (forall ((BOUND_VARIABLE_1211374 tptp.nat) (BOUND_VARIABLE_1211375 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1211374) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1211375 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6105 BOUND_VARIABLE_1211374) BOUND_VARIABLE_1211375))))) (let ((_let_3539 (forall ((BOUND_VARIABLE_1211341 tptp.nat) (BOUND_VARIABLE_1211342 tptp.nat) (BOUND_VARIABLE_1211343 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (let ((_let_9 (ho_4442 (ho_4448 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1211341) _let_9))) _let_6))) (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1211342) _let_9))) BOUND_VARIABLE_1211343) (ho_4442 (ho_4458 (ho_4718 k_6106 BOUND_VARIABLE_1211341) BOUND_VARIABLE_1211342) BOUND_VARIABLE_1211343))))))))))))))) (let ((_let_3540 (forall ((BOUND_VARIABLE_1211308 tptp.nat) (BOUND_VARIABLE_1211309 tptp.nat) (BOUND_VARIABLE_1211310 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (let ((_let_9 (ho_4442 (ho_4448 _let_8 _let_3) _let_6))) (let ((_let_10 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1211308) _let_9))) _let_6))) (ho_4442 (ho_4458 _let_10 BOUND_VARIABLE_1211309) _let_9))) BOUND_VARIABLE_1211310) (ho_4442 (ho_4458 (ho_4718 k_6107 BOUND_VARIABLE_1211308) BOUND_VARIABLE_1211309) BOUND_VARIABLE_1211310))))))))))))))) (let ((_let_3541 (forall ((BOUND_VARIABLE_1211275 tptp.nat) (BOUND_VARIABLE_1211276 tptp.nat) (BOUND_VARIABLE_1211277 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 _let_1) _let_4))) (let ((_let_8 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1211275) _let_7))) _let_4))) (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1211276) _let_7))) BOUND_VARIABLE_1211277) (ho_4258 (ho_4273 (ho_4715 k_6108 BOUND_VARIABLE_1211275) BOUND_VARIABLE_1211276) BOUND_VARIABLE_1211277))))))))))))) (let ((_let_3542 (forall ((BOUND_VARIABLE_1211242 tptp.nat) (BOUND_VARIABLE_1211243 tptp.nat) (BOUND_VARIABLE_1211244 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 _let_1) _let_4))) (let ((_let_8 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1211242) _let_7))) _let_4))) (ho_4258 (ho_4273 _let_8 BOUND_VARIABLE_1211243) _let_7))) BOUND_VARIABLE_1211244) (ho_4258 (ho_4273 (ho_4715 k_6109 BOUND_VARIABLE_1211242) BOUND_VARIABLE_1211243) BOUND_VARIABLE_1211244))))))))))))) (let ((_let_3543 (forall ((BOUND_VARIABLE_1211209 tptp.nat) (BOUND_VARIABLE_1211210 tptp.nat) (BOUND_VARIABLE_1211211 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (let ((_let_4 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1211209) _let_3))) _let_2))) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1211210) _let_3))) BOUND_VARIABLE_1211211) (ho_4703 (ho_4709 (ho_4721 k_6110 BOUND_VARIABLE_1211209) BOUND_VARIABLE_1211210) BOUND_VARIABLE_1211211))))))))) (let ((_let_3544 (forall ((BOUND_VARIABLE_1211176 tptp.nat) (BOUND_VARIABLE_1211177 tptp.nat) (BOUND_VARIABLE_1211178 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (let ((_let_4 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1211176) _let_3))) _let_2))) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1211177) _let_3))) BOUND_VARIABLE_1211178) (ho_4703 (ho_4709 (ho_4721 k_6111 BOUND_VARIABLE_1211176) BOUND_VARIABLE_1211177) BOUND_VARIABLE_1211178))))))))) (let ((_let_3545 (forall ((BOUND_VARIABLE_1211116 tptp.rat) (BOUND_VARIABLE_1211117 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4213 k_4212 _let_1))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4216 (ho_4215 k_4221 _let_7) _let_8))) (let ((_let_10 (ho_4447 _let_6 k_4697))) (= (ho_4316 (ho_4799 k_6112 BOUND_VARIABLE_1211116) BOUND_VARIABLE_1211117) (ho_4442 (ho_4448 _let_10 (ho_4442 (ho_4448 _let_10 (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1211117)) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1211117 _let_9)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4699 k_4742 BOUND_VARIABLE_1211116)) _let_9) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1211117) _let_7)) _let_3)))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1211117) _let_7)) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) _let_5)))))))))))))))))) (let ((_let_3546 (forall ((BOUND_VARIABLE_1211037 tptp.rat) (BOUND_VARIABLE_1211038 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4213 k_4212 _let_1))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4216 (ho_4215 k_4221 _let_7) _let_8))) (let ((_let_10 (ho_4447 _let_6 k_4697))) (let ((_let_11 (ho_4448 _let_10 (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1211038)))) (= (ho_4316 (ho_4799 k_6113 BOUND_VARIABLE_1211037) BOUND_VARIABLE_1211038) (ho_4442 _let_11 (ho_4442 (ho_4448 _let_10 (ho_4442 _let_11 (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1211038 _let_9)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4699 (ho_4744 k_4743 BOUND_VARIABLE_1211038) BOUND_VARIABLE_1211037)) _let_9) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1211038) _let_7)) _let_3)))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1211038) _let_7)) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) _let_5)))))))))))))))))))) (let ((_let_3547 (forall ((BOUND_VARIABLE_1210978 tptp.real) (BOUND_VARIABLE_1210979 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 _let_5) _let_6))) (let ((_let_8 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6114 BOUND_VARIABLE_1210978) BOUND_VARIABLE_1210979) (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1210979)) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1210979 _let_7)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4696 k_4745 BOUND_VARIABLE_1210978)) _let_7) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210979) _let_5)) _let_1)))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1210979) _let_5)) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3)))))))))))))))) (let ((_let_3548 (forall ((BOUND_VARIABLE_1210900 tptp.real) (BOUND_VARIABLE_1210901 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 _let_5) _let_6))) (let ((_let_8 (ho_4264 _let_4 k_4275))) (let ((_let_9 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1210901)))) (= (ho_4245 (ho_4244 k_6115 BOUND_VARIABLE_1210900) BOUND_VARIABLE_1210901) (ho_4258 _let_9 (ho_4258 (ho_4265 _let_8 (ho_4258 _let_9 (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1210901 _let_7)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4696 (ho_4747 k_4746 BOUND_VARIABLE_1210901) BOUND_VARIABLE_1210900)) _let_7) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210901) _let_5)) _let_1)))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1210901) _let_5)) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3)))))))))))))))))) (let ((_let_3549 (forall ((BOUND_VARIABLE_1210820 tptp.complex) (BOUND_VARIABLE_1210821 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 k_6015 BOUND_VARIABLE_1210821))) (let ((_let_4 (ho_4769 k_4768 _let_3))) (let ((_let_5 (ho_4769 k_4773 _let_3))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4257 _let_6 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) (ho_4245 (ho_4244 k_4243 _let_5) _let_2)) (ho_4245 (ho_4244 k_4243 _let_4) _let_2))))) (let ((_let_10 (ho_4264 _let_7 k_4275))) (let ((_let_11 (ho_4247 k_4246 _let_1))) (let ((_let_12 (ho_4701 k_4700 tptp.one))) (let ((_let_13 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_14 (ho_4216 (ho_4215 k_4221 _let_13) _let_2))) (= (ho_4767 (ho_4766 k_6116 BOUND_VARIABLE_1210820) BOUND_VARIABLE_1210821) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 _let_12)) BOUND_VARIABLE_1210821)) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1210821 _let_14)) _let_12) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4712 k_4748 BOUND_VARIABLE_1210820)) _let_14) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210821) _let_13)) _let_12)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 _let_5) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4257 _let_6 k_4248) _let_4)) _let_9))))))))))))))))))))))) (let ((_let_3550 (forall ((BOUND_VARIABLE_1210721 tptp.complex) (BOUND_VARIABLE_1210722 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 k_6015 BOUND_VARIABLE_1210722))) (let ((_let_4 (ho_4769 k_4768 _let_3))) (let ((_let_5 (ho_4769 k_4773 _let_3))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4257 _let_6 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) (ho_4245 (ho_4244 k_4243 _let_5) _let_2)) (ho_4245 (ho_4244 k_4243 _let_4) _let_2))))) (let ((_let_10 (ho_4264 _let_7 k_4275))) (let ((_let_11 (ho_4247 k_4246 _let_1))) (let ((_let_12 (ho_4701 k_4700 tptp.one))) (let ((_let_13 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_14 (ho_4216 (ho_4215 k_4221 _let_13) _let_2))) (let ((_let_15 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 _let_12)) BOUND_VARIABLE_1210722)))) (= (ho_4767 (ho_4766 k_6117 BOUND_VARIABLE_1210721) BOUND_VARIABLE_1210722) (ho_4703 _let_15 (ho_4703 (ho_4705 k_4710 (ho_4703 _let_15 (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1210722 _let_14)) _let_12) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4712 (ho_4750 k_4749 BOUND_VARIABLE_1210722) BOUND_VARIABLE_1210721)) _let_14) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210722) _let_13)) _let_12)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 _let_5) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4257 _let_6 k_4248) _let_4)) _let_9))))))))))))))))))))))))) (let ((_let_3551 (forall ((BOUND_VARIABLE_1210694 tptp.rat) (BOUND_VARIABLE_1210695 tptp.nat) (BOUND_VARIABLE_1210696 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1210694) _let_3))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1210695) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1210696) (ho_4442 (ho_4458 (ho_4699 k_6118 BOUND_VARIABLE_1210694) BOUND_VARIABLE_1210695) BOUND_VARIABLE_1210696)))))))))))) (let ((_let_3552 (forall ((BOUND_VARIABLE_1210671 tptp.rat) (BOUND_VARIABLE_1210672 tptp.nat) (BOUND_VARIABLE_1210673 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1210671)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1210672) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1210673) (ho_4442 (ho_4458 (ho_4699 k_6119 BOUND_VARIABLE_1210671) BOUND_VARIABLE_1210672) BOUND_VARIABLE_1210673)))))))))))) (let ((_let_3553 (forall ((BOUND_VARIABLE_1210644 tptp.real) (BOUND_VARIABLE_1210645 tptp.nat) (BOUND_VARIABLE_1210646 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1210644) _let_1))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1210645) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1210646) (ho_4258 (ho_4273 (ho_4696 k_6120 BOUND_VARIABLE_1210644) BOUND_VARIABLE_1210645) BOUND_VARIABLE_1210646)))))))))) (let ((_let_3554 (forall ((BOUND_VARIABLE_1210621 tptp.real) (BOUND_VARIABLE_1210622 tptp.nat) (BOUND_VARIABLE_1210623 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1210621)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1210622) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1210623) (ho_4258 (ho_4273 (ho_4696 k_6121 BOUND_VARIABLE_1210621) BOUND_VARIABLE_1210622) BOUND_VARIABLE_1210623)))))))))) (let ((_let_3555 (forall ((BOUND_VARIABLE_1210598 tptp.complex) (BOUND_VARIABLE_1210599 tptp.nat) (BOUND_VARIABLE_1210600 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1210598) _let_1))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1210599) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1210600) (ho_4703 (ho_4709 (ho_4712 k_6122 BOUND_VARIABLE_1210598) BOUND_VARIABLE_1210599) BOUND_VARIABLE_1210600)))))) (let ((_let_3556 (forall ((BOUND_VARIABLE_1210577 tptp.complex) (BOUND_VARIABLE_1210578 tptp.nat) (BOUND_VARIABLE_1210579 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1210577)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1210578) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1210579) (ho_4703 (ho_4709 (ho_4712 k_6123 BOUND_VARIABLE_1210577) BOUND_VARIABLE_1210578) BOUND_VARIABLE_1210579)))))) (let ((_let_3557 (forall ((BOUND_VARIABLE_1210550 tptp.rat) (BOUND_VARIABLE_1210551 tptp.nat) (BOUND_VARIABLE_1210552 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1210550) _let_3))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1210551) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1210552) (ho_4442 (ho_4458 (ho_4699 k_6124 BOUND_VARIABLE_1210550) BOUND_VARIABLE_1210551) BOUND_VARIABLE_1210552)))))))))))) (let ((_let_3558 (forall ((BOUND_VARIABLE_1210527 tptp.rat) (BOUND_VARIABLE_1210528 tptp.nat) (BOUND_VARIABLE_1210529 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1210527)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1210528) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1210529) (ho_4442 (ho_4458 (ho_4699 k_6125 BOUND_VARIABLE_1210527) BOUND_VARIABLE_1210528) BOUND_VARIABLE_1210529)))))))))))) (let ((_let_3559 (forall ((BOUND_VARIABLE_1210500 tptp.real) (BOUND_VARIABLE_1210501 tptp.nat) (BOUND_VARIABLE_1210502 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1210500) _let_1))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1210501) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1210502) (ho_4258 (ho_4273 (ho_4696 k_6126 BOUND_VARIABLE_1210500) BOUND_VARIABLE_1210501) BOUND_VARIABLE_1210502)))))))))) (let ((_let_3560 (forall ((BOUND_VARIABLE_1210477 tptp.real) (BOUND_VARIABLE_1210478 tptp.nat) (BOUND_VARIABLE_1210479 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1210477)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1210478) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1210479) (ho_4258 (ho_4273 (ho_4696 k_6127 BOUND_VARIABLE_1210477) BOUND_VARIABLE_1210478) BOUND_VARIABLE_1210479)))))))))) (let ((_let_3561 (forall ((BOUND_VARIABLE_1210454 tptp.complex) (BOUND_VARIABLE_1210455 tptp.nat) (BOUND_VARIABLE_1210456 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1210454) _let_1))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1210455) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1210456) (ho_4703 (ho_4709 (ho_4712 k_6128 BOUND_VARIABLE_1210454) BOUND_VARIABLE_1210455) BOUND_VARIABLE_1210456)))))) (let ((_let_3562 (forall ((BOUND_VARIABLE_1210433 tptp.complex) (BOUND_VARIABLE_1210434 tptp.nat) (BOUND_VARIABLE_1210435 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1210433)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1210434) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1210435) (ho_4703 (ho_4709 (ho_4712 k_6129 BOUND_VARIABLE_1210433) BOUND_VARIABLE_1210434) BOUND_VARIABLE_1210435)))))) (let ((_let_3563 (forall ((BOUND_VARIABLE_1210372 tptp.complex) (BOUND_VARIABLE_1210373 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 BOUND_VARIABLE_1210372)) BOUND_VARIABLE_1210373))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210373 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1210373) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1210373) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6130 BOUND_VARIABLE_1210372) BOUND_VARIABLE_1210373) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3564 (forall ((BOUND_VARIABLE_1210312 tptp.complex) (BOUND_VARIABLE_1210313 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1210312) BOUND_VARIABLE_1210313))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210313 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1210313) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1210313) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6131 BOUND_VARIABLE_1210312) BOUND_VARIABLE_1210313) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3565 (forall ((BOUND_VARIABLE_1210262 tptp.real) (BOUND_VARIABLE_1210263 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_8 (ho_4264 _let_5 k_4275))) (= (ho_4245 (ho_4244 k_6132 BOUND_VARIABLE_1210262) BOUND_VARIABLE_1210263) (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210263 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1210263) _let_7))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_7) BOUND_VARIABLE_1210263) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)) (ho_4245 (ho_4244 k_4243 (ho_4258 _let_2 BOUND_VARIABLE_1210262)) BOUND_VARIABLE_1210263)))))))))))))) (let ((_let_3566 (forall ((BOUND_VARIABLE_1210216 tptp.real) (BOUND_VARIABLE_1210217 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6133 BOUND_VARIABLE_1210216) BOUND_VARIABLE_1210217) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210217 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1210217) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1210217) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1210216) BOUND_VARIABLE_1210217))))))))))))) (let ((_let_3567 (forall ((BOUND_VARIABLE_1210148 tptp.complex) (BOUND_VARIABLE_1210149 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 BOUND_VARIABLE_1210148)) BOUND_VARIABLE_1210149))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210149 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210149) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1210149) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6134 BOUND_VARIABLE_1210148) BOUND_VARIABLE_1210149) (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1)))))))))))))))))))))))))) (let ((_let_3568 (forall ((BOUND_VARIABLE_1210083 tptp.complex) (BOUND_VARIABLE_1210084 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1210083) BOUND_VARIABLE_1210084))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210084 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210084) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1210084) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6135 BOUND_VARIABLE_1210083) BOUND_VARIABLE_1210084) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_3569 (forall ((BOUND_VARIABLE_1210026 tptp.real) (BOUND_VARIABLE_1210027 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4257 _let_1 k_4248))) (let ((_let_3 (ho_4247 k_4246 tptp.one))) (let ((_let_4 (ho_4258 _let_2 _let_3))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_3) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_10 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_11 (ho_4219 k_4218 k_4217))) (let ((_let_12 (ho_4264 _let_5 k_4275))) (= (ho_4245 (ho_4244 k_6136 BOUND_VARIABLE_1210026) BOUND_VARIABLE_1210027) (ho_4258 _let_2 (ho_4258 (ho_4265 _let_12 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1210027 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_12 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1210027) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_11 (ho_4216 (ho_4215 k_4221 _let_8) _let_9)) _let_10)) (ho_4209 (ho_4220 _let_11 _let_8) _let_10))))) _let_9))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_9) BOUND_VARIABLE_1210027) _let_8)) _let_6))))) (ho_4245 (ho_4244 k_4243 (ho_4258 _let_2 BOUND_VARIABLE_1210026)) BOUND_VARIABLE_1210027))))))))))))))))))) (let ((_let_3570 (forall ((BOUND_VARIABLE_1209975 tptp.real) (BOUND_VARIABLE_1209976 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6137 BOUND_VARIABLE_1209975) BOUND_VARIABLE_1209976) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1209976 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1209976) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1209976) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1209975) BOUND_VARIABLE_1209976))))))))))))))))) (let ((_let_3571 (forall ((BOUND_VARIABLE_1209906 tptp.real) (BOUND_VARIABLE_1209907 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4216 (ho_4215 k_4221 _let_5) _let_6))) (let ((_let_8 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6138 BOUND_VARIABLE_1209906) BOUND_VARIABLE_1209907) (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1209907)) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1209907 _let_7)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4715 (ho_4714 k_4751 BOUND_VARIABLE_1209906) BOUND_VARIABLE_1209907)) _let_7) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1209907) _let_5)) _let_1)))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1209907) _let_5)) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3)))))))))))))))) (let ((_let_3572 (forall ((BOUND_VARIABLE_1209896 tptp.nat) (BOUND_VARIABLE_1209897 tptp.nat)) (= (ho_4288 (ho_4287 k_6139 BOUND_VARIABLE_1209896) BOUND_VARIABLE_1209897) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209897)) (ho_4290 k_4289 BOUND_VARIABLE_1209896)))))) (let ((_let_3573 (forall ((BOUND_VARIABLE_1209860 tptp.real) (BOUND_VARIABLE_1209861 tptp.nat) (BOUND_VARIABLE_1209862 tptp.nat) (BOUND_VARIABLE_1209863 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1209860) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1209861) _let_6))) _let_1))) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1209862) _let_6))) BOUND_VARIABLE_1209863) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_6140 BOUND_VARIABLE_1209860) BOUND_VARIABLE_1209861) BOUND_VARIABLE_1209862) BOUND_VARIABLE_1209863)))))))))))) (let ((_let_3574 (forall ((BOUND_VARIABLE_1209790 tptp.rat) (BOUND_VARIABLE_1209791 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4213 k_4212 _let_1))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4216 (ho_4215 k_4221 _let_7) _let_8))) (let ((_let_10 (ho_4447 _let_6 k_4697))) (= (ho_4316 (ho_4799 k_6141 BOUND_VARIABLE_1209790) BOUND_VARIABLE_1209791) (ho_4442 (ho_4448 _let_10 (ho_4442 (ho_4448 _let_10 (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1209791)) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1209791 _let_9)) _let_3) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4718 (ho_4717 k_4752 BOUND_VARIABLE_1209790) BOUND_VARIABLE_1209791)) _let_9) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1209791) _let_7)) _let_3)))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1209791) _let_7)) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) _let_5)))))))))))))))))) (let ((_let_3575 (forall ((BOUND_VARIABLE_1209780 tptp.nat) (BOUND_VARIABLE_1209781 tptp.nat)) (= (ho_4288 (ho_4287 k_6142 BOUND_VARIABLE_1209780) BOUND_VARIABLE_1209781) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209781)) (ho_4290 k_4289 BOUND_VARIABLE_1209780)))))) (let ((_let_3576 (forall ((BOUND_VARIABLE_1209744 tptp.rat) (BOUND_VARIABLE_1209745 tptp.nat) (BOUND_VARIABLE_1209746 tptp.nat) (BOUND_VARIABLE_1209747 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1209744) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209745) _let_8))) _let_3))) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209746) _let_8))) BOUND_VARIABLE_1209747) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_6143 BOUND_VARIABLE_1209744) BOUND_VARIABLE_1209745) BOUND_VARIABLE_1209746) BOUND_VARIABLE_1209747)))))))))))))) (let ((_let_3577 (forall ((BOUND_VARIABLE_1209654 tptp.complex) (BOUND_VARIABLE_1209655 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 k_6015 BOUND_VARIABLE_1209655))) (let ((_let_4 (ho_4769 k_4768 _let_3))) (let ((_let_5 (ho_4769 k_4773 _let_3))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4257 _let_6 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) (ho_4245 (ho_4244 k_4243 _let_5) _let_2)) (ho_4245 (ho_4244 k_4243 _let_4) _let_2))))) (let ((_let_10 (ho_4264 _let_7 k_4275))) (let ((_let_11 (ho_4247 k_4246 _let_1))) (let ((_let_12 (ho_4701 k_4700 tptp.one))) (let ((_let_13 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_14 (ho_4216 (ho_4215 k_4221 _let_13) _let_2))) (= (ho_4767 (ho_4766 k_6144 BOUND_VARIABLE_1209654) BOUND_VARIABLE_1209655) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 (ho_4703 k_4702 _let_12)) BOUND_VARIABLE_1209655)) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1209655 _let_14)) _let_12) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4721 (ho_4720 k_4753 BOUND_VARIABLE_1209654) BOUND_VARIABLE_1209655)) _let_14) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1209655) _let_13)) _let_12)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 _let_5) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4257 _let_6 k_4248) _let_4)) _let_9))))))))))))))))))))))) (let ((_let_3578 (forall ((BOUND_VARIABLE_1209644 tptp.nat) (BOUND_VARIABLE_1209645 tptp.nat)) (= (ho_4288 (ho_4287 k_6145 BOUND_VARIABLE_1209644) BOUND_VARIABLE_1209645) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209645)) (ho_4290 k_4289 BOUND_VARIABLE_1209644)))))) (let ((_let_3579 (forall ((BOUND_VARIABLE_1209609 tptp.complex) (BOUND_VARIABLE_1209610 tptp.nat) (BOUND_VARIABLE_1209611 tptp.nat) (BOUND_VARIABLE_1209612 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (let ((_let_3 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1209609) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1209610) _let_2))) _let_1))) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1209611) _let_2))) BOUND_VARIABLE_1209612) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_6146 BOUND_VARIABLE_1209609) BOUND_VARIABLE_1209610) BOUND_VARIABLE_1209611) BOUND_VARIABLE_1209612)))))))) (let ((_let_3580 (forall ((BOUND_VARIABLE_1209600 tptp.int) (BOUND_VARIABLE_1209601 tptp.int)) (= (ho_4310 (ho_4309 k_6147 BOUND_VARIABLE_1209600) BOUND_VARIABLE_1209601) (= BOUND_VARIABLE_1209600 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1209601) BOUND_VARIABLE_1209600)))))) (let ((_let_3581 (forall ((BOUND_VARIABLE_1209591 tptp.int) (BOUND_VARIABLE_1209592 tptp.int)) (= (ho_4310 (ho_4309 k_6148 BOUND_VARIABLE_1209591) BOUND_VARIABLE_1209592) (= BOUND_VARIABLE_1209591 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1209592) BOUND_VARIABLE_1209591)))))) (let ((_let_3582 (forall ((BOUND_VARIABLE_1209569 tptp.nat) (BOUND_VARIABLE_1209570 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209569) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209570) _let_2))) (ho_4216 (ho_4215 k_6149 BOUND_VARIABLE_1209569) BOUND_VARIABLE_1209570)))))))) (let ((_let_3583 (forall ((BOUND_VARIABLE_1209564 tptp.nat)) (= BOUND_VARIABLE_1209564 (ho_4216 k_6150 BOUND_VARIABLE_1209564))))) (let ((_let_3584 (forall ((BOUND_VARIABLE_1209509 tptp.nat) (BOUND_VARIABLE_1209510 tptp.nat) (BOUND_VARIABLE_1209511 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209509) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209510) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1209511 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6151 BOUND_VARIABLE_1209509) BOUND_VARIABLE_1209510) BOUND_VARIABLE_1209511))))) (let ((_let_3585 (forall ((BOUND_VARIABLE_1209499 tptp.nat) (BOUND_VARIABLE_1209500 tptp.nat)) (= (ho_4288 (ho_4287 k_6152 BOUND_VARIABLE_1209499) BOUND_VARIABLE_1209500) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209500)) (ho_4290 k_4289 BOUND_VARIABLE_1209499)))))) (let ((_let_3586 (forall ((BOUND_VARIABLE_1308913 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1209480 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1308913 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209480) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6153 BOUND_VARIABLE_1308913) BOUND_VARIABLE_1209480)))))))) (let ((_let_3587 (forall ((BOUND_VARIABLE_1209469 tptp.nat) (BOUND_VARIABLE_1209470 tptp.nat)) (= (ho_4288 (ho_4287 k_6154 BOUND_VARIABLE_1209469) BOUND_VARIABLE_1209470) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1209470)) (ho_4290 k_4289 BOUND_VARIABLE_1209469)))))) (let ((_let_3588 (forall ((BOUND_VARIABLE_1209459 tptp.nat) (BOUND_VARIABLE_1209460 tptp.nat)) (= (ho_4288 (ho_4287 k_6155 BOUND_VARIABLE_1209459) BOUND_VARIABLE_1209460) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209460)) (ho_4290 k_4289 BOUND_VARIABLE_1209459)))))) (let ((_let_3589 (forall ((BOUND_VARIABLE_1308950 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1209440 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1308950 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209440) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6156 BOUND_VARIABLE_1308950) BOUND_VARIABLE_1209440)))))))) (let ((_let_3590 (forall ((BOUND_VARIABLE_1209429 tptp.nat) (BOUND_VARIABLE_1209430 tptp.nat)) (= (ho_4288 (ho_4287 k_6157 BOUND_VARIABLE_1209429) BOUND_VARIABLE_1209430) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1209430)) (ho_4290 k_4289 BOUND_VARIABLE_1209429)))))) (let ((_let_3591 (forall ((BOUND_VARIABLE_1209419 tptp.nat) (BOUND_VARIABLE_1209420 tptp.nat)) (= (ho_4288 (ho_4287 k_6158 BOUND_VARIABLE_1209419) BOUND_VARIABLE_1209420) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209420)) (ho_4290 k_4289 BOUND_VARIABLE_1209419)))))) (let ((_let_3592 (forall ((BOUND_VARIABLE_1308987 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1209400 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4316 BOUND_VARIABLE_1308987 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209400) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4316 (ho_4249 k_6159 BOUND_VARIABLE_1308987) BOUND_VARIABLE_1209400)))))))) (let ((_let_3593 (forall ((BOUND_VARIABLE_1209389 tptp.nat) (BOUND_VARIABLE_1209390 tptp.nat)) (= (ho_4288 (ho_4287 k_6160 BOUND_VARIABLE_1209389) BOUND_VARIABLE_1209390) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1209390)) (ho_4290 k_4289 BOUND_VARIABLE_1209389)))))) (let ((_let_3594 (forall ((BOUND_VARIABLE_1209379 tptp.nat) (BOUND_VARIABLE_1209380 tptp.nat)) (= (ho_4288 (ho_4287 k_6161 BOUND_VARIABLE_1209379) BOUND_VARIABLE_1209380) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1209380)) (ho_4290 k_4289 BOUND_VARIABLE_1209379)))))) (let ((_let_3595 (forall ((BOUND_VARIABLE_1309024 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1209360 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4245 BOUND_VARIABLE_1309024 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1209360) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4245 (ho_4473 k_6162 BOUND_VARIABLE_1309024) BOUND_VARIABLE_1209360)))))))) (let ((_let_3596 (forall ((BOUND_VARIABLE_1209349 tptp.nat) (BOUND_VARIABLE_1209350 tptp.nat)) (= (ho_4288 (ho_4287 k_6163 BOUND_VARIABLE_1209349) BOUND_VARIABLE_1209350) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1209350)) (ho_4290 k_4289 BOUND_VARIABLE_1209349)))))) (let ((_let_3597 (forall ((BOUND_VARIABLE_1309048 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1309045 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1209323 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 (ho_4767 BOUND_VARIABLE_1309048 BOUND_VARIABLE_1209323)) (ho_4703 k_4702 (ho_4767 BOUND_VARIABLE_1309045 BOUND_VARIABLE_1209323))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_4245 (ho_6166 (ho_6165 k_6164 BOUND_VARIABLE_1309048) BOUND_VARIABLE_1309045) BOUND_VARIABLE_1209323)))))))))) (let ((_let_3598 (forall ((BOUND_VARIABLE_1309083 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1309080 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1209304 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 k_6167 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_4245 BOUND_VARIABLE_1309083 BOUND_VARIABLE_1209304)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4245 BOUND_VARIABLE_1309080 BOUND_VARIABLE_1209304)))) (ho_4245 (ho_4473 (ho_5457 k_6168 BOUND_VARIABLE_1309083) BOUND_VARIABLE_1309080) BOUND_VARIABLE_1209304)))))) (let ((_let_3599 (forall ((BOUND_VARIABLE_1309105 |u_(-> tptp.product_prod_nat_nat tptp.complex)|) (BOUND_VARIABLE_1309100 |u_(-> tptp.product_prod_nat_nat tptp.complex)|) (BOUND_VARIABLE_1209276 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 (ho_6169 BOUND_VARIABLE_1309105 BOUND_VARIABLE_1209276)) (ho_4703 k_4702 (ho_6169 BOUND_VARIABLE_1309100 BOUND_VARIABLE_1209276))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_6173 (ho_6172 (ho_6171 k_6170 BOUND_VARIABLE_1309105) BOUND_VARIABLE_1309100) BOUND_VARIABLE_1209276)))))))))) (let ((_let_3600 (forall ((BOUND_VARIABLE_1309143 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1309140 |u_(-> tptp.complex tptp.complex)|) (BOUND_VARIABLE_1209248 tptp.complex)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 (ho_4703 BOUND_VARIABLE_1309143 BOUND_VARIABLE_1209248)) (ho_4703 k_4702 (ho_4703 BOUND_VARIABLE_1309140 BOUND_VARIABLE_1209248))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_4769 (ho_6176 (ho_6175 k_6174 BOUND_VARIABLE_1309143) BOUND_VARIABLE_1309140) BOUND_VARIABLE_1209248)))))))))) (let ((_let_3601 (forall ((BOUND_VARIABLE_1309181 |u_(-> tptp.int tptp.complex)|) (BOUND_VARIABLE_1309176 |u_(-> tptp.int tptp.complex)|) (BOUND_VARIABLE_1209220 tptp.int)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 (ho_6177 BOUND_VARIABLE_1309181 BOUND_VARIABLE_1209220)) (ho_4703 k_4702 (ho_6177 BOUND_VARIABLE_1309176 BOUND_VARIABLE_1209220))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_6181 (ho_6180 (ho_6179 k_6178 BOUND_VARIABLE_1309181) BOUND_VARIABLE_1309176) BOUND_VARIABLE_1209220)))))))))) (let ((_let_3602 (forall ((BOUND_VARIABLE_1309219 |u_(-> tptp.real tptp.complex)|) (BOUND_VARIABLE_1309216 |u_(-> tptp.real tptp.complex)|) (BOUND_VARIABLE_1209192 tptp.real)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 (ho_4771 BOUND_VARIABLE_1309219 BOUND_VARIABLE_1209192)) (ho_4703 k_4702 (ho_4771 BOUND_VARIABLE_1309216 BOUND_VARIABLE_1209192))))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_4258 (ho_6184 (ho_6183 k_6182 BOUND_VARIABLE_1309219) BOUND_VARIABLE_1309216) BOUND_VARIABLE_1209192)))))))))) (let ((_let_3603 (forall ((BOUND_VARIABLE_1309254 |u_(-> tptp.product_prod_nat_nat tptp.real)|) (BOUND_VARIABLE_1309251 |u_(-> tptp.product_prod_nat_nat tptp.real)|) (BOUND_VARIABLE_1209173 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 k_6167 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_6173 BOUND_VARIABLE_1309254 BOUND_VARIABLE_1209173)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_6173 BOUND_VARIABLE_1309251 BOUND_VARIABLE_1209173)))) (ho_6173 (ho_6187 (ho_6186 k_6185 BOUND_VARIABLE_1309254) BOUND_VARIABLE_1309251) BOUND_VARIABLE_1209173)))))) (let ((_let_3604 (forall ((BOUND_VARIABLE_1309279 |u_(-> tptp.complex tptp.real)|) (BOUND_VARIABLE_1309276 |u_(-> tptp.complex tptp.real)|) (BOUND_VARIABLE_1209154 tptp.complex)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 k_6167 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_4769 BOUND_VARIABLE_1309279 BOUND_VARIABLE_1209154)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4769 BOUND_VARIABLE_1309276 BOUND_VARIABLE_1209154)))) (ho_4769 (ho_6190 (ho_6189 k_6188 BOUND_VARIABLE_1309279) BOUND_VARIABLE_1309276) BOUND_VARIABLE_1209154)))))) (let ((_let_3605 (forall ((BOUND_VARIABLE_1309304 |u_(-> tptp.int tptp.real)|) (BOUND_VARIABLE_1309301 |u_(-> tptp.int tptp.real)|) (BOUND_VARIABLE_1209135 tptp.int)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 k_6167 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_6181 BOUND_VARIABLE_1309304 BOUND_VARIABLE_1209135)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_6181 BOUND_VARIABLE_1309301 BOUND_VARIABLE_1209135)))) (ho_6181 (ho_6193 (ho_6192 k_6191 BOUND_VARIABLE_1309304) BOUND_VARIABLE_1309301) BOUND_VARIABLE_1209135)))))) (let ((_let_3606 (forall ((BOUND_VARIABLE_1309329 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1309326 |u_(-> tptp.real tptp.real)|) (BOUND_VARIABLE_1209116 tptp.real)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 k_6167 (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_1) k_4259) (ho_4258 BOUND_VARIABLE_1309329 BOUND_VARIABLE_1209116)) (ho_4258 (ho_4257 _let_1 k_4248) (ho_4258 BOUND_VARIABLE_1309326 BOUND_VARIABLE_1209116)))) (ho_4258 (ho_4946 (ho_5517 k_6194 BOUND_VARIABLE_1309329) BOUND_VARIABLE_1309326) BOUND_VARIABLE_1209116)))))) (let ((_let_3607 (forall ((BOUND_VARIABLE_1209087 tptp.nat) (BOUND_VARIABLE_1209088 tptp.nat) (BOUND_VARIABLE_1209089 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209087) _let_8))) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209088) _let_8))) BOUND_VARIABLE_1209089) (ho_4442 (ho_4458 (ho_4718 k_6195 BOUND_VARIABLE_1209087) BOUND_VARIABLE_1209088) BOUND_VARIABLE_1209089)))))))))))))) (let ((_let_3608 (forall ((BOUND_VARIABLE_1209064 tptp.rat) (BOUND_VARIABLE_1209065 tptp.nat) (BOUND_VARIABLE_1209066 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1209064)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1209065) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1209066) (ho_4442 (ho_4458 (ho_4699 k_6196 BOUND_VARIABLE_1209064) BOUND_VARIABLE_1209065) BOUND_VARIABLE_1209066)))))))))))) (let ((_let_3609 (forall ((BOUND_VARIABLE_1209030 tptp.rat) (BOUND_VARIABLE_1209031 tptp.nat) (BOUND_VARIABLE_1209032 tptp.nat) (BOUND_VARIABLE_1209033 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1209030) (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209031) _let_8))))) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1209032) _let_8))) BOUND_VARIABLE_1209033) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_6197 BOUND_VARIABLE_1209030) BOUND_VARIABLE_1209031) BOUND_VARIABLE_1209032) BOUND_VARIABLE_1209033)))))))))))))) (let ((_let_3610 (forall ((BOUND_VARIABLE_1209003 tptp.nat) (BOUND_VARIABLE_1209004 tptp.nat) (BOUND_VARIABLE_1209005 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1209003) _let_6))) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1209004) _let_6))) BOUND_VARIABLE_1209005) (ho_4258 (ho_4273 (ho_4715 k_6198 BOUND_VARIABLE_1209003) BOUND_VARIABLE_1209004) BOUND_VARIABLE_1209005)))))))))))) (let ((_let_3611 (forall ((BOUND_VARIABLE_1208980 tptp.real) (BOUND_VARIABLE_1208981 tptp.nat) (BOUND_VARIABLE_1208982 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1208980)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1208981) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1208982) (ho_4258 (ho_4273 (ho_4696 k_6199 BOUND_VARIABLE_1208980) BOUND_VARIABLE_1208981) BOUND_VARIABLE_1208982)))))))))) (let ((_let_3612 (forall ((BOUND_VARIABLE_1208946 tptp.real) (BOUND_VARIABLE_1208947 tptp.nat) (BOUND_VARIABLE_1208948 tptp.nat) (BOUND_VARIABLE_1208949 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1208946) (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1208947) _let_6))))) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1208948) _let_6))) BOUND_VARIABLE_1208949) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_6200 BOUND_VARIABLE_1208946) BOUND_VARIABLE_1208947) BOUND_VARIABLE_1208948) BOUND_VARIABLE_1208949)))))))))))) (let ((_let_3613 (forall ((BOUND_VARIABLE_1208923 tptp.rat) (BOUND_VARIABLE_1208924 tptp.nat) (BOUND_VARIABLE_1208925 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1208923)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1208924) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1208925) (ho_4442 (ho_4458 (ho_4699 k_6201 BOUND_VARIABLE_1208923) BOUND_VARIABLE_1208924) BOUND_VARIABLE_1208925)))))))))))) (let ((_let_3614 (forall ((BOUND_VARIABLE_1208896 tptp.rat) (BOUND_VARIABLE_1208897 tptp.nat) (BOUND_VARIABLE_1208898 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1208896) _let_6))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1208897) (ho_4442 (ho_4448 _let_8 _let_3) _let_6)))) BOUND_VARIABLE_1208898) (ho_4442 (ho_4458 (ho_4699 k_6202 BOUND_VARIABLE_1208896) BOUND_VARIABLE_1208897) BOUND_VARIABLE_1208898))))))))))))) (let ((_let_3615 (forall ((BOUND_VARIABLE_1208873 tptp.real) (BOUND_VARIABLE_1208874 tptp.nat) (BOUND_VARIABLE_1208875 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1208873)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1208874) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1208875) (ho_4258 (ho_4273 (ho_4696 k_6203 BOUND_VARIABLE_1208873) BOUND_VARIABLE_1208874) BOUND_VARIABLE_1208875)))))))))) (let ((_let_3616 (forall ((BOUND_VARIABLE_1208846 tptp.real) (BOUND_VARIABLE_1208847 tptp.nat) (BOUND_VARIABLE_1208848 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1208846) _let_4))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1208847) (ho_4258 (ho_4265 _let_6 _let_1) _let_4)))) BOUND_VARIABLE_1208848) (ho_4258 (ho_4273 (ho_4696 k_6204 BOUND_VARIABLE_1208846) BOUND_VARIABLE_1208847) BOUND_VARIABLE_1208848))))))))))) (let ((_let_3617 (forall ((BOUND_VARIABLE_1208825 tptp.complex) (BOUND_VARIABLE_1208826 tptp.nat) (BOUND_VARIABLE_1208827 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1208825)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1208826) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1208827) (ho_4703 (ho_4709 (ho_4712 k_6205 BOUND_VARIABLE_1208825) BOUND_VARIABLE_1208826) BOUND_VARIABLE_1208827)))))) (let ((_let_3618 (forall ((BOUND_VARIABLE_1208802 tptp.complex) (BOUND_VARIABLE_1208803 tptp.nat) (BOUND_VARIABLE_1208804 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1208802) _let_2))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1208803) (ho_4703 (ho_4705 k_4704 _let_1) _let_2)))) BOUND_VARIABLE_1208804) (ho_4703 (ho_4709 (ho_4712 k_6206 BOUND_VARIABLE_1208802) BOUND_VARIABLE_1208803) BOUND_VARIABLE_1208804))))))) (let ((_let_3619 (forall ((BOUND_VARIABLE_1208775 tptp.rat) (BOUND_VARIABLE_1208776 tptp.nat) (BOUND_VARIABLE_1208777 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1208775) _let_3))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1208776) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1208777) (ho_4442 (ho_4458 (ho_4699 k_6207 BOUND_VARIABLE_1208775) BOUND_VARIABLE_1208776) BOUND_VARIABLE_1208777)))))))))))) (let ((_let_3620 (forall ((BOUND_VARIABLE_1208752 tptp.rat) (BOUND_VARIABLE_1208753 tptp.nat) (BOUND_VARIABLE_1208754 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1208752)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1208753) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1208754) (ho_4442 (ho_4458 (ho_4699 k_6208 BOUND_VARIABLE_1208752) BOUND_VARIABLE_1208753) BOUND_VARIABLE_1208754)))))))))))) (let ((_let_3621 (forall ((BOUND_VARIABLE_1208725 tptp.real) (BOUND_VARIABLE_1208726 tptp.nat) (BOUND_VARIABLE_1208727 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1208725) _let_1))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1208726) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1208727) (ho_4258 (ho_4273 (ho_4696 k_6209 BOUND_VARIABLE_1208725) BOUND_VARIABLE_1208726) BOUND_VARIABLE_1208727)))))))))) (let ((_let_3622 (forall ((BOUND_VARIABLE_1208702 tptp.real) (BOUND_VARIABLE_1208703 tptp.nat) (BOUND_VARIABLE_1208704 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1208702)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1208703) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1208704) (ho_4258 (ho_4273 (ho_4696 k_6210 BOUND_VARIABLE_1208702) BOUND_VARIABLE_1208703) BOUND_VARIABLE_1208704)))))))))) (let ((_let_3623 (forall ((BOUND_VARIABLE_1208679 tptp.complex) (BOUND_VARIABLE_1208680 tptp.nat) (BOUND_VARIABLE_1208681 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1208679) _let_1))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1208680) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1208681) (ho_4703 (ho_4709 (ho_4712 k_6211 BOUND_VARIABLE_1208679) BOUND_VARIABLE_1208680) BOUND_VARIABLE_1208681)))))) (let ((_let_3624 (forall ((BOUND_VARIABLE_1208658 tptp.complex) (BOUND_VARIABLE_1208659 tptp.nat) (BOUND_VARIABLE_1208660 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1208658)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1208659) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1208660) (ho_4703 (ho_4709 (ho_4712 k_6212 BOUND_VARIABLE_1208658) BOUND_VARIABLE_1208659) BOUND_VARIABLE_1208660)))))) (let ((_let_3625 (forall ((BOUND_VARIABLE_1208578 tptp.complex) (BOUND_VARIABLE_1208579 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208578) BOUND_VARIABLE_1208579))) (let ((_let_4 (ho_4247 k_4246 tptp.one))) (let ((_let_5 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_6 (ho_4258 (ho_4257 _let_5 k_4248) _let_4))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_5))) (let ((_let_8 (ho_4264 _let_7 k_4259))) (let ((_let_9 (ho_4258 (ho_4265 _let_8 _let_4) _let_6))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_11 (ho_4257 _let_5 k_4274))) (let ((_let_12 (ho_4264 _let_7 k_4275))) (let ((_let_13 (ho_4265 _let_12 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208579 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_12 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208579) _let_2))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_2) BOUND_VARIABLE_1208579) _let_10)) _let_9)))) _let_9)))) (let ((_let_14 (ho_4247 k_4246 _let_1))) (let ((_let_15 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_13 (ho_4769 k_4773 _let_3)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_12 (ho_4258 (ho_4265 _let_12 _let_14) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_14)))) (ho_4771 k_4770 (ho_4258 _let_13 (ho_4769 k_4768 _let_3))))))) (= (ho_4245 (ho_5759 k_6213 BOUND_VARIABLE_1208578) BOUND_VARIABLE_1208579) (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_2 (ho_4216 (ho_4215 k_4221 _let_10) _let_2))) _let_9) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_15)) _let_2)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_15)) _let_2))))))))))))))))))))))) (let ((_let_3626 (forall ((BOUND_VARIABLE_1208530 tptp.real) (BOUND_VARIABLE_1208531 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6214 BOUND_VARIABLE_1208530) BOUND_VARIABLE_1208531) (ho_4258 k_6167 (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208531 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208531) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1208531) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1208530) BOUND_VARIABLE_1208531)))))))))))))) (let ((_let_3627 (forall ((BOUND_VARIABLE_1208445 tptp.complex) (BOUND_VARIABLE_1208446 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208445) BOUND_VARIABLE_1208446))) (let ((_let_4 (ho_4247 k_4246 tptp.one))) (let ((_let_5 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_6 (ho_4258 (ho_4257 _let_5 k_4248) _let_4))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_5))) (let ((_let_8 (ho_4264 _let_7 k_4259))) (let ((_let_9 (ho_4258 (ho_4265 _let_8 _let_4) _let_6))) (let ((_let_10 (ho_4196 k_4195 tptp.one))) (let ((_let_11 (ho_4213 k_4212 _let_10))) (let ((_let_12 (ho_4257 _let_5 k_4274))) (let ((_let_13 (ho_4209 (ho_4211 k_4210 _let_10) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_10)))) (let ((_let_14 (ho_4219 k_4218 k_4217))) (let ((_let_15 (ho_4216 (ho_4215 k_4221 _let_11) _let_2))) (let ((_let_16 (ho_4264 _let_7 k_4275))) (let ((_let_17 (ho_4265 _let_16 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208446 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_9) (ho_4258 (ho_4265 _let_16 (ho_4245 (ho_4244 k_4243 _let_6) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1208446) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_14 _let_15) _let_13)) (ho_4209 (ho_4220 _let_14 _let_11) _let_13))))) _let_2))) (ho_4258 _let_12 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_2) BOUND_VARIABLE_1208446) _let_11)) _let_9))))))) (let ((_let_18 (ho_4247 k_4246 _let_1))) (let ((_let_19 (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_17 (ho_4769 k_4773 _let_3)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_16 (ho_4258 (ho_4265 _let_16 _let_18) (ho_4506 k_4505 k_4504))) (ho_4258 _let_12 _let_18)))) (ho_4771 k_4770 (ho_4258 _let_17 (ho_4769 k_4768 _let_3))))))) (= (ho_4245 (ho_5759 k_6215 BOUND_VARIABLE_1208445) BOUND_VARIABLE_1208446) (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_2 _let_15)) _let_9) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_19)) _let_2)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_19)) _let_2))))))))))))))))))))))))))) (let ((_let_3628 (forall ((BOUND_VARIABLE_1208392 tptp.real) (BOUND_VARIABLE_1208393 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6216 BOUND_VARIABLE_1208392) BOUND_VARIABLE_1208393) (ho_4258 k_6167 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208393 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1208393) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1208393) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1208392) BOUND_VARIABLE_1208393)))))))))))))))))) (let ((_let_3629 (forall ((BOUND_VARIABLE_1208332 tptp.complex) (BOUND_VARIABLE_1208333 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208332) BOUND_VARIABLE_1208333))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208333 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208333) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1208333) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6217 BOUND_VARIABLE_1208332) BOUND_VARIABLE_1208333) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3630 (forall ((BOUND_VARIABLE_1208272 tptp.complex) (BOUND_VARIABLE_1208273 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208272) BOUND_VARIABLE_1208273))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208273 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208273) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1208273) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6218 BOUND_VARIABLE_1208272) BOUND_VARIABLE_1208273) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3631 (forall ((BOUND_VARIABLE_1208226 tptp.real) (BOUND_VARIABLE_1208227 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6219 BOUND_VARIABLE_1208226) BOUND_VARIABLE_1208227) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208227 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208227) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1208227) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1208226) BOUND_VARIABLE_1208227))))))))))))) (let ((_let_3632 (forall ((BOUND_VARIABLE_1208180 tptp.real) (BOUND_VARIABLE_1208181 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6220 BOUND_VARIABLE_1208180) BOUND_VARIABLE_1208181) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208181 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1208181) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1208181) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1208180) BOUND_VARIABLE_1208181))))))))))))) (let ((_let_3633 (forall ((BOUND_VARIABLE_1208115 tptp.complex) (BOUND_VARIABLE_1208116 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208115) BOUND_VARIABLE_1208116))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208116 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1208116) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1208116) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6221 BOUND_VARIABLE_1208115) BOUND_VARIABLE_1208116) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_3634 (forall ((BOUND_VARIABLE_1208050 tptp.complex) (BOUND_VARIABLE_1208051 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1208050) BOUND_VARIABLE_1208051))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208051 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1208051) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1208051) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6222 BOUND_VARIABLE_1208050) BOUND_VARIABLE_1208051) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_3635 (forall ((BOUND_VARIABLE_1207999 tptp.real) (BOUND_VARIABLE_1208000 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6223 BOUND_VARIABLE_1207999) BOUND_VARIABLE_1208000) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1208000 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1208000) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1208000) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1207999) BOUND_VARIABLE_1208000))))))))))))))))) (let ((_let_3636 (forall ((BOUND_VARIABLE_1207948 tptp.real) (BOUND_VARIABLE_1207949 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6224 BOUND_VARIABLE_1207948) BOUND_VARIABLE_1207949) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1207949 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1207949) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1207949) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1207948) BOUND_VARIABLE_1207949))))))))))))))))) (let ((_let_3637 (forall ((BOUND_VARIABLE_1207889 tptp.nat) (BOUND_VARIABLE_1207890 tptp.nat) (BOUND_VARIABLE_1207891 tptp.nat) (BOUND_VARIABLE_1207892 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207889) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207890) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207891) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207892 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_6225 BOUND_VARIABLE_1207889) BOUND_VARIABLE_1207890) BOUND_VARIABLE_1207891) BOUND_VARIABLE_1207892))))) (let ((_let_3638 (forall ((BOUND_VARIABLE_1207845 tptp.nat) (BOUND_VARIABLE_1207846 tptp.nat) (BOUND_VARIABLE_1207847 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207845) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207846) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207847 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6226 BOUND_VARIABLE_1207845) BOUND_VARIABLE_1207846) BOUND_VARIABLE_1207847))))) (let ((_let_3639 (forall ((BOUND_VARIABLE_1207782 tptp.nat) (BOUND_VARIABLE_1207783 tptp.nat) (BOUND_VARIABLE_1207784 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207782) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207783) _let_2)))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1207784 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6227 BOUND_VARIABLE_1207782) BOUND_VARIABLE_1207783) BOUND_VARIABLE_1207784))))) (let ((_let_3640 (forall ((BOUND_VARIABLE_1207723 tptp.nat) (BOUND_VARIABLE_1207724 tptp.nat) (BOUND_VARIABLE_1207725 tptp.nat) (BOUND_VARIABLE_1207726 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207723) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207724) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207725) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207726 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_6228 BOUND_VARIABLE_1207723) BOUND_VARIABLE_1207724) BOUND_VARIABLE_1207725) BOUND_VARIABLE_1207726))))) (let ((_let_3641 (forall ((BOUND_VARIABLE_1207679 tptp.nat) (BOUND_VARIABLE_1207680 tptp.nat) (BOUND_VARIABLE_1207681 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207679) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207680) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207681 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6229 BOUND_VARIABLE_1207679) BOUND_VARIABLE_1207680) BOUND_VARIABLE_1207681))))) (let ((_let_3642 (forall ((BOUND_VARIABLE_1207616 tptp.nat) (BOUND_VARIABLE_1207617 tptp.nat) (BOUND_VARIABLE_1207618 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207616) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207617) _let_2)))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1207618 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6230 BOUND_VARIABLE_1207616) BOUND_VARIABLE_1207617) BOUND_VARIABLE_1207618))))) (let ((_let_3643 (forall ((BOUND_VARIABLE_1207557 tptp.nat) (BOUND_VARIABLE_1207558 tptp.nat) (BOUND_VARIABLE_1207559 tptp.nat) (BOUND_VARIABLE_1207560 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207557) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 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BOUND_VARIABLE_1207514) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207515 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6232 BOUND_VARIABLE_1207513) BOUND_VARIABLE_1207514) BOUND_VARIABLE_1207515))))) (let ((_let_3645 (forall ((BOUND_VARIABLE_1207450 tptp.nat) (BOUND_VARIABLE_1207451 tptp.nat) (BOUND_VARIABLE_1207452 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207450) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207451) _let_2)))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1207452 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6233 BOUND_VARIABLE_1207450) BOUND_VARIABLE_1207451) BOUND_VARIABLE_1207452))))) (let ((_let_3646 (forall ((BOUND_VARIABLE_1207391 tptp.nat) (BOUND_VARIABLE_1207392 tptp.nat) (BOUND_VARIABLE_1207393 tptp.nat) (BOUND_VARIABLE_1207394 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207391) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207392) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207393) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207394 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_6234 BOUND_VARIABLE_1207391) BOUND_VARIABLE_1207392) BOUND_VARIABLE_1207393) BOUND_VARIABLE_1207394))))) (let ((_let_3647 (forall ((BOUND_VARIABLE_1207347 tptp.nat) (BOUND_VARIABLE_1207348 tptp.nat) (BOUND_VARIABLE_1207349 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207347) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207348) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207349 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6235 BOUND_VARIABLE_1207347) BOUND_VARIABLE_1207348) BOUND_VARIABLE_1207349))))) (let ((_let_3648 (forall ((BOUND_VARIABLE_1207284 tptp.nat) (BOUND_VARIABLE_1207285 tptp.nat) (BOUND_VARIABLE_1207286 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207284) _let_2)))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 _let_5 _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 _let_5 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207285) _let_2)))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1207286 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6236 BOUND_VARIABLE_1207284) BOUND_VARIABLE_1207285) BOUND_VARIABLE_1207286))))) (let ((_let_3649 (forall ((BOUND_VARIABLE_1207275 tptp.int) (BOUND_VARIABLE_1207276 tptp.int)) (= (ho_4310 (ho_4309 k_6237 BOUND_VARIABLE_1207275) BOUND_VARIABLE_1207276) (= BOUND_VARIABLE_1207275 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207276) BOUND_VARIABLE_1207275)))))) (let ((_let_3650 (forall ((BOUND_VARIABLE_1207266 tptp.int) (BOUND_VARIABLE_1207267 tptp.int)) (= (ho_4310 (ho_4309 k_6238 BOUND_VARIABLE_1207266) BOUND_VARIABLE_1207267) (= BOUND_VARIABLE_1207266 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207267) BOUND_VARIABLE_1207266)))))) (let ((_let_3651 (forall ((BOUND_VARIABLE_1207257 tptp.int) (BOUND_VARIABLE_1207258 tptp.int)) (= (ho_4310 (ho_4309 k_6239 BOUND_VARIABLE_1207257) BOUND_VARIABLE_1207258) (= BOUND_VARIABLE_1207257 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207258) BOUND_VARIABLE_1207257)))))) (let ((_let_3652 (forall ((BOUND_VARIABLE_1207248 tptp.int) (BOUND_VARIABLE_1207249 tptp.int)) (= (ho_4310 (ho_4309 k_6240 BOUND_VARIABLE_1207248) BOUND_VARIABLE_1207249) (= BOUND_VARIABLE_1207248 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207249) BOUND_VARIABLE_1207248)))))) (let ((_let_3653 (forall ((BOUND_VARIABLE_1207239 tptp.int) (BOUND_VARIABLE_1207240 tptp.int)) (= (ho_4310 (ho_4309 k_6241 BOUND_VARIABLE_1207239) BOUND_VARIABLE_1207240) (= BOUND_VARIABLE_1207239 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207240) BOUND_VARIABLE_1207239)))))) (let ((_let_3654 (forall ((BOUND_VARIABLE_1207230 tptp.int) (BOUND_VARIABLE_1207231 tptp.int)) (= (ho_4310 (ho_4309 k_6242 BOUND_VARIABLE_1207230) BOUND_VARIABLE_1207231) (= BOUND_VARIABLE_1207230 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1207231) BOUND_VARIABLE_1207230)))))) (let ((_let_3655 (forall ((BOUND_VARIABLE_1310539 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1207221 tptp.nat) (BOUND_VARIABLE_1207222 tptp.int)) (= (ho_4209 (ho_4220 (ho_6244 k_6243 BOUND_VARIABLE_1310539) BOUND_VARIABLE_1207221) BOUND_VARIABLE_1207222) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1310539 BOUND_VARIABLE_1207221)) BOUND_VARIABLE_1207222))))) (let ((_let_3656 (forall ((BOUND_VARIABLE_1207176 tptp.nat) (BOUND_VARIABLE_1207177 tptp.nat) (BOUND_VARIABLE_1207178 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207176) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207177) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207178 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6245 BOUND_VARIABLE_1207176) BOUND_VARIABLE_1207177) BOUND_VARIABLE_1207178))))) (let ((_let_3657 (forall ((BOUND_VARIABLE_1207132 tptp.nat) (BOUND_VARIABLE_1207133 tptp.nat) (BOUND_VARIABLE_1207134 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207132) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207133) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207134 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6246 BOUND_VARIABLE_1207132) BOUND_VARIABLE_1207133) BOUND_VARIABLE_1207134))))) (let ((_let_3658 (forall ((BOUND_VARIABLE_1310610 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1207109 tptp.nat) (BOUND_VARIABLE_1207110 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1310610 BOUND_VARIABLE_1207109)) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207110) _let_2))) (ho_4216 (ho_4215 (ho_4730 k_6247 BOUND_VARIABLE_1310610) BOUND_VARIABLE_1207109) BOUND_VARIABLE_1207110)))))))) (let ((_let_3659 (forall ((BOUND_VARIABLE_1207064 tptp.nat) (BOUND_VARIABLE_1207065 tptp.nat) (BOUND_VARIABLE_1207066 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1207064) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1207065) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1207066 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6248 BOUND_VARIABLE_1207064) BOUND_VARIABLE_1207065) BOUND_VARIABLE_1207066))))) (let ((_let_3660 (forall ((BOUND_VARIABLE_1310654 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1207051 tptp.nat) (BOUND_VARIABLE_1207052 tptp.rat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1310654 BOUND_VARIABLE_1207051)) BOUND_VARIABLE_1207052) (ho_4442 (ho_4458 (ho_6250 k_6249 BOUND_VARIABLE_1310654) BOUND_VARIABLE_1207051) BOUND_VARIABLE_1207052))))) (let ((_let_3661 (forall ((BOUND_VARIABLE_1310672 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1207037 tptp.nat) (BOUND_VARIABLE_1207038 tptp.real)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1310672 BOUND_VARIABLE_1207037)) BOUND_VARIABLE_1207038) (ho_4258 (ho_4273 (ho_6252 k_6251 BOUND_VARIABLE_1310672) BOUND_VARIABLE_1207037) BOUND_VARIABLE_1207038))))) (let ((_let_3662 (forall ((BOUND_VARIABLE_1206992 tptp.nat) (BOUND_VARIABLE_1206993 tptp.nat) (BOUND_VARIABLE_1206994 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206992) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206993) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206994 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6253 BOUND_VARIABLE_1206992) BOUND_VARIABLE_1206993) BOUND_VARIABLE_1206994))))) (let ((_let_3663 (forall ((BOUND_VARIABLE_1310720 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1206983 tptp.nat) (BOUND_VARIABLE_1206984 tptp.complex)) (= (ho_4703 (ho_4709 (ho_6255 k_6254 BOUND_VARIABLE_1310720) BOUND_VARIABLE_1206983) BOUND_VARIABLE_1206984) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1310720 BOUND_VARIABLE_1206983)) BOUND_VARIABLE_1206984))))) (let ((_let_3664 (forall ((BOUND_VARIABLE_1206938 tptp.nat) (BOUND_VARIABLE_1206939 tptp.nat) (BOUND_VARIABLE_1206940 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206938) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206939) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206940 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6256 BOUND_VARIABLE_1206938) BOUND_VARIABLE_1206939) BOUND_VARIABLE_1206940))))) (let ((_let_3665 (forall ((BOUND_VARIABLE_1310764 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1206915 tptp.nat)) (= (ho_6080 (ho_6079 k_6078 (ho_4726 BOUND_VARIABLE_1310764 BOUND_VARIABLE_1206915)) (ho_4516 k_4515 (ho_4287 k_4754 BOUND_VARIABLE_1206915))) (ho_4335 (ho_6258 k_6257 BOUND_VARIABLE_1310764) BOUND_VARIABLE_1206915))))) (let ((_let_3666 (forall ((BOUND_VARIABLE_1206904 tptp.nat) (BOUND_VARIABLE_1206905 tptp.nat)) (= (ho_4288 (ho_4287 k_6259 BOUND_VARIABLE_1206904) BOUND_VARIABLE_1206905) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206905)) (ho_4290 k_4289 BOUND_VARIABLE_1206904)))))) (let ((_let_3667 (forall ((BOUND_VARIABLE_1310794 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1206824 tptp.nat) (BOUND_VARIABLE_1206825 tptp.nat)) (= (ho_6080 (ho_6079 k_6078 (ho_4726 (ho_4756 k_4755 BOUND_VARIABLE_1310794) BOUND_VARIABLE_1206825)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4757 BOUND_VARIABLE_1206825) BOUND_VARIABLE_1206824))) (ho_4335 (ho_4726 (ho_4756 k_6260 BOUND_VARIABLE_1310794) BOUND_VARIABLE_1206824) BOUND_VARIABLE_1206825))))) (let ((_let_3668 (forall ((BOUND_VARIABLE_1206813 tptp.nat) (BOUND_VARIABLE_1206814 tptp.nat)) (= (ho_4288 (ho_4287 k_6261 BOUND_VARIABLE_1206813) BOUND_VARIABLE_1206814) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206814)) (ho_4290 k_4289 BOUND_VARIABLE_1206813)))))) (let ((_let_3669 (forall ((BOUND_VARIABLE_1310822 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1206790 tptp.nat)) (= (ho_5346 (ho_6084 k_6083 (ho_4215 BOUND_VARIABLE_1310822 BOUND_VARIABLE_1206790)) (ho_4516 k_4515 (ho_4287 k_4758 BOUND_VARIABLE_1206790))) (ho_4216 (ho_6263 k_6262 BOUND_VARIABLE_1310822) BOUND_VARIABLE_1206790))))) (let ((_let_3670 (forall ((BOUND_VARIABLE_1206779 tptp.nat) (BOUND_VARIABLE_1206780 tptp.nat)) (= (ho_4288 (ho_4287 k_6264 BOUND_VARIABLE_1206779) BOUND_VARIABLE_1206780) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206780)) (ho_4290 k_4289 BOUND_VARIABLE_1206779)))))) (let ((_let_3671 (forall ((BOUND_VARIABLE_1310852 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1206699 tptp.nat) (BOUND_VARIABLE_1206700 tptp.nat)) (= (ho_5346 (ho_6084 k_6083 (ho_4215 (ho_4760 k_4759 BOUND_VARIABLE_1310852) BOUND_VARIABLE_1206700)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4761 BOUND_VARIABLE_1206700) BOUND_VARIABLE_1206699))) (ho_4216 (ho_4215 (ho_4760 k_6265 BOUND_VARIABLE_1310852) BOUND_VARIABLE_1206699) BOUND_VARIABLE_1206700))))) (let ((_let_3672 (forall ((BOUND_VARIABLE_1206688 tptp.nat) (BOUND_VARIABLE_1206689 tptp.nat)) (= (ho_4288 (ho_4287 k_6266 BOUND_VARIABLE_1206688) BOUND_VARIABLE_1206689) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206689)) (ho_4290 k_4289 BOUND_VARIABLE_1206688)))))) (let ((_let_3673 (forall ((BOUND_VARIABLE_1206646 tptp.nat) (BOUND_VARIABLE_1206647 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) _let_5))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1206646) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1206647 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6267 BOUND_VARIABLE_1206646) BOUND_VARIABLE_1206647))))) (let ((_let_3674 (forall ((BOUND_VARIABLE_1310907 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1206627 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1310907 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206627) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6268 BOUND_VARIABLE_1310907) BOUND_VARIABLE_1206627)))))))) (let ((_let_3675 (forall ((BOUND_VARIABLE_1206616 tptp.nat) (BOUND_VARIABLE_1206617 tptp.nat)) (= (ho_4288 (ho_4287 k_6269 BOUND_VARIABLE_1206616) BOUND_VARIABLE_1206617) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206617)) (ho_4290 k_4289 BOUND_VARIABLE_1206616)))))) (let ((_let_3676 (forall ((BOUND_VARIABLE_1206574 tptp.nat) (BOUND_VARIABLE_1206575 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) _let_5))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1206574) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1206575 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6270 BOUND_VARIABLE_1206574) BOUND_VARIABLE_1206575))))) (let ((_let_3677 (forall ((BOUND_VARIABLE_1310957 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1206555 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1310957 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206555) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6271 BOUND_VARIABLE_1310957) BOUND_VARIABLE_1206555)))))))) (let ((_let_3678 (forall ((BOUND_VARIABLE_1206544 tptp.nat) (BOUND_VARIABLE_1206545 tptp.nat)) (= (ho_4288 (ho_4287 k_6272 BOUND_VARIABLE_1206544) BOUND_VARIABLE_1206545) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206545)) (ho_4290 k_4289 BOUND_VARIABLE_1206544)))))) (let ((_let_3679 (forall ((BOUND_VARIABLE_1206520 tptp.nat) (BOUND_VARIABLE_1206521 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206521)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206520) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6273 BOUND_VARIABLE_1206520) BOUND_VARIABLE_1206521)))))))) (let ((_let_3680 (forall ((BOUND_VARIABLE_1310999 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1206501 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1310999 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206501) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6274 BOUND_VARIABLE_1310999) BOUND_VARIABLE_1206501)))))))) (let ((_let_3681 (forall ((BOUND_VARIABLE_1206490 tptp.nat) (BOUND_VARIABLE_1206491 tptp.nat)) (= (ho_4288 (ho_4287 k_6275 BOUND_VARIABLE_1206490) BOUND_VARIABLE_1206491) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206491)) (ho_4290 k_4289 BOUND_VARIABLE_1206490)))))) (let ((_let_3682 (forall ((BOUND_VARIABLE_1206466 tptp.nat) (BOUND_VARIABLE_1206467 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206467)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206466) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6276 BOUND_VARIABLE_1206466) BOUND_VARIABLE_1206467)))))))) (let ((_let_3683 (forall ((BOUND_VARIABLE_1311041 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1206447 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1311041 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206447) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6277 BOUND_VARIABLE_1311041) BOUND_VARIABLE_1206447)))))))) (let ((_let_3684 (forall ((BOUND_VARIABLE_1206436 tptp.nat) (BOUND_VARIABLE_1206437 tptp.nat)) (= (ho_4288 (ho_4287 k_6278 BOUND_VARIABLE_1206436) BOUND_VARIABLE_1206437) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206437)) (ho_4290 k_4289 BOUND_VARIABLE_1206436)))))) (let ((_let_3685 (forall ((BOUND_VARIABLE_1206412 tptp.nat) (BOUND_VARIABLE_1206413 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206413)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206412) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6279 BOUND_VARIABLE_1206412) BOUND_VARIABLE_1206413)))))))) (let ((_let_3686 (forall ((BOUND_VARIABLE_1311083 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1206393 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4316 BOUND_VARIABLE_1311083 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206393) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4316 (ho_4249 k_6280 BOUND_VARIABLE_1311083) BOUND_VARIABLE_1206393)))))))) (let ((_let_3687 (forall ((BOUND_VARIABLE_1206382 tptp.nat) (BOUND_VARIABLE_1206383 tptp.nat)) (= (ho_4288 (ho_4287 k_6281 BOUND_VARIABLE_1206382) BOUND_VARIABLE_1206383) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206383)) (ho_4290 k_4289 BOUND_VARIABLE_1206382)))))) (let ((_let_3688 (forall ((BOUND_VARIABLE_1206358 tptp.nat) (BOUND_VARIABLE_1206359 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206359)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206358) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6282 BOUND_VARIABLE_1206358) BOUND_VARIABLE_1206359)))))))) (let ((_let_3689 (forall ((BOUND_VARIABLE_1311125 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1206339 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4245 BOUND_VARIABLE_1311125 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206339) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4245 (ho_4473 k_6283 BOUND_VARIABLE_1311125) BOUND_VARIABLE_1206339)))))))) (let ((_let_3690 (forall ((BOUND_VARIABLE_1206328 tptp.nat) (BOUND_VARIABLE_1206329 tptp.nat)) (= (ho_4288 (ho_4287 k_6284 BOUND_VARIABLE_1206328) BOUND_VARIABLE_1206329) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1206329)) (ho_4290 k_4289 BOUND_VARIABLE_1206328)))))) (let ((_let_3691 (forall ((BOUND_VARIABLE_1311151 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1206309 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1311151 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206309) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6285 BOUND_VARIABLE_1311151) BOUND_VARIABLE_1206309)))))))) (let ((_let_3692 (forall ((BOUND_VARIABLE_1206264 tptp.nat) (BOUND_VARIABLE_1206265 tptp.nat) (BOUND_VARIABLE_1206266 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206264) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206265) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206266 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6286 BOUND_VARIABLE_1206264) BOUND_VARIABLE_1206265) BOUND_VARIABLE_1206266))))) (let ((_let_3693 (forall ((BOUND_VARIABLE_1311193 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1206245 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1311193 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206245) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6287 BOUND_VARIABLE_1311193) BOUND_VARIABLE_1206245)))))))) (let ((_let_3694 (forall ((BOUND_VARIABLE_1206200 tptp.nat) (BOUND_VARIABLE_1206201 tptp.nat) (BOUND_VARIABLE_1206202 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206200) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206201) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206202 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6288 BOUND_VARIABLE_1206200) BOUND_VARIABLE_1206201) BOUND_VARIABLE_1206202))))) (let ((_let_3695 (forall ((BOUND_VARIABLE_1311235 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1206181 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4316 BOUND_VARIABLE_1311235 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206181) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4316 (ho_4249 k_6289 BOUND_VARIABLE_1311235) BOUND_VARIABLE_1206181)))))))) (let ((_let_3696 (forall ((BOUND_VARIABLE_1206136 tptp.nat) (BOUND_VARIABLE_1206137 tptp.nat) (BOUND_VARIABLE_1206138 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206136) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206137) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206138 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6290 BOUND_VARIABLE_1206136) BOUND_VARIABLE_1206137) BOUND_VARIABLE_1206138))))) (let ((_let_3697 (forall ((BOUND_VARIABLE_1311277 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1206117 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4245 BOUND_VARIABLE_1311277 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206117) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4245 (ho_4473 k_6291 BOUND_VARIABLE_1311277) BOUND_VARIABLE_1206117)))))))) (let ((_let_3698 (forall ((BOUND_VARIABLE_1206072 tptp.nat) (BOUND_VARIABLE_1206073 tptp.nat) (BOUND_VARIABLE_1206074 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1206072) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206073) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1206074 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6292 BOUND_VARIABLE_1206072) BOUND_VARIABLE_1206073) BOUND_VARIABLE_1206074))))) (let ((_let_3699 (forall ((BOUND_VARIABLE_1206048 tptp.nat) (BOUND_VARIABLE_1206049 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206049)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206048) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6293 BOUND_VARIABLE_1206048) BOUND_VARIABLE_1206049)))))))) (let ((_let_3700 (forall ((BOUND_VARIABLE_1311335 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1206029 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1311335 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1206029) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6294 BOUND_VARIABLE_1311335) BOUND_VARIABLE_1206029)))))))) (let ((_let_3701 (forall ((BOUND_VARIABLE_1206018 tptp.nat) (BOUND_VARIABLE_1206019 tptp.nat)) (= (ho_4288 (ho_4287 k_6295 BOUND_VARIABLE_1206018) BOUND_VARIABLE_1206019) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1206019)) (ho_4290 k_4289 BOUND_VARIABLE_1206018)))))) (let ((_let_3702 (forall ((BOUND_VARIABLE_1205994 tptp.nat) (BOUND_VARIABLE_1205995 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205995)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205994) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6296 BOUND_VARIABLE_1205994) BOUND_VARIABLE_1205995)))))))) (let ((_let_3703 (forall ((BOUND_VARIABLE_1311377 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1205975 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1311377 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205975) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6297 BOUND_VARIABLE_1311377) BOUND_VARIABLE_1205975)))))))) (let ((_let_3704 (forall ((BOUND_VARIABLE_1205964 tptp.nat) (BOUND_VARIABLE_1205965 tptp.nat)) (= (ho_4288 (ho_4287 k_6298 BOUND_VARIABLE_1205964) BOUND_VARIABLE_1205965) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205965)) (ho_4290 k_4289 BOUND_VARIABLE_1205964)))))) (let ((_let_3705 (forall ((BOUND_VARIABLE_1205940 tptp.nat) (BOUND_VARIABLE_1205941 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205941)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205940) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6299 BOUND_VARIABLE_1205940) BOUND_VARIABLE_1205941)))))))) (let ((_let_3706 (forall ((BOUND_VARIABLE_1311419 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1205921 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4316 BOUND_VARIABLE_1311419 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205921) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4316 (ho_4249 k_6300 BOUND_VARIABLE_1311419) BOUND_VARIABLE_1205921)))))))) (let ((_let_3707 (forall ((BOUND_VARIABLE_1205910 tptp.nat) (BOUND_VARIABLE_1205911 tptp.nat)) (= (ho_4288 (ho_4287 k_6301 BOUND_VARIABLE_1205910) BOUND_VARIABLE_1205911) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205911)) (ho_4290 k_4289 BOUND_VARIABLE_1205910)))))) (let ((_let_3708 (forall ((BOUND_VARIABLE_1205886 tptp.nat) (BOUND_VARIABLE_1205887 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205887)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205886) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6302 BOUND_VARIABLE_1205886) BOUND_VARIABLE_1205887)))))))) (let ((_let_3709 (forall ((BOUND_VARIABLE_1311461 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1205867 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4245 BOUND_VARIABLE_1311461 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205867) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4245 (ho_4473 k_6303 BOUND_VARIABLE_1311461) BOUND_VARIABLE_1205867)))))))) (let ((_let_3710 (forall ((BOUND_VARIABLE_1205856 tptp.nat) (BOUND_VARIABLE_1205857 tptp.nat)) (= (ho_4288 (ho_4287 k_6304 BOUND_VARIABLE_1205856) BOUND_VARIABLE_1205857) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1205857)) (ho_4290 k_4289 BOUND_VARIABLE_1205856)))))) (let ((_let_3711 (forall ((BOUND_VARIABLE_1205833 tptp.rat) (BOUND_VARIABLE_1205834 tptp.nat) (BOUND_VARIABLE_1205835 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1205833)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205834) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1205835) (ho_4442 (ho_4458 (ho_4699 k_6305 BOUND_VARIABLE_1205833) BOUND_VARIABLE_1205834) BOUND_VARIABLE_1205835)))))))))))) (let ((_let_3712 (forall ((BOUND_VARIABLE_1205810 tptp.real) (BOUND_VARIABLE_1205811 tptp.nat) (BOUND_VARIABLE_1205812 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1205810)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205811) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1205812) (ho_4258 (ho_4273 (ho_4696 k_6306 BOUND_VARIABLE_1205810) BOUND_VARIABLE_1205811) BOUND_VARIABLE_1205812)))))))))) (let ((_let_3713 (forall ((BOUND_VARIABLE_1205787 tptp.rat) (BOUND_VARIABLE_1205788 tptp.nat) (BOUND_VARIABLE_1205789 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1205787)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205788) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1205789) (ho_4442 (ho_4458 (ho_4699 k_6307 BOUND_VARIABLE_1205787) BOUND_VARIABLE_1205788) BOUND_VARIABLE_1205789)))))))))))) (let ((_let_3714 (forall ((BOUND_VARIABLE_1205764 tptp.real) (BOUND_VARIABLE_1205765 tptp.nat) (BOUND_VARIABLE_1205766 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1205764)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205765) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1205766) (ho_4258 (ho_4273 (ho_4696 k_6308 BOUND_VARIABLE_1205764) BOUND_VARIABLE_1205765) BOUND_VARIABLE_1205766)))))))))) (let ((_let_3715 (forall ((BOUND_VARIABLE_1205741 tptp.rat) (BOUND_VARIABLE_1205742 tptp.nat) (BOUND_VARIABLE_1205743 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1205741)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205742) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1205743) (ho_4442 (ho_4458 (ho_4699 k_6309 BOUND_VARIABLE_1205741) BOUND_VARIABLE_1205742) BOUND_VARIABLE_1205743)))))))))))) (let ((_let_3716 (forall ((BOUND_VARIABLE_1205718 tptp.real) (BOUND_VARIABLE_1205719 tptp.nat) (BOUND_VARIABLE_1205720 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1205718)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205719) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1205720) (ho_4258 (ho_4273 (ho_4696 k_6310 BOUND_VARIABLE_1205718) BOUND_VARIABLE_1205719) BOUND_VARIABLE_1205720)))))))))) (let ((_let_3717 (forall ((BOUND_VARIABLE_1205695 tptp.rat) (BOUND_VARIABLE_1205696 tptp.nat) (BOUND_VARIABLE_1205697 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1205695)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205696) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1205697) (ho_4442 (ho_4458 (ho_4699 k_6311 BOUND_VARIABLE_1205695) BOUND_VARIABLE_1205696) BOUND_VARIABLE_1205697)))))))))))) (let ((_let_3718 (forall ((BOUND_VARIABLE_1205668 tptp.rat) (BOUND_VARIABLE_1205669 tptp.nat) (BOUND_VARIABLE_1205670 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1205668) _let_6))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205669) (ho_4442 (ho_4448 _let_8 _let_3) _let_6)))) BOUND_VARIABLE_1205670) (ho_4442 (ho_4458 (ho_4699 k_6312 BOUND_VARIABLE_1205668) BOUND_VARIABLE_1205669) BOUND_VARIABLE_1205670))))))))))))) (let ((_let_3719 (forall ((BOUND_VARIABLE_1205645 tptp.real) (BOUND_VARIABLE_1205646 tptp.nat) (BOUND_VARIABLE_1205647 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1205645)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205646) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1205647) (ho_4258 (ho_4273 (ho_4696 k_6313 BOUND_VARIABLE_1205645) BOUND_VARIABLE_1205646) BOUND_VARIABLE_1205647)))))))))) (let ((_let_3720 (forall ((BOUND_VARIABLE_1205618 tptp.real) (BOUND_VARIABLE_1205619 tptp.nat) (BOUND_VARIABLE_1205620 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1205618) _let_4))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205619) (ho_4258 (ho_4265 _let_6 _let_1) _let_4)))) BOUND_VARIABLE_1205620) (ho_4258 (ho_4273 (ho_4696 k_6314 BOUND_VARIABLE_1205618) BOUND_VARIABLE_1205619) BOUND_VARIABLE_1205620))))))))))) (let ((_let_3721 (forall ((BOUND_VARIABLE_1205597 tptp.complex) (BOUND_VARIABLE_1205598 tptp.nat) (BOUND_VARIABLE_1205599 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1205597)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1205598) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1205599) (ho_4703 (ho_4709 (ho_4712 k_6315 BOUND_VARIABLE_1205597) BOUND_VARIABLE_1205598) BOUND_VARIABLE_1205599)))))) (let ((_let_3722 (forall ((BOUND_VARIABLE_1205574 tptp.complex) (BOUND_VARIABLE_1205575 tptp.nat) (BOUND_VARIABLE_1205576 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1205574) _let_2))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1205575) (ho_4703 (ho_4705 k_4704 _let_1) _let_2)))) BOUND_VARIABLE_1205576) (ho_4703 (ho_4709 (ho_4712 k_6316 BOUND_VARIABLE_1205574) BOUND_VARIABLE_1205575) BOUND_VARIABLE_1205576))))))) (let ((_let_3723 (forall ((BOUND_VARIABLE_1205551 tptp.rat) (BOUND_VARIABLE_1205552 tptp.nat) (BOUND_VARIABLE_1205553 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1205551)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205552) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1205553) (ho_4442 (ho_4458 (ho_4699 k_6317 BOUND_VARIABLE_1205551) BOUND_VARIABLE_1205552) BOUND_VARIABLE_1205553)))))))))))) (let ((_let_3724 (forall ((BOUND_VARIABLE_1205524 tptp.rat) (BOUND_VARIABLE_1205525 tptp.nat) (BOUND_VARIABLE_1205526 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4442 _let_5 _let_3))) (let ((_let_7 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_8 (ho_4447 _let_7 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_7 k_4697) (ho_4442 (ho_4448 _let_8 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_8 BOUND_VARIABLE_1205524) _let_6))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1205525) (ho_4442 (ho_4448 _let_8 _let_3) _let_6)))) BOUND_VARIABLE_1205526) (ho_4442 (ho_4458 (ho_4699 k_6318 BOUND_VARIABLE_1205524) BOUND_VARIABLE_1205525) BOUND_VARIABLE_1205526))))))))))))) (let ((_let_3725 (forall ((BOUND_VARIABLE_1205501 tptp.real) (BOUND_VARIABLE_1205502 tptp.nat) (BOUND_VARIABLE_1205503 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1205501)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205502) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1205503) (ho_4258 (ho_4273 (ho_4696 k_6319 BOUND_VARIABLE_1205501) BOUND_VARIABLE_1205502) BOUND_VARIABLE_1205503)))))))))) (let ((_let_3726 (forall ((BOUND_VARIABLE_1205474 tptp.real) (BOUND_VARIABLE_1205475 tptp.nat) (BOUND_VARIABLE_1205476 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_5 k_4275) (ho_4258 (ho_4265 _let_6 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_6 BOUND_VARIABLE_1205474) _let_4))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1205475) (ho_4258 (ho_4265 _let_6 _let_1) _let_4)))) BOUND_VARIABLE_1205476) (ho_4258 (ho_4273 (ho_4696 k_6320 BOUND_VARIABLE_1205474) BOUND_VARIABLE_1205475) BOUND_VARIABLE_1205476))))))))))) (let ((_let_3727 (forall ((BOUND_VARIABLE_1205453 tptp.complex) (BOUND_VARIABLE_1205454 tptp.nat) (BOUND_VARIABLE_1205455 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1205453)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1205454) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1205455) (ho_4703 (ho_4709 (ho_4712 k_6321 BOUND_VARIABLE_1205453) BOUND_VARIABLE_1205454) BOUND_VARIABLE_1205455)))))) (let ((_let_3728 (forall ((BOUND_VARIABLE_1205430 tptp.complex) (BOUND_VARIABLE_1205431 tptp.nat) (BOUND_VARIABLE_1205432 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1205430) _let_2))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1205431) (ho_4703 (ho_4705 k_4704 _let_1) _let_2)))) BOUND_VARIABLE_1205432) (ho_4703 (ho_4709 (ho_4712 k_6322 BOUND_VARIABLE_1205430) BOUND_VARIABLE_1205431) BOUND_VARIABLE_1205432))))))) (let ((_let_3729 (forall ((BOUND_VARIABLE_1205376 tptp.nat) (BOUND_VARIABLE_1205377 tptp.nat) (BOUND_VARIABLE_1205378 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205376) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205377) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1205378 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6323 BOUND_VARIABLE_1205376) BOUND_VARIABLE_1205377) BOUND_VARIABLE_1205378))))) (let ((_let_3730 (forall ((BOUND_VARIABLE_1205332 tptp.nat) (BOUND_VARIABLE_1205333 tptp.nat) (BOUND_VARIABLE_1205334 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205332) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205333) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1205334 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6324 BOUND_VARIABLE_1205332) BOUND_VARIABLE_1205333) BOUND_VARIABLE_1205334))))) (let ((_let_3731 (forall ((BOUND_VARIABLE_1205278 tptp.nat) (BOUND_VARIABLE_1205279 tptp.nat) (BOUND_VARIABLE_1205280 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205278) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205279) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1205280 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6325 BOUND_VARIABLE_1205278) BOUND_VARIABLE_1205279) BOUND_VARIABLE_1205280))))) (let ((_let_3732 (forall ((BOUND_VARIABLE_1205234 tptp.nat) (BOUND_VARIABLE_1205235 tptp.nat) (BOUND_VARIABLE_1205236 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205234) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205235) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1205236 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6326 BOUND_VARIABLE_1205234) BOUND_VARIABLE_1205235) BOUND_VARIABLE_1205236))))) (let ((_let_3733 (forall ((BOUND_VARIABLE_1205180 tptp.nat) (BOUND_VARIABLE_1205181 tptp.nat) (BOUND_VARIABLE_1205182 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205180) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205181) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1205182 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6327 BOUND_VARIABLE_1205180) BOUND_VARIABLE_1205181) BOUND_VARIABLE_1205182))))) (let ((_let_3734 (forall ((BOUND_VARIABLE_1205136 tptp.nat) (BOUND_VARIABLE_1205137 tptp.nat) (BOUND_VARIABLE_1205138 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205136) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205137) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1205138 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6328 BOUND_VARIABLE_1205136) BOUND_VARIABLE_1205137) BOUND_VARIABLE_1205138))))) (let ((_let_3735 (forall ((BOUND_VARIABLE_1205082 tptp.nat) (BOUND_VARIABLE_1205083 tptp.nat) (BOUND_VARIABLE_1205084 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205082) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205083) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1205084 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6329 BOUND_VARIABLE_1205082) BOUND_VARIABLE_1205083) BOUND_VARIABLE_1205084))))) (let ((_let_3736 (forall ((BOUND_VARIABLE_1205038 tptp.nat) (BOUND_VARIABLE_1205039 tptp.nat) (BOUND_VARIABLE_1205040 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1205038) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1205039) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1205040 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6330 BOUND_VARIABLE_1205038) BOUND_VARIABLE_1205039) BOUND_VARIABLE_1205040))))) (let ((_let_3737 (forall ((BOUND_VARIABLE_1204994 tptp.nat) (BOUND_VARIABLE_1204995 tptp.nat) (BOUND_VARIABLE_1204996 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1204994) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204995) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1204996 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6331 BOUND_VARIABLE_1204994) BOUND_VARIABLE_1204995) BOUND_VARIABLE_1204996))))) (let ((_let_3738 (forall ((BOUND_VARIABLE_1204939 tptp.nat) (BOUND_VARIABLE_1204940 tptp.nat) (BOUND_VARIABLE_1204941 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 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k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1204895) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204896) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1204897 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6333 BOUND_VARIABLE_1204895) BOUND_VARIABLE_1204896) BOUND_VARIABLE_1204897))))) (let ((_let_3740 (forall ((BOUND_VARIABLE_1204840 tptp.nat) (BOUND_VARIABLE_1204841 tptp.nat) (BOUND_VARIABLE_1204842 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204840) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204841) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1204842 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6334 BOUND_VARIABLE_1204840) BOUND_VARIABLE_1204841) BOUND_VARIABLE_1204842))))) (let ((_let_3741 (forall ((BOUND_VARIABLE_1204796 tptp.nat) (BOUND_VARIABLE_1204797 tptp.nat) (BOUND_VARIABLE_1204798 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1204796) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204797) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1204798 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6335 BOUND_VARIABLE_1204796) BOUND_VARIABLE_1204797) BOUND_VARIABLE_1204798))))) (let ((_let_3742 (forall ((BOUND_VARIABLE_1204741 tptp.nat) (BOUND_VARIABLE_1204742 tptp.nat) (BOUND_VARIABLE_1204743 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204741) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204742) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1204743 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6336 BOUND_VARIABLE_1204741) BOUND_VARIABLE_1204742) BOUND_VARIABLE_1204743))))) (let ((_let_3743 (forall ((BOUND_VARIABLE_1204697 tptp.nat) (BOUND_VARIABLE_1204698 tptp.nat) (BOUND_VARIABLE_1204699 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1204697) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204698) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1204699 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6337 BOUND_VARIABLE_1204697) BOUND_VARIABLE_1204698) BOUND_VARIABLE_1204699))))) (let ((_let_3744 (forall ((BOUND_VARIABLE_1204642 tptp.nat) (BOUND_VARIABLE_1204643 tptp.nat) (BOUND_VARIABLE_1204644 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204642) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1204643) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1204644 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6338 BOUND_VARIABLE_1204642) BOUND_VARIABLE_1204643) BOUND_VARIABLE_1204644))))) (let ((_let_3745 (forall ((BOUND_VARIABLE_1204590 tptp.nat) (BOUND_VARIABLE_1204591 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204590) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1204591 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6339 BOUND_VARIABLE_1204590) BOUND_VARIABLE_1204591))))) (let ((_let_3746 (forall ((BOUND_VARIABLE_1204548 tptp.nat) (BOUND_VARIABLE_1204549 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204548) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204549 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6340 BOUND_VARIABLE_1204548) BOUND_VARIABLE_1204549))))) (let ((_let_3747 (forall ((BOUND_VARIABLE_1204496 tptp.nat) (BOUND_VARIABLE_1204497 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204496) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1204497 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6341 BOUND_VARIABLE_1204496) BOUND_VARIABLE_1204497))))) (let ((_let_3748 (forall ((BOUND_VARIABLE_1204454 tptp.nat) (BOUND_VARIABLE_1204455 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204454) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204455 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6342 BOUND_VARIABLE_1204454) BOUND_VARIABLE_1204455))))) (let ((_let_3749 (forall ((BOUND_VARIABLE_1204402 tptp.nat) (BOUND_VARIABLE_1204403 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204402) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1204403 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6343 BOUND_VARIABLE_1204402) BOUND_VARIABLE_1204403))))) (let ((_let_3750 (forall ((BOUND_VARIABLE_1204360 tptp.nat) (BOUND_VARIABLE_1204361 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204360) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204361 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6344 BOUND_VARIABLE_1204360) BOUND_VARIABLE_1204361))))) (let ((_let_3751 (forall ((BOUND_VARIABLE_1204308 tptp.nat) (BOUND_VARIABLE_1204309 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204308) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1204309 (ho_4216 (ho_4468 k_4467 _let_6) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_6))))))))))))) (ho_4288 (ho_4287 k_6345 BOUND_VARIABLE_1204308) BOUND_VARIABLE_1204309))))) (let ((_let_3752 (forall ((BOUND_VARIABLE_1204266 tptp.nat) (BOUND_VARIABLE_1204267 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204266) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204267 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6346 BOUND_VARIABLE_1204266) BOUND_VARIABLE_1204267))))) (let ((_let_3753 (forall ((BOUND_VARIABLE_1204257 tptp.int) (BOUND_VARIABLE_1204258 tptp.int)) (= (ho_4310 (ho_4309 k_6347 BOUND_VARIABLE_1204257) BOUND_VARIABLE_1204258) (= BOUND_VARIABLE_1204257 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204258) BOUND_VARIABLE_1204257)))))) (let ((_let_3754 (forall ((BOUND_VARIABLE_1204248 tptp.int) (BOUND_VARIABLE_1204249 tptp.int)) (= (ho_4310 (ho_4309 k_6348 BOUND_VARIABLE_1204248) BOUND_VARIABLE_1204249) (= BOUND_VARIABLE_1204248 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204249) BOUND_VARIABLE_1204248)))))) (let ((_let_3755 (forall ((BOUND_VARIABLE_1204239 tptp.int) (BOUND_VARIABLE_1204240 tptp.int)) (= (ho_4310 (ho_4309 k_6349 BOUND_VARIABLE_1204239) BOUND_VARIABLE_1204240) (= BOUND_VARIABLE_1204239 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204240) BOUND_VARIABLE_1204239)))))) (let ((_let_3756 (forall ((BOUND_VARIABLE_1204230 tptp.int) (BOUND_VARIABLE_1204231 tptp.int)) (= (ho_4310 (ho_4309 k_6350 BOUND_VARIABLE_1204230) BOUND_VARIABLE_1204231) (= BOUND_VARIABLE_1204230 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204231) BOUND_VARIABLE_1204230)))))) (let ((_let_3757 (forall ((BOUND_VARIABLE_1204221 tptp.int) (BOUND_VARIABLE_1204222 tptp.int)) (= (ho_4310 (ho_4309 k_6351 BOUND_VARIABLE_1204221) BOUND_VARIABLE_1204222) (= BOUND_VARIABLE_1204221 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204222) BOUND_VARIABLE_1204221)))))) (let ((_let_3758 (forall ((BOUND_VARIABLE_1204212 tptp.int) (BOUND_VARIABLE_1204213 tptp.int)) (= (ho_4310 (ho_4309 k_6352 BOUND_VARIABLE_1204212) BOUND_VARIABLE_1204213) (= BOUND_VARIABLE_1204212 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204213) BOUND_VARIABLE_1204212)))))) (let ((_let_3759 (forall ((BOUND_VARIABLE_1204203 tptp.int) (BOUND_VARIABLE_1204204 tptp.int)) (= (ho_4310 (ho_4309 k_6353 BOUND_VARIABLE_1204203) BOUND_VARIABLE_1204204) (= BOUND_VARIABLE_1204203 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204204) BOUND_VARIABLE_1204203)))))) (let ((_let_3760 (forall ((BOUND_VARIABLE_1204194 tptp.int) (BOUND_VARIABLE_1204195 tptp.int)) (= (ho_4310 (ho_4309 k_6354 BOUND_VARIABLE_1204194) BOUND_VARIABLE_1204195) (= BOUND_VARIABLE_1204194 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204195) BOUND_VARIABLE_1204194)))))) (let ((_let_3761 (forall ((BOUND_VARIABLE_1204185 tptp.int) (BOUND_VARIABLE_1204186 tptp.int)) (= (ho_4310 (ho_4309 k_6355 BOUND_VARIABLE_1204185) BOUND_VARIABLE_1204186) (= BOUND_VARIABLE_1204185 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204186) BOUND_VARIABLE_1204185)))))) (let ((_let_3762 (forall ((BOUND_VARIABLE_1204176 tptp.int) (BOUND_VARIABLE_1204177 tptp.int)) (= (ho_4310 (ho_4309 k_6356 BOUND_VARIABLE_1204176) BOUND_VARIABLE_1204177) (= BOUND_VARIABLE_1204176 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204177) BOUND_VARIABLE_1204176)))))) (let ((_let_3763 (forall ((BOUND_VARIABLE_1204167 tptp.int) (BOUND_VARIABLE_1204168 tptp.int)) (= (ho_4310 (ho_4309 k_6357 BOUND_VARIABLE_1204167) BOUND_VARIABLE_1204168) (= BOUND_VARIABLE_1204167 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1204168) BOUND_VARIABLE_1204167)))))) (let ((_let_3764 (forall ((BOUND_VARIABLE_1204150 tptp.int) (BOUND_VARIABLE_1204151 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1204150) (ho_4209 _let_2 (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1204151) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1))))) (ho_4335 (ho_4334 k_6358 BOUND_VARIABLE_1204150) BOUND_VARIABLE_1204151))))))) (let ((_let_3765 (forall ((BOUND_VARIABLE_1204108 tptp.nat) (BOUND_VARIABLE_1204109 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204108) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204109 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6359 BOUND_VARIABLE_1204108) BOUND_VARIABLE_1204109))))) (let ((_let_3766 (forall ((BOUND_VARIABLE_1204093 tptp.nat) (BOUND_VARIABLE_1204094 tptp.nat)) (= (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1204093) (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) BOUND_VARIABLE_1204094) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4216 (ho_4215 k_6360 BOUND_VARIABLE_1204093) BOUND_VARIABLE_1204094))))) (let ((_let_3767 (forall ((BOUND_VARIABLE_1204051 tptp.nat) (BOUND_VARIABLE_1204052 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1204051) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1204052 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6361 BOUND_VARIABLE_1204051) BOUND_VARIABLE_1204052))))) (let ((_let_3768 (forall ((BOUND_VARIABLE_1204028 tptp.real) (BOUND_VARIABLE_1204029 tptp.nat) (BOUND_VARIABLE_1204030 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1204028)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1204029) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1204030) (ho_4258 (ho_4273 (ho_4696 k_6362 BOUND_VARIABLE_1204028) BOUND_VARIABLE_1204029) BOUND_VARIABLE_1204030)))))))))) (let ((_let_3769 (forall ((BOUND_VARIABLE_1204010 tptp.real) (BOUND_VARIABLE_1204011 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_2) k_4259))) (= (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1204010) (ho_4258 _let_3 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1204011) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 _let_3 _let_1))))) (ho_4245 (ho_4244 k_6363 BOUND_VARIABLE_1204010) BOUND_VARIABLE_1204011))))))))) (let ((_let_3770 (forall ((BOUND_VARIABLE_1203968 tptp.nat) (BOUND_VARIABLE_1203969 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1203968) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1203969 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6364 BOUND_VARIABLE_1203968) BOUND_VARIABLE_1203969))))) (let ((_let_3771 (forall ((BOUND_VARIABLE_1203945 tptp.rat) (BOUND_VARIABLE_1203946 tptp.nat) (BOUND_VARIABLE_1203947 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1203945)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1203946) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1203947) (ho_4442 (ho_4458 (ho_4699 k_6365 BOUND_VARIABLE_1203945) BOUND_VARIABLE_1203946) BOUND_VARIABLE_1203947)))))))))))) (let ((_let_3772 (forall ((BOUND_VARIABLE_1203927 tptp.rat) (BOUND_VARIABLE_1203928 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_4) k_4443))) (= (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1203927) (ho_4442 _let_5 (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1203928) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 _let_5 _let_3))))) (ho_4316 (ho_4799 k_6366 BOUND_VARIABLE_1203927) BOUND_VARIABLE_1203928))))))))))) (let ((_let_3773 (forall ((BOUND_VARIABLE_1203885 tptp.nat) (BOUND_VARIABLE_1203886 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1203885) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1203886 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6367 BOUND_VARIABLE_1203885) BOUND_VARIABLE_1203886))))) (let ((_let_3774 (forall ((BOUND_VARIABLE_1203864 tptp.complex) (BOUND_VARIABLE_1203865 tptp.nat) (BOUND_VARIABLE_1203866 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1203864)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1203865) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1203866) (ho_4703 (ho_4709 (ho_4712 k_6368 BOUND_VARIABLE_1203864) BOUND_VARIABLE_1203865) BOUND_VARIABLE_1203866)))))) (let ((_let_3775 (forall ((BOUND_VARIABLE_1203847 tptp.complex) (BOUND_VARIABLE_1203848 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1203847) (ho_4703 k_4702 (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1203848) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) (ho_4767 (ho_4766 k_6369 BOUND_VARIABLE_1203847) BOUND_VARIABLE_1203848)))))) (let ((_let_3776 (forall ((BOUND_VARIABLE_1203805 tptp.nat) (BOUND_VARIABLE_1203806 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1203805) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1203806 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6370 BOUND_VARIABLE_1203805) BOUND_VARIABLE_1203806))))) (let ((_let_3777 (forall ((BOUND_VARIABLE_1312812 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1203776 tptp.nat) (BOUND_VARIABLE_1203777 tptp.nat) (BOUND_VARIABLE_1203778 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1312812 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203776) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203777) _let_2)))) BOUND_VARIABLE_1203778)) (ho_4335 (ho_4726 (ho_6373 (ho_6372 k_6371 BOUND_VARIABLE_1312812) BOUND_VARIABLE_1203776) BOUND_VARIABLE_1203777) BOUND_VARIABLE_1203778)))))))) (let ((_let_3778 (forall ((BOUND_VARIABLE_1203731 tptp.nat) (BOUND_VARIABLE_1203732 tptp.nat) (BOUND_VARIABLE_1203733 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1203731) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203732) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203733 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6374 BOUND_VARIABLE_1203731) BOUND_VARIABLE_1203732) BOUND_VARIABLE_1203733))))) (let ((_let_3779 (forall ((BOUND_VARIABLE_1312869 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1203702 tptp.nat) (BOUND_VARIABLE_1203703 tptp.nat) (BOUND_VARIABLE_1203704 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1312869 (ho_4216 (ho_4215 k_4223 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203702) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203703) _let_2)))) BOUND_VARIABLE_1203704)) (ho_4216 (ho_4215 (ho_4269 (ho_6376 k_6375 BOUND_VARIABLE_1312869) BOUND_VARIABLE_1203702) BOUND_VARIABLE_1203703) BOUND_VARIABLE_1203704)))))))) (let ((_let_3780 (forall ((BOUND_VARIABLE_1203657 tptp.nat) (BOUND_VARIABLE_1203658 tptp.nat) (BOUND_VARIABLE_1203659 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1203657) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203658) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203659 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6377 BOUND_VARIABLE_1203657) BOUND_VARIABLE_1203658) BOUND_VARIABLE_1203659))))) (let ((_let_3781 (forall ((BOUND_VARIABLE_1312921 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1203634 tptp.nat) (BOUND_VARIABLE_1203635 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1312921 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1203634) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203635) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4335 (ho_4726 (ho_4834 k_6378 BOUND_VARIABLE_1312921) BOUND_VARIABLE_1203634) BOUND_VARIABLE_1203635)))))))) (let ((_let_3782 (forall ((BOUND_VARIABLE_1203623 tptp.nat) (BOUND_VARIABLE_1203624 tptp.nat)) (= (ho_4288 (ho_4287 k_6379 BOUND_VARIABLE_1203623) BOUND_VARIABLE_1203624) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1203624)) (ho_4290 k_4289 BOUND_VARIABLE_1203623)))))) (let ((_let_3783 (forall ((BOUND_VARIABLE_1312951 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1203600 tptp.nat) (BOUND_VARIABLE_1203601 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1312951 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1203600) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203601) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4216 (ho_4215 (ho_4730 k_6380 BOUND_VARIABLE_1312951) BOUND_VARIABLE_1203600) BOUND_VARIABLE_1203601)))))))) (let ((_let_3784 (forall ((BOUND_VARIABLE_1203589 tptp.nat) (BOUND_VARIABLE_1203590 tptp.nat)) (= (ho_4288 (ho_4287 k_6381 BOUND_VARIABLE_1203589) BOUND_VARIABLE_1203590) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1203590)) (ho_4290 k_4289 BOUND_VARIABLE_1203589)))))) (let ((_let_3785 (forall ((BOUND_VARIABLE_1203562 tptp.nat) (BOUND_VARIABLE_1203563 tptp.nat) (BOUND_VARIABLE_1203564 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1203562) _let_8))) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1203563) _let_8))) BOUND_VARIABLE_1203564) (ho_4442 (ho_4458 (ho_4718 k_6382 BOUND_VARIABLE_1203562) BOUND_VARIABLE_1203563) BOUND_VARIABLE_1203564)))))))))))))) (let ((_let_3786 (forall ((BOUND_VARIABLE_1203535 tptp.nat) (BOUND_VARIABLE_1203536 tptp.nat) (BOUND_VARIABLE_1203537 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1203535) _let_6))) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1203536) _let_6))) BOUND_VARIABLE_1203537) (ho_4258 (ho_4273 (ho_4715 k_6383 BOUND_VARIABLE_1203535) BOUND_VARIABLE_1203536) BOUND_VARIABLE_1203537)))))))))))) (let ((_let_3787 (forall ((BOUND_VARIABLE_1203508 tptp.rat) (BOUND_VARIABLE_1203509 tptp.nat) (BOUND_VARIABLE_1203510 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1203508) _let_3))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1203509) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1203510) (ho_4442 (ho_4458 (ho_4699 k_6384 BOUND_VARIABLE_1203508) BOUND_VARIABLE_1203509) BOUND_VARIABLE_1203510)))))))))))) (let ((_let_3788 (forall ((BOUND_VARIABLE_1203485 tptp.rat) (BOUND_VARIABLE_1203486 tptp.nat) (BOUND_VARIABLE_1203487 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1203485)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1203486) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1203487) (ho_4442 (ho_4458 (ho_4699 k_6385 BOUND_VARIABLE_1203485) BOUND_VARIABLE_1203486) BOUND_VARIABLE_1203487)))))))))))) (let ((_let_3789 (forall ((BOUND_VARIABLE_1203458 tptp.real) (BOUND_VARIABLE_1203459 tptp.nat) (BOUND_VARIABLE_1203460 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1203458) _let_1))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1203459) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1203460) (ho_4258 (ho_4273 (ho_4696 k_6386 BOUND_VARIABLE_1203458) BOUND_VARIABLE_1203459) BOUND_VARIABLE_1203460)))))))))) (let ((_let_3790 (forall ((BOUND_VARIABLE_1203435 tptp.real) (BOUND_VARIABLE_1203436 tptp.nat) (BOUND_VARIABLE_1203437 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1203435)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1203436) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1203437) (ho_4258 (ho_4273 (ho_4696 k_6387 BOUND_VARIABLE_1203435) BOUND_VARIABLE_1203436) BOUND_VARIABLE_1203437)))))))))) (let ((_let_3791 (forall ((BOUND_VARIABLE_1203412 tptp.complex) (BOUND_VARIABLE_1203413 tptp.nat) (BOUND_VARIABLE_1203414 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1203412) _let_1))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1203413) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1203414) (ho_4703 (ho_4709 (ho_4712 k_6388 BOUND_VARIABLE_1203412) BOUND_VARIABLE_1203413) BOUND_VARIABLE_1203414)))))) (let ((_let_3792 (forall ((BOUND_VARIABLE_1203391 tptp.complex) (BOUND_VARIABLE_1203392 tptp.nat) (BOUND_VARIABLE_1203393 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1203391)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1203392) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1203393) (ho_4703 (ho_4709 (ho_4712 k_6389 BOUND_VARIABLE_1203391) BOUND_VARIABLE_1203392) BOUND_VARIABLE_1203393)))))) (let ((_let_3793 (forall ((BOUND_VARIABLE_1203382 tptp.int) (BOUND_VARIABLE_1203383 tptp.int)) (= (ho_4310 (ho_4309 k_6390 BOUND_VARIABLE_1203382) BOUND_VARIABLE_1203383) (= BOUND_VARIABLE_1203382 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203383) BOUND_VARIABLE_1203382)))))) (let ((_let_3794 (forall ((BOUND_VARIABLE_1203373 tptp.int) (BOUND_VARIABLE_1203374 tptp.int)) (= (ho_4310 (ho_4309 k_6391 BOUND_VARIABLE_1203373) BOUND_VARIABLE_1203374) (= BOUND_VARIABLE_1203373 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203374) BOUND_VARIABLE_1203373)))))) (let ((_let_3795 (forall ((BOUND_VARIABLE_1203364 tptp.int) (BOUND_VARIABLE_1203365 tptp.int)) (= (ho_4310 (ho_4309 k_6392 BOUND_VARIABLE_1203364) BOUND_VARIABLE_1203365) (= BOUND_VARIABLE_1203364 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203365) BOUND_VARIABLE_1203364)))))) (let ((_let_3796 (forall ((BOUND_VARIABLE_1203355 tptp.int) (BOUND_VARIABLE_1203356 tptp.int)) (= (ho_4310 (ho_4309 k_6393 BOUND_VARIABLE_1203355) BOUND_VARIABLE_1203356) (= BOUND_VARIABLE_1203355 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203356) BOUND_VARIABLE_1203355)))))) (let ((_let_3797 (forall ((BOUND_VARIABLE_1203346 tptp.int) (BOUND_VARIABLE_1203347 tptp.int)) (= (ho_4310 (ho_4309 k_6394 BOUND_VARIABLE_1203346) BOUND_VARIABLE_1203347) (= BOUND_VARIABLE_1203346 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203347) BOUND_VARIABLE_1203346)))))) (let ((_let_3798 (forall ((BOUND_VARIABLE_1203337 tptp.int) (BOUND_VARIABLE_1203338 tptp.int)) (= (ho_4310 (ho_4309 k_6395 BOUND_VARIABLE_1203337) BOUND_VARIABLE_1203338) (= BOUND_VARIABLE_1203337 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203338) BOUND_VARIABLE_1203337)))))) (let ((_let_3799 (forall ((BOUND_VARIABLE_1203328 tptp.int) (BOUND_VARIABLE_1203329 tptp.int)) (= (ho_4310 (ho_4309 k_6396 BOUND_VARIABLE_1203328) BOUND_VARIABLE_1203329) (= BOUND_VARIABLE_1203328 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203329) BOUND_VARIABLE_1203328)))))) (let ((_let_3800 (forall ((BOUND_VARIABLE_1203319 tptp.int) (BOUND_VARIABLE_1203320 tptp.int)) (= (ho_4310 (ho_4309 k_6397 BOUND_VARIABLE_1203319) BOUND_VARIABLE_1203320) (= BOUND_VARIABLE_1203319 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203320) BOUND_VARIABLE_1203319)))))) (let ((_let_3801 (forall ((BOUND_VARIABLE_1203310 tptp.int) (BOUND_VARIABLE_1203311 tptp.int)) (= (ho_4310 (ho_4309 k_6398 BOUND_VARIABLE_1203310) BOUND_VARIABLE_1203311) (= BOUND_VARIABLE_1203310 (ho_4209 (ho_4211 k_4311 BOUND_VARIABLE_1203311) BOUND_VARIABLE_1203310)))))) (let ((_let_3802 (forall ((BOUND_VARIABLE_1203240 tptp.nat) (BOUND_VARIABLE_1203241 tptp.nat) (BOUND_VARIABLE_1203242 tptp.nat) (BOUND_VARIABLE_1203243 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203242) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203240) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203241) _let_2)) _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203243 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_6399 BOUND_VARIABLE_1203240) BOUND_VARIABLE_1203241) BOUND_VARIABLE_1203242) BOUND_VARIABLE_1203243))))) (let ((_let_3803 (forall ((BOUND_VARIABLE_1313250 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1203216 tptp.nat) (BOUND_VARIABLE_1203217 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1313250 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203217) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203216) _let_2)))) (ho_4335 (ho_4726 (ho_4834 k_6400 BOUND_VARIABLE_1313250) BOUND_VARIABLE_1203216) BOUND_VARIABLE_1203217)))))))) (let ((_let_3804 (forall ((BOUND_VARIABLE_1203171 tptp.nat) (BOUND_VARIABLE_1203172 tptp.nat) (BOUND_VARIABLE_1203173 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1203171) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203172) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203173 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6401 BOUND_VARIABLE_1203171) BOUND_VARIABLE_1203172) BOUND_VARIABLE_1203173))))) (let ((_let_3805 (forall ((BOUND_VARIABLE_1203101 tptp.nat) (BOUND_VARIABLE_1203102 tptp.nat) (BOUND_VARIABLE_1203103 tptp.nat) (BOUND_VARIABLE_1203104 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203103) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203101) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203102) _let_2)) _let_4))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203104 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 (ho_4302 k_6402 BOUND_VARIABLE_1203101) BOUND_VARIABLE_1203102) BOUND_VARIABLE_1203103) BOUND_VARIABLE_1203104))))) (let ((_let_3806 (forall ((BOUND_VARIABLE_1313337 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1203077 tptp.nat) (BOUND_VARIABLE_1203078 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1313337 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203078) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203077) _let_2)))) (ho_4216 (ho_4215 (ho_4730 k_6403 BOUND_VARIABLE_1313337) BOUND_VARIABLE_1203077) BOUND_VARIABLE_1203078)))))))) (let ((_let_3807 (forall ((BOUND_VARIABLE_1203032 tptp.nat) (BOUND_VARIABLE_1203033 tptp.nat) (BOUND_VARIABLE_1203034 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1203032) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1203033) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1203034 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6404 BOUND_VARIABLE_1203032) BOUND_VARIABLE_1203033) BOUND_VARIABLE_1203034))))) (let ((_let_3808 (forall ((BOUND_VARIABLE_1203022 tptp.int) (BOUND_VARIABLE_1313379 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1203024 tptp.int)) (= (ho_4209 (ho_6407 (ho_6406 k_6405 BOUND_VARIABLE_1203022) BOUND_VARIABLE_1313379) BOUND_VARIABLE_1203024) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1203022) (ho_4213 BOUND_VARIABLE_1313379 BOUND_VARIABLE_1203024)))))) (let ((_let_3809 (forall ((BOUND_VARIABLE_1203012 tptp.int) (BOUND_VARIABLE_1313401 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1203014 tptp.nat)) (= (ho_4335 (ho_6410 (ho_6409 k_6408 BOUND_VARIABLE_1203012) BOUND_VARIABLE_1313401) BOUND_VARIABLE_1203014) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1203012) (ho_4216 BOUND_VARIABLE_1313401 BOUND_VARIABLE_1203014)))))) (let ((_let_3810 (forall ((BOUND_VARIABLE_1203002 tptp.nat) (BOUND_VARIABLE_1313423 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1203004 tptp.nat)) (= (ho_4216 (ho_5088 (ho_5087 k_6411 BOUND_VARIABLE_1203002) BOUND_VARIABLE_1313423) BOUND_VARIABLE_1203004) (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1203002) (ho_4216 BOUND_VARIABLE_1313423 BOUND_VARIABLE_1203004)))))) (let ((_let_3811 (forall ((BOUND_VARIABLE_1202992 tptp.complex) (BOUND_VARIABLE_1313437 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202994 tptp.nat)) (= (ho_4767 (ho_6414 (ho_6413 k_6412 BOUND_VARIABLE_1202992) BOUND_VARIABLE_1313437) BOUND_VARIABLE_1202994) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1202992) (ho_4216 BOUND_VARIABLE_1313437 BOUND_VARIABLE_1202994)))))) (let ((_let_3812 (forall ((BOUND_VARIABLE_1202982 tptp.real) (BOUND_VARIABLE_1313459 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202984 tptp.nat)) (= (ho_4245 (ho_5390 (ho_6416 k_6415 BOUND_VARIABLE_1202982) BOUND_VARIABLE_1313459) BOUND_VARIABLE_1202984) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1202982) (ho_4216 BOUND_VARIABLE_1313459 BOUND_VARIABLE_1202984)))))) (let ((_let_3813 (forall ((BOUND_VARIABLE_1202917 tptp.nat) (BOUND_VARIABLE_1202918 tptp.nat) (BOUND_VARIABLE_1202919 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202917) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202918) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1202919 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6417 BOUND_VARIABLE_1202917) BOUND_VARIABLE_1202918) BOUND_VARIABLE_1202919))))) (let ((_let_3814 (forall ((BOUND_VARIABLE_1313516 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1202898 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4335 BOUND_VARIABLE_1313516 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202898) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4335 (ho_5994 k_6418 BOUND_VARIABLE_1313516) BOUND_VARIABLE_1202898)))))))) (let ((_let_3815 (forall ((BOUND_VARIABLE_1202853 tptp.nat) (BOUND_VARIABLE_1202854 tptp.nat) (BOUND_VARIABLE_1202855 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1202853) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202854) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1202855 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6419 BOUND_VARIABLE_1202853) BOUND_VARIABLE_1202854) BOUND_VARIABLE_1202855))))) (let ((_let_3816 (forall ((BOUND_VARIABLE_1202788 tptp.nat) (BOUND_VARIABLE_1202789 tptp.nat) (BOUND_VARIABLE_1202790 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202788) _let_2)) _let_4))) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202789) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1202790 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6420 BOUND_VARIABLE_1202788) BOUND_VARIABLE_1202789) BOUND_VARIABLE_1202790))))) (let ((_let_3817 (forall ((BOUND_VARIABLE_1313595 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202769 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4216 BOUND_VARIABLE_1313595 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202769) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))) (ho_4216 (ho_5088 k_6421 BOUND_VARIABLE_1313595) BOUND_VARIABLE_1202769)))))))) (let ((_let_3818 (forall ((BOUND_VARIABLE_1202724 tptp.nat) (BOUND_VARIABLE_1202725 tptp.nat) (BOUND_VARIABLE_1202726 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1202724) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202725) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1202726 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6422 BOUND_VARIABLE_1202724) BOUND_VARIABLE_1202725) BOUND_VARIABLE_1202726))))) (let ((_let_3819 (forall ((BOUND_VARIABLE_1313644 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1202618 tptp.int) (BOUND_VARIABLE_1202619 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1202618) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1202618)) BOUND_VARIABLE_1202618))) (let ((_let_5 (ho_4213 k_4212 _let_4))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4209 BOUND_VARIABLE_1313644 BOUND_VARIABLE_1202619))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_8) _let_5)) _let_3)) (ho_4209 (ho_4220 _let_6 _let_5) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 BOUND_VARIABLE_1202618))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4211 (ho_6424 k_6423 BOUND_VARIABLE_1313644) BOUND_VARIABLE_1202618) BOUND_VARIABLE_1202619) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1202618 _let_3)) _let_7) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 _let_7))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_4) (ho_5598 k_5597 (forall ((BOUND_VARIABLE_854699 tptp.int)) (not (= (ho_4209 BOUND_VARIABLE_1313644 BOUND_VARIABLE_1202619) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1202618) BOUND_VARIABLE_854699))))))) (ho_4209 _let_2 _let_9)))))))))))))))))))) (let ((_let_3820 (forall ((BOUND_VARIABLE_1313717 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1202511 tptp.int) (BOUND_VARIABLE_1202512 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1202511) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1202511)) BOUND_VARIABLE_1202511))) (let ((_let_5 (ho_4213 k_4212 _let_4))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4209 BOUND_VARIABLE_1313717 BOUND_VARIABLE_1202512))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_8) _let_5)) _let_3)) (ho_4209 (ho_4220 _let_6 _let_5) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 BOUND_VARIABLE_1202511))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4209 (ho_4211 (ho_6424 k_6425 BOUND_VARIABLE_1313717) BOUND_VARIABLE_1202511) BOUND_VARIABLE_1202512) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1202511 _let_3)) _let_7) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 _let_7))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_4) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= (ho_4209 BOUND_VARIABLE_1313717 BOUND_VARIABLE_1202512) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1202511) K3))))))) (ho_4209 _let_2 _let_9)))))))))))))))))))) (let ((_let_3821 (forall ((BOUND_VARIABLE_1313786 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1202404 tptp.int) (BOUND_VARIABLE_1202405 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1202404) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1202404)) BOUND_VARIABLE_1202404))) (let ((_let_5 (ho_4213 k_4212 _let_4))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4335 BOUND_VARIABLE_1313786 BOUND_VARIABLE_1202405))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_8) _let_5)) _let_3)) (ho_4209 (ho_4220 _let_6 _let_5) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 BOUND_VARIABLE_1202404))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4335 (ho_4334 (ho_6427 k_6426 BOUND_VARIABLE_1313786) BOUND_VARIABLE_1202404) BOUND_VARIABLE_1202405) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1202404 _let_3)) _let_7) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 _let_7))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_4) (ho_5598 k_5597 (forall ((BOUND_VARIABLE_854429 tptp.int)) (not (= (ho_4335 BOUND_VARIABLE_1313786 BOUND_VARIABLE_1202405) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1202404) BOUND_VARIABLE_854429))))))) (ho_4209 _let_2 _let_9)))))))))))))))))))) (let ((_let_3822 (forall ((BOUND_VARIABLE_1313859 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1202297 tptp.int) (BOUND_VARIABLE_1202298 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1202297) _let_1)) _let_3))) (ho_4209 _let_2 BOUND_VARIABLE_1202297)) BOUND_VARIABLE_1202297))) (let ((_let_5 (ho_4213 k_4212 _let_4))) (let ((_let_6 (ho_4219 k_4218 k_4217))) (let ((_let_7 (ho_4335 BOUND_VARIABLE_1313859 BOUND_VARIABLE_1202298))) (let ((_let_8 (ho_4213 k_4212 (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_3 (ho_4209 (ho_4211 k_4311 (ho_4209 (ho_4211 k_4210 _let_7) _let_1)) _let_3))) (ho_4209 _let_2 _let_7)) _let_7)))) (let ((_let_9 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4223 _let_8) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_6 (ho_4216 (ho_4215 k_4221 _let_8) _let_5)) _let_3)) (ho_4209 (ho_4220 _let_6 _let_5) _let_3))))) _let_3))) (let ((_let_10 (ho_4209 k_4594 BOUND_VARIABLE_1202297))) (let ((_let_11 (ho_4211 k_4222 _let_10))) (= (ho_4335 (ho_4334 (ho_6427 k_6428 BOUND_VARIABLE_1313859) BOUND_VARIABLE_1202297) BOUND_VARIABLE_1202298) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1202297 _let_3)) _let_7) (ho_4209 (ho_4211 (ho_4593 k_4592 (= _let_10 (ho_4209 k_4594 _let_7))) (ho_4209 _let_11 _let_9)) (ho_4209 _let_11 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4222 _let_4) (ho_5598 k_5597 (forall ((K3 tptp.int)) (not (= (ho_4335 BOUND_VARIABLE_1313859 BOUND_VARIABLE_1202298) (ho_4209 (ho_4211 k_4222 BOUND_VARIABLE_1202297) K3))))))) (ho_4209 _let_2 _let_9)))))))))))))))))))) (let ((_let_3823 (forall ((BOUND_VARIABLE_1313918 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202268 tptp.nat) (BOUND_VARIABLE_1202269 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4216 BOUND_VARIABLE_1313918 BOUND_VARIABLE_1202269))) (= (ho_4216 (ho_4215 k_4223 _let_4) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4221 _let_4) BOUND_VARIABLE_1202268)) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202268) _let_2)))) (ho_4216 (ho_4215 (ho_4730 k_6429 BOUND_VARIABLE_1313918) BOUND_VARIABLE_1202268) BOUND_VARIABLE_1202269))))))))) (let ((_let_3824 (forall ((BOUND_VARIABLE_1313942 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1202258 tptp.nat) (BOUND_VARIABLE_1202259 tptp.int)) (= (ho_4209 (ho_4220 (ho_4219 k_6430 BOUND_VARIABLE_1313942) BOUND_VARIABLE_1202258) BOUND_VARIABLE_1202259) (ho_4335 (ho_4334 k_4333 (ho_4209 BOUND_VARIABLE_1313942 BOUND_VARIABLE_1202259)) BOUND_VARIABLE_1202258))))) (let ((_let_3825 (forall ((BOUND_VARIABLE_1313956 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1202248 tptp.nat) (BOUND_VARIABLE_1202249 tptp.nat)) (= (ho_4335 (ho_4726 (ho_4834 k_6431 BOUND_VARIABLE_1313956) BOUND_VARIABLE_1202248) BOUND_VARIABLE_1202249) (ho_4335 (ho_4334 k_4333 (ho_4335 BOUND_VARIABLE_1313956 BOUND_VARIABLE_1202249)) BOUND_VARIABLE_1202248))))) (let ((_let_3826 (forall ((BOUND_VARIABLE_1313970 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202238 tptp.nat) (BOUND_VARIABLE_1202239 tptp.nat)) (= (ho_4216 (ho_4215 (ho_4730 k_6432 BOUND_VARIABLE_1313970) BOUND_VARIABLE_1202238) BOUND_VARIABLE_1202239) (ho_4216 (ho_4215 k_4214 (ho_4216 BOUND_VARIABLE_1313970 BOUND_VARIABLE_1202239)) BOUND_VARIABLE_1202238))))) (let ((_let_3827 (forall ((BOUND_VARIABLE_1313985 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1313984 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1202228 tptp.int)) (= (ho_4209 (ho_5096 (ho_6434 k_6433 BOUND_VARIABLE_1313985) BOUND_VARIABLE_1313984) BOUND_VARIABLE_1202228) (ho_4209 (ho_4211 k_4222 (ho_4209 BOUND_VARIABLE_1313985 BOUND_VARIABLE_1202228)) (ho_4209 BOUND_VARIABLE_1313984 BOUND_VARIABLE_1202228)))))) (let ((_let_3828 (forall ((BOUND_VARIABLE_1314005 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1314004 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1202217 tptp.nat)) (= (ho_4335 (ho_5994 (ho_5993 k_6435 BOUND_VARIABLE_1314005) BOUND_VARIABLE_1314004) BOUND_VARIABLE_1202217) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1314005 BOUND_VARIABLE_1202217)) (ho_4335 BOUND_VARIABLE_1314004 BOUND_VARIABLE_1202217)))))) (let ((_let_3829 (forall ((BOUND_VARIABLE_1314021 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1314017 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1202192 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1314021 BOUND_VARIABLE_1202192)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1314017 BOUND_VARIABLE_1202192)) _let_2))) (ho_4216 (ho_5088 (ho_5820 k_6436 BOUND_VARIABLE_1314021) BOUND_VARIABLE_1314017) BOUND_VARIABLE_1202192)))))))) (let ((_let_3830 (forall ((BOUND_VARIABLE_1202136 tptp.nat) (BOUND_VARIABLE_1202137 tptp.nat) (BOUND_VARIABLE_1202138 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1202136) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202137) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1202138 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6437 BOUND_VARIABLE_1202136) BOUND_VARIABLE_1202137) BOUND_VARIABLE_1202138))))) (let ((_let_3831 (forall ((BOUND_VARIABLE_1202082 tptp.nat) (BOUND_VARIABLE_1202083 tptp.nat) (BOUND_VARIABLE_1202084 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1202082) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202083) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1202084 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6438 BOUND_VARIABLE_1202082) BOUND_VARIABLE_1202083) BOUND_VARIABLE_1202084))))) (let ((_let_3832 (forall ((BOUND_VARIABLE_1202038 tptp.nat) (BOUND_VARIABLE_1202039 tptp.nat) (BOUND_VARIABLE_1202040 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1202038) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1202039) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1202040 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6439 BOUND_VARIABLE_1202038) BOUND_VARIABLE_1202039) BOUND_VARIABLE_1202040))))) (let ((_let_3833 (forall ((BOUND_VARIABLE_1201984 tptp.nat) (BOUND_VARIABLE_1201985 tptp.nat) (BOUND_VARIABLE_1201986 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201984) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201985) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201986 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6440 BOUND_VARIABLE_1201984) BOUND_VARIABLE_1201985) BOUND_VARIABLE_1201986))))) (let ((_let_3834 (forall ((BOUND_VARIABLE_1201930 tptp.nat) (BOUND_VARIABLE_1201931 tptp.nat) (BOUND_VARIABLE_1201932 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201930) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201931) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201932 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6441 BOUND_VARIABLE_1201930) BOUND_VARIABLE_1201931) BOUND_VARIABLE_1201932))))) (let ((_let_3835 (forall ((BOUND_VARIABLE_1201886 tptp.nat) (BOUND_VARIABLE_1201887 tptp.nat) (BOUND_VARIABLE_1201888 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201886) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201887) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1201888 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6442 BOUND_VARIABLE_1201886) BOUND_VARIABLE_1201887) BOUND_VARIABLE_1201888))))) (let ((_let_3836 (forall ((BOUND_VARIABLE_1201832 tptp.nat) (BOUND_VARIABLE_1201833 tptp.nat) (BOUND_VARIABLE_1201834 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201832) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201833) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201834 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6443 BOUND_VARIABLE_1201832) BOUND_VARIABLE_1201833) BOUND_VARIABLE_1201834))))) (let ((_let_3837 (forall ((BOUND_VARIABLE_1201778 tptp.nat) (BOUND_VARIABLE_1201779 tptp.nat) (BOUND_VARIABLE_1201780 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201778) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 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(ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6445 BOUND_VARIABLE_1201734) BOUND_VARIABLE_1201735) BOUND_VARIABLE_1201736))))) (let ((_let_3839 (forall ((BOUND_VARIABLE_1201680 tptp.nat) (BOUND_VARIABLE_1201681 tptp.nat) (BOUND_VARIABLE_1201682 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201680) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201681) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201682 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6446 BOUND_VARIABLE_1201680) BOUND_VARIABLE_1201681) BOUND_VARIABLE_1201682))))) (let ((_let_3840 (forall ((BOUND_VARIABLE_1201626 tptp.nat) (BOUND_VARIABLE_1201627 tptp.nat) (BOUND_VARIABLE_1201628 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201626) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201627) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201628 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6447 BOUND_VARIABLE_1201626) BOUND_VARIABLE_1201627) BOUND_VARIABLE_1201628))))) (let ((_let_3841 (forall ((BOUND_VARIABLE_1201582 tptp.nat) (BOUND_VARIABLE_1201583 tptp.nat) (BOUND_VARIABLE_1201584 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201582) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201583) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1201584 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6448 BOUND_VARIABLE_1201582) BOUND_VARIABLE_1201583) BOUND_VARIABLE_1201584))))) (let ((_let_3842 (forall ((BOUND_VARIABLE_1201528 tptp.nat) (BOUND_VARIABLE_1201529 tptp.nat) (BOUND_VARIABLE_1201530 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201528) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201529) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201530 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6449 BOUND_VARIABLE_1201528) BOUND_VARIABLE_1201529) BOUND_VARIABLE_1201530))))) (let ((_let_3843 (forall ((BOUND_VARIABLE_1201474 tptp.nat) (BOUND_VARIABLE_1201475 tptp.nat) (BOUND_VARIABLE_1201476 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201474) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201475) _let_2)) _let_4))) _let_2)) _let_4))))) (or (not (= BOUND_VARIABLE_1201476 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6450 BOUND_VARIABLE_1201474) BOUND_VARIABLE_1201475) BOUND_VARIABLE_1201476))))) (let ((_let_3844 (forall ((BOUND_VARIABLE_1201430 tptp.nat) (BOUND_VARIABLE_1201431 tptp.nat) (BOUND_VARIABLE_1201432 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4464 (ho_4463 k_4462 BOUND_VARIABLE_1201430) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201431) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2)))))) (or (not (= BOUND_VARIABLE_1201432 (ho_4216 (ho_4468 k_4467 _let_4) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_4))))))))))) (ho_4288 (ho_4287 (ho_4303 k_6451 BOUND_VARIABLE_1201430) BOUND_VARIABLE_1201431) BOUND_VARIABLE_1201432))))) (let ((_let_3845 (forall ((BOUND_VARIABLE_1201406 tptp.nat) (BOUND_VARIABLE_1201407 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201407)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201406) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6452 BOUND_VARIABLE_1201406) BOUND_VARIABLE_1201407)))))))) (let ((_let_3846 (forall ((BOUND_VARIABLE_1201396 tptp.nat) (BOUND_VARIABLE_1201397 tptp.nat)) (= (ho_4288 (ho_4287 k_6453 BOUND_VARIABLE_1201396) BOUND_VARIABLE_1201397) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201397)) (ho_4290 k_4289 BOUND_VARIABLE_1201396)))))) (let ((_let_3847 (forall ((BOUND_VARIABLE_1201372 tptp.nat) (BOUND_VARIABLE_1201373 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201373)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201372) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6454 BOUND_VARIABLE_1201372) BOUND_VARIABLE_1201373)))))))) (let ((_let_3848 (forall ((BOUND_VARIABLE_1201362 tptp.nat) (BOUND_VARIABLE_1201363 tptp.nat)) (= (ho_4288 (ho_4287 k_6455 BOUND_VARIABLE_1201362) BOUND_VARIABLE_1201363) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201363)) (ho_4290 k_4289 BOUND_VARIABLE_1201362)))))) (let ((_let_3849 (forall ((BOUND_VARIABLE_1201338 tptp.nat) (BOUND_VARIABLE_1201339 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201339)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201338) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6456 BOUND_VARIABLE_1201338) BOUND_VARIABLE_1201339)))))))) (let ((_let_3850 (forall ((BOUND_VARIABLE_1201328 tptp.nat) (BOUND_VARIABLE_1201329 tptp.nat)) (= (ho_4288 (ho_4287 k_6457 BOUND_VARIABLE_1201328) BOUND_VARIABLE_1201329) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201329)) (ho_4290 k_4289 BOUND_VARIABLE_1201328)))))) (let ((_let_3851 (forall ((BOUND_VARIABLE_1201304 tptp.nat) (BOUND_VARIABLE_1201305 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201305)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201304) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6458 BOUND_VARIABLE_1201304) BOUND_VARIABLE_1201305)))))))) (let ((_let_3852 (forall ((BOUND_VARIABLE_1201294 tptp.nat) (BOUND_VARIABLE_1201295 tptp.nat)) (= (ho_4288 (ho_4287 k_6459 BOUND_VARIABLE_1201294) BOUND_VARIABLE_1201295) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1201295)) (ho_4290 k_4289 BOUND_VARIABLE_1201294)))))) (let ((_let_3853 (forall ((BOUND_VARIABLE_1201284 tptp.nat) (BOUND_VARIABLE_1201285 tptp.nat)) (= (ho_4288 (ho_4287 k_6460 BOUND_VARIABLE_1201284) BOUND_VARIABLE_1201285) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201285)) (ho_4290 k_4289 BOUND_VARIABLE_1201284)))))) (let ((_let_3854 (forall ((BOUND_VARIABLE_1201260 tptp.nat) (BOUND_VARIABLE_1201261 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201261)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201260) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6461 BOUND_VARIABLE_1201260) BOUND_VARIABLE_1201261)))))))) (let ((_let_3855 (forall ((BOUND_VARIABLE_1201236 tptp.nat) (BOUND_VARIABLE_1201237 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201237)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201236) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6462 BOUND_VARIABLE_1201236) BOUND_VARIABLE_1201237)))))))) (let ((_let_3856 (forall ((BOUND_VARIABLE_1201226 tptp.nat) (BOUND_VARIABLE_1201227 tptp.nat)) (= (ho_4288 (ho_4287 k_6463 BOUND_VARIABLE_1201226) BOUND_VARIABLE_1201227) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201227)) (ho_4290 k_4289 BOUND_VARIABLE_1201226)))))) (let ((_let_3857 (forall ((BOUND_VARIABLE_1201202 tptp.nat) (BOUND_VARIABLE_1201203 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201203)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201202) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6464 BOUND_VARIABLE_1201202) BOUND_VARIABLE_1201203)))))))) (let ((_let_3858 (forall ((BOUND_VARIABLE_1201192 tptp.nat) (BOUND_VARIABLE_1201193 tptp.nat)) (= (ho_4288 (ho_4287 k_6465 BOUND_VARIABLE_1201192) BOUND_VARIABLE_1201193) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201193)) (ho_4290 k_4289 BOUND_VARIABLE_1201192)))))) (let ((_let_3859 (forall ((BOUND_VARIABLE_1201168 tptp.nat) (BOUND_VARIABLE_1201169 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201169)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1201168) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6466 BOUND_VARIABLE_1201168) BOUND_VARIABLE_1201169)))))))) (let ((_let_3860 (forall ((BOUND_VARIABLE_1201158 tptp.nat) (BOUND_VARIABLE_1201159 tptp.nat)) (= (ho_4288 (ho_4287 k_6467 BOUND_VARIABLE_1201158) BOUND_VARIABLE_1201159) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1201159)) (ho_4290 k_4289 BOUND_VARIABLE_1201158)))))) (let ((_let_3861 (forall ((BOUND_VARIABLE_1201139 tptp.nat) (BOUND_VARIABLE_1201140 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 _let_8)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1201139) _let_8))) BOUND_VARIABLE_1201140) (ho_4442 (ho_4458 k_6468 BOUND_VARIABLE_1201139) BOUND_VARIABLE_1201140))))))))))))) (let ((_let_3862 (forall ((BOUND_VARIABLE_1201120 tptp.nat) (BOUND_VARIABLE_1201121 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 _let_6)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1201120) _let_6))) BOUND_VARIABLE_1201121) (ho_4258 (ho_4273 k_6469 BOUND_VARIABLE_1201120) BOUND_VARIABLE_1201121))))))))))) (let ((_let_3863 (forall ((BOUND_VARIABLE_1201102 tptp.nat) (BOUND_VARIABLE_1201103 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 _let_2)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1201102) _let_2))) BOUND_VARIABLE_1201103) (ho_4703 (ho_4709 k_6470 BOUND_VARIABLE_1201102) BOUND_VARIABLE_1201103))))))) (let ((_let_3864 (forall ((BOUND_VARIABLE_1201097 tptp.nat)) (= BOUND_VARIABLE_1201097 (ho_4216 k_6471 BOUND_VARIABLE_1201097))))) (let ((_let_3865 (forall ((BOUND_VARIABLE_1201020 tptp.real) (BOUND_VARIABLE_1201021 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4258 _let_3 _let_1))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_6 (ho_4264 _let_5 k_4259))) (let ((_let_7 (ho_4258 (ho_4265 _let_6 _let_1) _let_4))) (let ((_let_8 (ho_4272 k_4271 k_4270))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4257 _let_2 k_4274))) (let ((_let_11 (ho_4264 _let_5 k_4275))) (let ((_let_12 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_13 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_14 (ho_4216 (ho_4215 k_4221 _let_12) _let_13))) (= (ho_4245 (ho_4244 k_6472 BOUND_VARIABLE_1201020) BOUND_VARIABLE_1201021) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_4) BOUND_VARIABLE_1201021)) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1201021 _let_14)) _let_1) (ho_4258 (ho_4273 (ho_4715 (ho_6006 k_6005 (ho_4696 k_4762 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_let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1200987)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1200988) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1200989) (ho_4258 (ho_4273 (ho_4696 k_6474 BOUND_VARIABLE_1200987) BOUND_VARIABLE_1200988) BOUND_VARIABLE_1200989)))))))))) (let ((_let_3868 (forall ((BOUND_VARIABLE_1200909 tptp.rat) (BOUND_VARIABLE_1200910 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)))) (let ((_let_4 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_5 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_6 (ho_4441 _let_5 k_4435))) (let ((_let_7 (ho_4442 _let_6 _let_4))) (let ((_let_8 (ho_4446 (ho_4445 k_4444 k_4436) _let_5))) (let ((_let_9 (ho_4447 _let_8 k_4443))) (let ((_let_10 (ho_4442 (ho_4448 _let_9 _let_4) _let_7))) (let ((_let_11 (ho_4457 k_4456 k_4455))) (let ((_let_12 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) (let ((_let_13 (ho_4441 _let_5 k_4449))) (let ((_let_14 (ho_4447 _let_8 k_4697))) (let ((_let_15 (ho_4213 k_4212 _let_1))) (let ((_let_16 (ho_4213 k_4212 _let_12))) (let ((_let_17 (ho_4216 (ho_4215 k_4221 _let_15) _let_16))) (= (ho_4316 (ho_4799 k_6475 BOUND_VARIABLE_1200909) BOUND_VARIABLE_1200910) (ho_4442 (ho_4448 _let_14 (ho_4442 (ho_4448 _let_14 (ho_4442 (ho_4448 _let_14 (ho_4316 (ho_4799 k_4798 _let_7) BOUND_VARIABLE_1200910)) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1200910 _let_17)) _let_4) (ho_4442 (ho_4458 (ho_4718 (ho_6011 k_6010 (ho_4699 k_4763 BOUND_VARIABLE_1200909)) _let_17) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1200910) _let_15)) _let_4)))) (ho_4442 _let_13 (ho_4442 (ho_4458 _let_11 (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_16) BOUND_VARIABLE_1200910) _let_15)) _let_10)))) (ho_4442 (ho_4448 _let_9 (ho_4442 (ho_4448 _let_14 BOUND_VARIABLE_1200909) (ho_4442 _let_13 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_12) _let_1)))))) (ho_4442 _let_6 (ho_4442 (ho_4458 _let_11 BOUND_VARIABLE_1200910) _let_10))))))))))))))))))))))))) (let ((_let_3869 (forall ((BOUND_VARIABLE_1200899 tptp.nat) (BOUND_VARIABLE_1200900 tptp.nat)) (= (ho_4288 (ho_4287 k_6476 BOUND_VARIABLE_1200899) BOUND_VARIABLE_1200900) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1200900)) (ho_4290 k_4289 BOUND_VARIABLE_1200899)))))) (let ((_let_3870 (forall ((BOUND_VARIABLE_1200876 tptp.rat) (BOUND_VARIABLE_1200877 tptp.nat) (BOUND_VARIABLE_1200878 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1200876)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1200877) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1200878) (ho_4442 (ho_4458 (ho_4699 k_6477 BOUND_VARIABLE_1200876) BOUND_VARIABLE_1200877) BOUND_VARIABLE_1200878)))))))))))) (let ((_let_3871 (forall ((BOUND_VARIABLE_1200779 tptp.complex) (BOUND_VARIABLE_1200780 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4193 k_4192 tptp.one))) (let ((_let_4 (ho_4213 k_4212 (ho_4196 k_4195 _let_3)))) (let ((_let_5 (ho_4701 k_4700 _let_3))) (let ((_let_6 (ho_4769 k_4768 _let_5))) (let ((_let_7 (ho_4769 k_4773 _let_5))) (let ((_let_8 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_9 (ho_4263 (ho_4262 k_4261 k_4252) _let_8))) (let ((_let_10 (ho_4264 _let_9 k_4259))) (let ((_let_11 (ho_4257 _let_8 k_4274))) (let ((_let_12 (ho_4258 _let_11 (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_7) _let_4)) (ho_4245 (ho_4244 k_4243 _let_6) _let_4))))) (let ((_let_13 (ho_4257 _let_8 k_4248))) (let ((_let_14 (ho_4264 _let_9 k_4275))) (let ((_let_15 (ho_4247 k_4246 _let_3))) (let ((_let_16 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_15) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_15)))))) (let ((_let_17 (ho_4767 k_6015 BOUND_VARIABLE_1200780))) (let ((_let_18 (ho_4769 k_4768 _let_17))) (let ((_let_19 (ho_4769 k_4773 _let_17))) (let ((_let_20 (ho_4258 _let_11 (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_19) _let_4)) (ho_4245 (ho_4244 k_4243 _let_18) _let_4))))) (let ((_let_21 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) (let ((_let_22 (ho_4216 (ho_4215 k_4221 _let_21) _let_4))) (= (ho_4767 (ho_4766 k_6478 BOUND_VARIABLE_1200779) BOUND_VARIABLE_1200780) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 _let_2) BOUND_VARIABLE_1200780)) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1200780 _let_22)) _let_1) (ho_4703 (ho_4709 (ho_4721 (ho_6017 k_6016 (ho_4712 k_4764 BOUND_VARIABLE_1200779)) _let_22) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1200780) _let_21)) _let_1)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_14 _let_19) _let_20))) (ho_4703 _let_16 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_14 (ho_4258 _let_13 _let_18)) _let_20)))))) (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4710 BOUND_VARIABLE_1200779) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_14 _let_7) _let_12))) (ho_4703 _let_16 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_14 (ho_4258 _let_13 _let_6)) _let_12)))))) (ho_4703 k_4702 (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1200780) (ho_4703 (ho_4705 k_4704 _let_1) _let_2))))))))))))))))))))))))))))))) (let ((_let_3872 (forall ((BOUND_VARIABLE_1200769 tptp.nat) (BOUND_VARIABLE_1200770 tptp.nat)) (= (ho_4288 (ho_4287 k_6479 BOUND_VARIABLE_1200769) BOUND_VARIABLE_1200770) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1200770)) (ho_4290 k_4289 BOUND_VARIABLE_1200769)))))) (let ((_let_3873 (forall ((BOUND_VARIABLE_1200748 tptp.complex) (BOUND_VARIABLE_1200749 tptp.nat) (BOUND_VARIABLE_1200750 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1200748)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1200749) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1200750) (ho_4703 (ho_4709 (ho_4712 k_6480 BOUND_VARIABLE_1200748) BOUND_VARIABLE_1200749) BOUND_VARIABLE_1200750)))))) (let ((_let_3874 (forall ((BOUND_VARIABLE_1200727 tptp.rat) (BOUND_VARIABLE_1200728 tptp.nat) (BOUND_VARIABLE_1200729 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_5 k_4697) (ho_4442 (ho_4448 _let_6 BOUND_VARIABLE_1200727) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1200728) (ho_4442 (ho_4448 _let_6 _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3))))) BOUND_VARIABLE_1200729) (ho_4442 (ho_4458 (ho_4699 k_6481 BOUND_VARIABLE_1200727) BOUND_VARIABLE_1200728) BOUND_VARIABLE_1200729))))))))))) (let ((_let_3875 (forall ((BOUND_VARIABLE_1200702 tptp.rat) (BOUND_VARIABLE_1200703 tptp.nat) (BOUND_VARIABLE_1200704 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)))) (let ((_let_4 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_5 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_5))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4447 _let_6 k_4697))) (= (ho_4442 (ho_4448 _let_8 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1200702) (ho_4442 (ho_4448 _let_8 _let_4) (ho_4442 (ho_4441 _let_5 k_4449) (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) _let_1))))))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1200703) (ho_4442 (ho_4448 _let_7 _let_4) (ho_4442 (ho_4441 _let_5 k_4435) _let_4))))) BOUND_VARIABLE_1200704) (ho_4442 (ho_4458 (ho_4699 k_6482 BOUND_VARIABLE_1200702) BOUND_VARIABLE_1200703) BOUND_VARIABLE_1200704))))))))))))) (let ((_let_3876 (forall ((BOUND_VARIABLE_1200682 tptp.rat) (BOUND_VARIABLE_1200683 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1200682) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1200683) (ho_4442 (ho_4448 _let_7 _let_5) (ho_4442 (ho_4441 _let_4 k_4435) _let_5)))) (ho_4442 (ho_4441 _let_4 k_4449) (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) _let_1)))))) (ho_4316 (ho_4799 k_6483 BOUND_VARIABLE_1200682) BOUND_VARIABLE_1200683)))))))))))) (let ((_let_3877 (forall ((BOUND_VARIABLE_1200622 tptp.nat) (BOUND_VARIABLE_1200623 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) _let_6)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_6) _let_2)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1200622) _let_2)))) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1200623 (ho_4216 (ho_4468 k_4467 _let_7) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_7)))))))))))))) (ho_4288 (ho_4287 k_6484 BOUND_VARIABLE_1200622) BOUND_VARIABLE_1200623))))) (let ((_let_3878 (forall ((BOUND_VARIABLE_1200601 tptp.real) (BOUND_VARIABLE_1200602 tptp.nat) (BOUND_VARIABLE_1200603 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1200601) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1200602) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1200603) (ho_4258 (ho_4273 (ho_4696 k_6485 BOUND_VARIABLE_1200601) BOUND_VARIABLE_1200602) BOUND_VARIABLE_1200603))))))))) (let ((_let_3879 (forall ((BOUND_VARIABLE_1200576 tptp.real) (BOUND_VARIABLE_1200577 tptp.nat) (BOUND_VARIABLE_1200578 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1200576) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one)))))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1200577) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1200578) (ho_4258 (ho_4273 (ho_4696 k_6486 BOUND_VARIABLE_1200576) BOUND_VARIABLE_1200577) BOUND_VARIABLE_1200578)))))))))) (let ((_let_3880 (forall ((BOUND_VARIABLE_1200556 tptp.real) (BOUND_VARIABLE_1200557 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (= (ho_4258 (ho_4265 _let_4 BOUND_VARIABLE_1200556) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4275) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1200557) (ho_4258 (ho_4265 _let_4 _let_2) (ho_4258 (ho_4257 _let_1 k_4248) _let_2)))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))))) (ho_4245 (ho_4244 k_6487 BOUND_VARIABLE_1200556) BOUND_VARIABLE_1200557))))))))) (let ((_let_3881 (forall ((BOUND_VARIABLE_1200496 tptp.nat) (BOUND_VARIABLE_1200497 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) _let_6)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_6) _let_2)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1200496) _let_2)))) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1200497 (ho_4216 (ho_4468 k_4467 _let_7) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_7)))))))))))))) (ho_4288 (ho_4287 k_6488 BOUND_VARIABLE_1200496) BOUND_VARIABLE_1200497))))) (let ((_let_3882 (forall ((BOUND_VARIABLE_1200476 tptp.complex) (BOUND_VARIABLE_1200477 tptp.nat) (BOUND_VARIABLE_1200478 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1200476) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1200477) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1200478) (ho_4703 (ho_4709 (ho_4712 k_6489 BOUND_VARIABLE_1200476) BOUND_VARIABLE_1200477) BOUND_VARIABLE_1200478)))))) (let ((_let_3883 (forall ((BOUND_VARIABLE_1200452 tptp.complex) (BOUND_VARIABLE_1200453 tptp.nat) (BOUND_VARIABLE_1200454 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4193 k_4192 tptp.one))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 _let_2)))) (let ((_let_4 (ho_4701 k_4700 _let_2))) (let ((_let_5 (ho_4769 k_4768 _let_4))) (let ((_let_6 (ho_4769 k_4773 _let_4))) (let ((_let_7 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_7))) (let ((_let_9 (ho_4257 _let_7 k_4274))) (let ((_let_10 (ho_4258 _let_9 (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) (ho_4245 (ho_4244 k_4243 _let_6) _let_3)) (ho_4245 (ho_4244 k_4243 _let_5) _let_3))))) (let ((_let_11 (ho_4264 _let_8 k_4275))) (let ((_let_12 (ho_4247 k_4246 _let_2))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1200452) (ho_4703 (ho_4705 k_4710 _let_1) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_11 _let_6) _let_10))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 _let_11 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4257 _let_7 k_4248) _let_5)) _let_10))))))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1200453) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1200454) (ho_4703 (ho_4709 (ho_4712 k_6490 BOUND_VARIABLE_1200452) BOUND_VARIABLE_1200453) BOUND_VARIABLE_1200454))))))))))))))))) (let ((_let_3884 (forall ((BOUND_VARIABLE_1200433 tptp.complex) (BOUND_VARIABLE_1200434 tptp.nat)) (let ((_let_1 (ho_4193 k_4192 tptp.one))) (let ((_let_2 (ho_4213 k_4212 (ho_4196 k_4195 _let_1)))) (let ((_let_3 (ho_4701 k_4700 _let_1))) (let ((_let_4 (ho_4769 k_4768 _let_3))) (let ((_let_5 (ho_4769 k_4773 _let_3))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_7 (ho_4263 (ho_4262 k_4261 k_4252) _let_6))) (let ((_let_8 (ho_4257 _let_6 k_4274))) (let ((_let_9 (ho_4258 _let_8 (ho_4258 (ho_4265 (ho_4264 _let_7 k_4259) (ho_4245 (ho_4244 k_4243 _let_5) _let_2)) (ho_4245 (ho_4244 k_4243 _let_4) _let_2))))) (let ((_let_10 (ho_4264 _let_7 k_4275))) (let ((_let_11 (ho_4247 k_4246 _let_1))) (let ((_let_12 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1200433) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1200434) (ho_4703 (ho_4705 k_4704 _let_12) (ho_4703 k_4702 _let_12)))) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 _let_5) _let_9))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_11) (ho_4506 k_4505 k_4504))) (ho_4258 _let_8 _let_11)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4257 _let_6 k_4248) _let_4)) _let_9)))))) (ho_4767 (ho_4766 k_6491 BOUND_VARIABLE_1200433) BOUND_VARIABLE_1200434))))))))))))))))) (let ((_let_3885 (forall ((BOUND_VARIABLE_1200373 tptp.nat) (BOUND_VARIABLE_1200374 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4209 (ho_4220 _let_4 _let_3) _let_2))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4464 (ho_4463 k_4462 (ho_4216 (ho_4215 k_4221 _let_3) _let_6)) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_4 _let_6) _let_2)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1200373) _let_2)))) _let_2)) _let_5))) _let_2)) _let_5))))) (or (not (= BOUND_VARIABLE_1200374 (ho_4216 (ho_4468 k_4467 _let_7) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_7)))))))))))))) (ho_4288 (ho_4287 k_6492 BOUND_VARIABLE_1200373) BOUND_VARIABLE_1200374))))) (let ((_let_3886 (forall ((BOUND_VARIABLE_1200248 tptp.complex) (BOUND_VARIABLE_1200249 tptp.complex) (BOUND_VARIABLE_1200250 tptp.nat)) (= (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4778 (ho_4777 k_4776 BOUND_VARIABLE_1200248) BOUND_VARIABLE_1200249) BOUND_VARIABLE_1200250)) (ho_4516 k_4515 (ho_4287 k_4780 BOUND_VARIABLE_1200250))) (ho_4767 (ho_4766 (ho_6497 k_6496 BOUND_VARIABLE_1200248) BOUND_VARIABLE_1200249) BOUND_VARIABLE_1200250))))) (let ((_let_3887 (forall ((BOUND_VARIABLE_1200188 tptp.complex) (BOUND_VARIABLE_1200189 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1200188) BOUND_VARIABLE_1200189))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1200189 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1200189) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1200189) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6498 BOUND_VARIABLE_1200188) BOUND_VARIABLE_1200189) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3888 (forall ((BOUND_VARIABLE_1200128 tptp.complex) (BOUND_VARIABLE_1200129 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1200128) BOUND_VARIABLE_1200129))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1200129 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1200129) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1200129) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 k_6499 BOUND_VARIABLE_1200128) BOUND_VARIABLE_1200129) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3889 (forall ((BOUND_VARIABLE_1200019 tptp.real) (BOUND_VARIABLE_1200020 tptp.real) (BOUND_VARIABLE_1200021 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4740 (ho_4782 k_4781 BOUND_VARIABLE_1200019) BOUND_VARIABLE_1200020) BOUND_VARIABLE_1200021)) (ho_4516 k_4515 (ho_4287 k_4783 BOUND_VARIABLE_1200021))) (ho_4245 (ho_4244 (ho_5451 k_6500 BOUND_VARIABLE_1200019) BOUND_VARIABLE_1200020) BOUND_VARIABLE_1200021))))) (let ((_let_3890 (forall ((BOUND_VARIABLE_1199973 tptp.real) (BOUND_VARIABLE_1199974 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6501 BOUND_VARIABLE_1199973) BOUND_VARIABLE_1199974) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199974 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1199974) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1199974) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199973) BOUND_VARIABLE_1199974))))))))))))) (let ((_let_3891 (forall ((BOUND_VARIABLE_1199927 tptp.real) (BOUND_VARIABLE_1199928 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6502 BOUND_VARIABLE_1199927) BOUND_VARIABLE_1199928) (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199928 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1199928) _let_6))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_6) BOUND_VARIABLE_1199928) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_5)))) _let_5)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199927) BOUND_VARIABLE_1199928))))))))))))) (let ((_let_3892 (forall ((BOUND_VARIABLE_1199804 tptp.complex) (BOUND_VARIABLE_1199805 tptp.complex) (BOUND_VARIABLE_1199806 tptp.nat)) (= (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4778 (ho_4777 k_4784 BOUND_VARIABLE_1199804) BOUND_VARIABLE_1199805) BOUND_VARIABLE_1199806)) (ho_4516 k_4515 (ho_4287 k_4785 BOUND_VARIABLE_1199806))) (ho_4767 (ho_4766 (ho_6497 k_6503 BOUND_VARIABLE_1199804) BOUND_VARIABLE_1199805) BOUND_VARIABLE_1199806))))) (let ((_let_3893 (forall ((BOUND_VARIABLE_1199741 tptp.complex) (BOUND_VARIABLE_1199742 tptp.complex) (BOUND_VARIABLE_1199743 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1199741) BOUND_VARIABLE_1199742)) BOUND_VARIABLE_1199743))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4193 k_4192 tptp.one))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 _let_7)))) (let ((_let_9 (ho_4257 _let_3 k_4274))) (let ((_let_10 (ho_4264 _let_5 k_4275))) (let ((_let_11 (ho_4265 _let_10 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199743 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_10 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1199743) _let_8))) (ho_4258 _let_9 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1199743) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)))) (let ((_let_12 (ho_4247 k_4246 _let_7))) (= (ho_4767 (ho_4766 (ho_6497 k_6504 BOUND_VARIABLE_1199741) BOUND_VARIABLE_1199742) BOUND_VARIABLE_1199743) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_10 (ho_4258 (ho_4265 _let_10 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 _let_11 (ho_4769 k_4768 _let_1))))))))))))))))))))) (let ((_let_3894 (forall ((BOUND_VARIABLE_1199634 tptp.real) (BOUND_VARIABLE_1199635 tptp.real) (BOUND_VARIABLE_1199636 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4740 (ho_4782 k_4786 BOUND_VARIABLE_1199634) BOUND_VARIABLE_1199635) BOUND_VARIABLE_1199636)) (ho_4516 k_4515 (ho_4287 k_4787 BOUND_VARIABLE_1199636))) (ho_4245 (ho_4244 (ho_5451 k_6505 BOUND_VARIABLE_1199634) BOUND_VARIABLE_1199635) BOUND_VARIABLE_1199636))))) (let ((_let_3895 (forall ((BOUND_VARIABLE_1199581 tptp.real) (BOUND_VARIABLE_1199582 tptp.real) (BOUND_VARIABLE_1199583 tptp.nat)) (let ((_let_1 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_2 (ho_4263 (ho_4262 k_4261 k_4252) _let_1))) (let ((_let_3 (ho_4264 _let_2 k_4259))) (let ((_let_4 (ho_4247 k_4246 tptp.one))) (let ((_let_5 (ho_4258 (ho_4257 _let_1 k_4248) _let_4))) (let ((_let_6 (ho_4258 (ho_4265 _let_3 _let_4) _let_5))) (let ((_let_7 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_8 (ho_4264 _let_2 k_4275))) (= (ho_4245 (ho_4244 (ho_5451 k_6506 BOUND_VARIABLE_1199581) BOUND_VARIABLE_1199582) BOUND_VARIABLE_1199583) (ho_4258 (ho_4265 _let_8 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199583 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) (ho_4258 (ho_4265 _let_8 (ho_4245 (ho_4244 k_4243 _let_5) (ho_4216 (ho_4215 k_4221 BOUND_VARIABLE_1199583) _let_7))) (ho_4258 (ho_4257 _let_1 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_7) BOUND_VARIABLE_1199583) (ho_4213 k_4212 (ho_4196 k_4195 tptp.one)))) _let_6)))) _let_6)) (ho_4245 (ho_4244 k_4243 (ho_4258 (ho_4265 _let_3 BOUND_VARIABLE_1199581) BOUND_VARIABLE_1199582)) BOUND_VARIABLE_1199583)))))))))))))) (let ((_let_3896 (forall ((BOUND_VARIABLE_1199454 tptp.complex) (BOUND_VARIABLE_1199455 tptp.complex) (BOUND_VARIABLE_1199456 tptp.nat)) (= (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4778 (ho_4777 k_4788 BOUND_VARIABLE_1199454) BOUND_VARIABLE_1199455) BOUND_VARIABLE_1199456)) (ho_4516 k_4515 (ho_4287 k_4789 BOUND_VARIABLE_1199456))) (ho_4767 (ho_4766 (ho_6497 k_6507 BOUND_VARIABLE_1199454) BOUND_VARIABLE_1199455) BOUND_VARIABLE_1199456))))) (let ((_let_3897 (forall ((BOUND_VARIABLE_1199389 tptp.complex) (BOUND_VARIABLE_1199390 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1199389) BOUND_VARIABLE_1199390))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199390 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1199390) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1199390) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6508 BOUND_VARIABLE_1199389) BOUND_VARIABLE_1199390) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_3898 (forall ((BOUND_VARIABLE_1199324 tptp.complex) (BOUND_VARIABLE_1199325 tptp.nat)) (let ((_let_1 (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1199324) BOUND_VARIABLE_1199325))) (let ((_let_2 (ho_4247 k_4246 tptp.one))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4258 (ho_4257 _let_3 k_4248) _let_2))) (let ((_let_5 (ho_4263 (ho_4262 k_4261 k_4252) _let_3))) (let ((_let_6 (ho_4258 (ho_4265 (ho_4264 _let_5 k_4259) _let_2) _let_4))) (let ((_let_7 (ho_4196 k_4195 tptp.one))) (let ((_let_8 (ho_4213 k_4212 _let_7))) (let ((_let_9 (ho_4193 k_4192 tptp.one))) (let ((_let_10 (ho_4213 k_4212 (ho_4196 k_4195 _let_9)))) (let ((_let_11 (ho_4257 _let_3 k_4274))) (let ((_let_12 (ho_4209 (ho_4211 k_4210 _let_7) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_7)))) (let ((_let_13 (ho_4219 k_4218 k_4217))) (let ((_let_14 (ho_4264 _let_5 k_4275))) (let ((_let_15 (ho_4265 _let_14 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199325 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_6) (ho_4258 (ho_4265 _let_14 (ho_4245 (ho_4244 k_4243 _let_4) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1199325) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_13 (ho_4216 (ho_4215 k_4221 _let_8) _let_10)) _let_12)) (ho_4209 (ho_4220 _let_13 _let_8) _let_12))))) _let_10))) (ho_4258 _let_11 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_10) BOUND_VARIABLE_1199325) _let_8)) _let_6))))))) (let ((_let_16 (ho_4247 k_4246 _let_9))) (= (ho_4767 (ho_4766 k_6509 BOUND_VARIABLE_1199324) BOUND_VARIABLE_1199325) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4773 _let_1)))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_14 (ho_4258 (ho_4265 _let_14 _let_16) (ho_4506 k_4505 k_4504))) (ho_4258 _let_11 _let_16)))) (ho_4771 k_4770 (ho_4258 _let_15 (ho_4769 k_4768 _let_1))))))))))))))))))))))))) (let ((_let_3899 (forall ((BOUND_VARIABLE_1199213 tptp.real) (BOUND_VARIABLE_1199214 tptp.real) (BOUND_VARIABLE_1199215 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4740 (ho_4782 k_4790 BOUND_VARIABLE_1199213) BOUND_VARIABLE_1199214) BOUND_VARIABLE_1199215)) (ho_4516 k_4515 (ho_4287 k_4791 BOUND_VARIABLE_1199215))) (ho_4245 (ho_4244 (ho_5451 k_6510 BOUND_VARIABLE_1199213) BOUND_VARIABLE_1199214) BOUND_VARIABLE_1199215))))) (let ((_let_3900 (forall ((BOUND_VARIABLE_1199162 tptp.real) (BOUND_VARIABLE_1199163 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6511 BOUND_VARIABLE_1199162) BOUND_VARIABLE_1199163) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199163 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1199163) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1199163) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199162) BOUND_VARIABLE_1199163))))))))))))))))) (let ((_let_3901 (forall ((BOUND_VARIABLE_1199111 tptp.real) (BOUND_VARIABLE_1199112 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4196 k_4195 tptp.one))) (let ((_let_7 (ho_4213 k_4212 _let_6))) (let ((_let_8 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_9 (ho_4209 (ho_4211 k_4210 _let_6) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_6)))) (let ((_let_10 (ho_4219 k_4218 k_4217))) (let ((_let_11 (ho_4264 _let_4 k_4275))) (= (ho_4245 (ho_4244 k_6512 BOUND_VARIABLE_1199111) BOUND_VARIABLE_1199112) (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 (ho_4277 k_4276 (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (not (= BOUND_VARIABLE_1199112 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 K3) _let_2))))))))))) _let_5) (ho_4258 (ho_4265 _let_11 (ho_4245 (ho_4244 k_4243 _let_3) (ho_4216 (ho_4215 k_4221 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1199112) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_10 (ho_4216 (ho_4215 k_4221 _let_7) _let_8)) _let_9)) (ho_4209 (ho_4220 _let_10 _let_7) _let_9))))) _let_8))) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 (ho_4269 (ho_4268 k_4267 k_4266) _let_8) BOUND_VARIABLE_1199112) _let_7)) _let_5))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199111) BOUND_VARIABLE_1199112))))))))))))))))) (let ((_let_3902 (forall ((BOUND_VARIABLE_1199092 tptp.nat) (BOUND_VARIABLE_1199093 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4259))) (let ((_let_5 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 (ho_4257 _let_2 k_4274) (ho_4247 k_4246 (ho_4193 k_4192 tptp.one))))) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1199092) (ho_4258 (ho_4265 _let_4 _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1))))) BOUND_VARIABLE_1199093) (ho_4258 (ho_4273 k_6513 BOUND_VARIABLE_1199092) BOUND_VARIABLE_1199093)))))))))) (let ((_let_3903 (forall ((BOUND_VARIABLE_1199073 tptp.nat) (BOUND_VARIABLE_1199074 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)))) (let ((_let_4 (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_5 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_5))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4447 _let_6 k_4697))) (= (ho_4442 (ho_4448 _let_8 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_8 _let_4) (ho_4442 (ho_4441 _let_5 k_4449) (ho_4434 k_4433 (ho_4432 _let_3 (ho_4428 (ho_4427 k_4426 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))) _let_1)))))) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1199073) (ho_4442 (ho_4448 _let_7 _let_4) (ho_4442 (ho_4441 _let_5 k_4435) _let_4))))) BOUND_VARIABLE_1199074) (ho_4442 (ho_4458 k_6514 BOUND_VARIABLE_1199073) BOUND_VARIABLE_1199074))))))))))))) (let ((_let_3904 (forall ((BOUND_VARIABLE_1199054 tptp.nat) (BOUND_VARIABLE_1199055 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4193 k_4192 tptp.one))) (let ((_let_3 (ho_4213 k_4212 (ho_4196 k_4195 _let_2)))) (let ((_let_4 (ho_4701 k_4700 _let_2))) (let ((_let_5 (ho_4769 k_4768 _let_4))) (let ((_let_6 (ho_4769 k_4773 _let_4))) (let ((_let_7 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_8 (ho_4263 (ho_4262 k_4261 k_4252) _let_7))) (let ((_let_9 (ho_4257 _let_7 k_4274))) (let ((_let_10 (ho_4258 _let_9 (ho_4258 (ho_4265 (ho_4264 _let_8 k_4259) (ho_4245 (ho_4244 k_4243 _let_6) _let_3)) (ho_4245 (ho_4244 k_4243 _let_5) _let_3))))) (let ((_let_11 (ho_4264 _let_8 k_4275))) (let ((_let_12 (ho_4247 k_4246 _let_2))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4710 _let_1) (ho_4703 (ho_4705 k_4704 (ho_4771 k_4770 (ho_4258 (ho_4265 _let_11 _let_6) _let_10))) (ho_4703 (ho_4705 k_4710 (ho_4771 k_4772 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4265 _let_11 _let_12) (ho_4506 k_4505 k_4504))) (ho_4258 _let_9 _let_12)))) (ho_4771 k_4770 (ho_4258 (ho_4265 _let_11 (ho_4258 (ho_4257 _let_7 k_4248) _let_5)) _let_10)))))) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1199054) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1199055) (ho_4703 (ho_4709 k_6515 BOUND_VARIABLE_1199054) BOUND_VARIABLE_1199055))))))))))))))))) (let ((_let_3905 (forall ((BOUND_VARIABLE_1315706 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1199039 tptp.real) (BOUND_VARIABLE_1199040 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1315706 BOUND_VARIABLE_1199040)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199039) BOUND_VARIABLE_1199040)) (ho_4245 (ho_4244 (ho_4512 k_6516 BOUND_VARIABLE_1315706) BOUND_VARIABLE_1199039) BOUND_VARIABLE_1199040))))) (let ((_let_3906 (forall ((BOUND_VARIABLE_1315722 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1199023 tptp.real) (BOUND_VARIABLE_1199024 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1315722 BOUND_VARIABLE_1199024)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1199023) BOUND_VARIABLE_1199024)) (ho_4245 (ho_4244 (ho_4512 k_6517 BOUND_VARIABLE_1315722) BOUND_VARIABLE_1199023) BOUND_VARIABLE_1199024))))) (let ((_let_3907 (forall ((BOUND_VARIABLE_1199012 tptp.nat) (BOUND_VARIABLE_1199013 tptp.nat)) (= (ho_4288 (ho_4287 k_6518 BOUND_VARIABLE_1199012) BOUND_VARIABLE_1199013) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1199013)) (ho_4290 k_4289 BOUND_VARIABLE_1199012)))))) (let ((_let_3908 (forall ((BOUND_VARIABLE_1315752 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1198909 tptp.real) (BOUND_VARIABLE_1198910 tptp.nat) (BOUND_VARIABLE_1198911 tptp.real) (BOUND_VARIABLE_1198912 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4740 (ho_4793 k_4792 BOUND_VARIABLE_1315752) BOUND_VARIABLE_1198909) BOUND_VARIABLE_1198912)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4794 BOUND_VARIABLE_1198912) BOUND_VARIABLE_1198910)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1198911) BOUND_VARIABLE_1198912)) (ho_4245 (ho_4244 (ho_4492 (ho_6521 (ho_6520 k_6519 BOUND_VARIABLE_1315752) BOUND_VARIABLE_1198909) BOUND_VARIABLE_1198910) BOUND_VARIABLE_1198911) BOUND_VARIABLE_1198912))))) (let ((_let_3909 (forall ((BOUND_VARIABLE_1198898 tptp.nat) (BOUND_VARIABLE_1198899 tptp.nat)) (= (ho_4288 (ho_4287 k_6522 BOUND_VARIABLE_1198898) BOUND_VARIABLE_1198899) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1198899)) (ho_4290 k_4289 BOUND_VARIABLE_1198898)))))) (let ((_let_3910 (forall ((BOUND_VARIABLE_1315795 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1198887 tptp.int) (BOUND_VARIABLE_1198888 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6523 BOUND_VARIABLE_1315795) BOUND_VARIABLE_1198887) BOUND_VARIABLE_1198888) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1315795 BOUND_VARIABLE_1198888)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1198887) BOUND_VARIABLE_1198888)))))) (let ((_let_3911 (forall ((BOUND_VARIABLE_1315811 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1198875 tptp.int) (BOUND_VARIABLE_1198876 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6524 BOUND_VARIABLE_1315811) BOUND_VARIABLE_1198875) BOUND_VARIABLE_1198876) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1315811 BOUND_VARIABLE_1198876)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1198875) BOUND_VARIABLE_1198876)))))) (let ((_let_3912 (forall ((BOUND_VARIABLE_1198864 tptp.nat) (BOUND_VARIABLE_1198865 tptp.nat)) (= (ho_4288 (ho_4287 k_6525 BOUND_VARIABLE_1198864) BOUND_VARIABLE_1198865) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198865)) (ho_4290 k_4289 BOUND_VARIABLE_1198864)))))) (let ((_let_3913 (forall ((BOUND_VARIABLE_1315840 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1198761 tptp.int) (BOUND_VARIABLE_1198762 tptp.nat) (BOUND_VARIABLE_1198763 tptp.int) (BOUND_VARIABLE_1198764 tptp.nat)) (= (ho_4209 (ho_4211 k_4222 (ho_6080 (ho_6079 k_6526 (ho_4726 (ho_4725 (ho_4796 k_4795 BOUND_VARIABLE_1315840) BOUND_VARIABLE_1198761) BOUND_VARIABLE_1198764)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4797 BOUND_VARIABLE_1198764) BOUND_VARIABLE_1198762)))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1198763) BOUND_VARIABLE_1198764)) (ho_4335 (ho_4334 (ho_6530 (ho_6529 (ho_6528 k_6527 BOUND_VARIABLE_1315840) BOUND_VARIABLE_1198761) BOUND_VARIABLE_1198762) BOUND_VARIABLE_1198763) BOUND_VARIABLE_1198764))))) (let ((_let_3914 (forall ((BOUND_VARIABLE_1198750 tptp.nat) (BOUND_VARIABLE_1198751 tptp.nat)) (= (ho_4288 (ho_4287 k_6531 BOUND_VARIABLE_1198750) BOUND_VARIABLE_1198751) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1198751)) (ho_4290 k_4289 BOUND_VARIABLE_1198750)))))) (let ((_let_3915 (forall ((BOUND_VARIABLE_1315886 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1198735 tptp.rat) (BOUND_VARIABLE_1198736 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1315886 BOUND_VARIABLE_1198736)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1198735) BOUND_VARIABLE_1198736)) (ho_4316 (ho_4799 (ho_6533 k_6532 BOUND_VARIABLE_1315886) BOUND_VARIABLE_1198735) BOUND_VARIABLE_1198736))))) (let ((_let_3916 (forall ((BOUND_VARIABLE_1315906 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1198719 tptp.rat) (BOUND_VARIABLE_1198720 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1315906 BOUND_VARIABLE_1198720)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1198719) BOUND_VARIABLE_1198720)) (ho_4316 (ho_4799 (ho_6533 k_6534 BOUND_VARIABLE_1315906) BOUND_VARIABLE_1198719) BOUND_VARIABLE_1198720))))) (let ((_let_3917 (forall ((BOUND_VARIABLE_1198708 tptp.nat) (BOUND_VARIABLE_1198709 tptp.nat)) (= (ho_4288 (ho_4287 k_6535 BOUND_VARIABLE_1198708) BOUND_VARIABLE_1198709) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198709)) (ho_4290 k_4289 BOUND_VARIABLE_1198708)))))) (let ((_let_3918 (forall ((BOUND_VARIABLE_1315936 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1198605 tptp.rat) (BOUND_VARIABLE_1198606 tptp.nat) (BOUND_VARIABLE_1198607 tptp.rat) (BOUND_VARIABLE_1198608 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_6089 (ho_6088 k_6536 (ho_4338 (ho_4736 (ho_4801 k_4800 BOUND_VARIABLE_1315936) BOUND_VARIABLE_1198605) BOUND_VARIABLE_1198608)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4802 BOUND_VARIABLE_1198608) BOUND_VARIABLE_1198606)))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1198607) BOUND_VARIABLE_1198608)) (ho_4316 (ho_4799 (ho_6540 (ho_6539 (ho_6538 k_6537 BOUND_VARIABLE_1315936) BOUND_VARIABLE_1198605) BOUND_VARIABLE_1198606) BOUND_VARIABLE_1198607) BOUND_VARIABLE_1198608))))) (let ((_let_3919 (forall ((BOUND_VARIABLE_1198594 tptp.nat) (BOUND_VARIABLE_1198595 tptp.nat)) (= (ho_4288 (ho_4287 k_6541 BOUND_VARIABLE_1198594) BOUND_VARIABLE_1198595) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1198595)) (ho_4290 k_4289 BOUND_VARIABLE_1198594)))))) (let ((_let_3920 (forall ((BOUND_VARIABLE_1315983 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1198583 tptp.complex) (BOUND_VARIABLE_1198584 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6542 BOUND_VARIABLE_1315983) BOUND_VARIABLE_1198583) BOUND_VARIABLE_1198584) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1315983 BOUND_VARIABLE_1198584)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1198583) BOUND_VARIABLE_1198584)))))) (let ((_let_3921 (forall ((BOUND_VARIABLE_1315999 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1198571 tptp.complex) (BOUND_VARIABLE_1198572 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6543 BOUND_VARIABLE_1315999) BOUND_VARIABLE_1198571) BOUND_VARIABLE_1198572) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1315999 BOUND_VARIABLE_1198572)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1198571) BOUND_VARIABLE_1198572)))))) (let ((_let_3922 (forall ((BOUND_VARIABLE_1198560 tptp.nat) (BOUND_VARIABLE_1198561 tptp.nat)) (= (ho_4288 (ho_4287 k_6544 BOUND_VARIABLE_1198560) BOUND_VARIABLE_1198561) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198561)) (ho_4290 k_4289 BOUND_VARIABLE_1198560)))))) (let ((_let_3923 (forall ((BOUND_VARIABLE_1316028 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1198457 tptp.complex) (BOUND_VARIABLE_1198458 tptp.nat) (BOUND_VARIABLE_1198459 tptp.complex) (BOUND_VARIABLE_1198460 tptp.nat)) (= (ho_4703 (ho_4705 k_4710 (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4778 (ho_4804 k_4803 BOUND_VARIABLE_1316028) BOUND_VARIABLE_1198457) BOUND_VARIABLE_1198460)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4805 BOUND_VARIABLE_1198460) BOUND_VARIABLE_1198458)))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1198459) BOUND_VARIABLE_1198460)) (ho_4767 (ho_4766 (ho_6548 (ho_6547 (ho_6546 k_6545 BOUND_VARIABLE_1316028) BOUND_VARIABLE_1198457) BOUND_VARIABLE_1198458) BOUND_VARIABLE_1198459) BOUND_VARIABLE_1198460))))) (let ((_let_3924 (forall ((BOUND_VARIABLE_1198446 tptp.nat) (BOUND_VARIABLE_1198447 tptp.nat)) (= (ho_4288 (ho_4287 k_6549 BOUND_VARIABLE_1198446) BOUND_VARIABLE_1198447) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1198447)) (ho_4290 k_4289 BOUND_VARIABLE_1198446)))))) (let ((_let_3925 (forall ((BOUND_VARIABLE_1316073 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1198431 tptp.real) (BOUND_VARIABLE_1198432 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1316073 BOUND_VARIABLE_1198432)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1198431) BOUND_VARIABLE_1198432)) (ho_4245 (ho_4244 (ho_4512 k_6550 BOUND_VARIABLE_1316073) BOUND_VARIABLE_1198431) BOUND_VARIABLE_1198432))))) (let ((_let_3926 (forall ((BOUND_VARIABLE_1198420 tptp.nat) (BOUND_VARIABLE_1198421 tptp.nat)) (= (ho_4288 (ho_4287 k_6551 BOUND_VARIABLE_1198420) BOUND_VARIABLE_1198421) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198421)) (ho_4290 k_4289 BOUND_VARIABLE_1198420)))))) (let ((_let_3927 (forall ((BOUND_VARIABLE_1316101 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1198409 tptp.complex) (BOUND_VARIABLE_1198410 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6552 BOUND_VARIABLE_1316101) BOUND_VARIABLE_1198409) BOUND_VARIABLE_1198410) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1316101 BOUND_VARIABLE_1198410)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1198409) BOUND_VARIABLE_1198410)))))) (let ((_let_3928 (forall ((BOUND_VARIABLE_1198398 tptp.nat) (BOUND_VARIABLE_1198399 tptp.nat)) (= (ho_4288 (ho_4287 k_6553 BOUND_VARIABLE_1198398) BOUND_VARIABLE_1198399) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198399)) (ho_4290 k_4289 BOUND_VARIABLE_1198398)))))) (let ((_let_3929 (forall ((BOUND_VARIABLE_1198378 tptp.nat) (BOUND_VARIABLE_1198379 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1198379)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198378) BOUND_VARIABLE_1198379)) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (ho_4245 (ho_4487 k_6554 BOUND_VARIABLE_1198378) BOUND_VARIABLE_1198379))))))))) (let ((_let_3930 (forall ((BOUND_VARIABLE_1198368 tptp.nat) (BOUND_VARIABLE_1198369 tptp.nat)) (= (ho_4288 (ho_4287 k_6555 BOUND_VARIABLE_1198368) BOUND_VARIABLE_1198369) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198369)) (ho_4290 k_4289 BOUND_VARIABLE_1198368)))))) (let ((_let_3931 (forall ((BOUND_VARIABLE_1198348 tptp.nat) (BOUND_VARIABLE_1198349 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1198349)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198348) BOUND_VARIABLE_1198349)) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) _let_5))) (ho_4316 (ho_4338 k_6556 BOUND_VARIABLE_1198348) BOUND_VARIABLE_1198349))))))))))) (let ((_let_3932 (forall ((BOUND_VARIABLE_1198338 tptp.nat) (BOUND_VARIABLE_1198339 tptp.nat)) (= (ho_4288 (ho_4287 k_6557 BOUND_VARIABLE_1198338) BOUND_VARIABLE_1198339) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198339)) (ho_4290 k_4289 BOUND_VARIABLE_1198338)))))) (let ((_let_3933 (forall ((BOUND_VARIABLE_1198318 tptp.nat) (BOUND_VARIABLE_1198319 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (= (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) BOUND_VARIABLE_1198319)) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198318) BOUND_VARIABLE_1198319)) (ho_4209 (ho_4211 k_4210 _let_1) _let_2))) (ho_4335 (ho_4726 k_6558 BOUND_VARIABLE_1198318) BOUND_VARIABLE_1198319))))))) (let ((_let_3934 (forall ((BOUND_VARIABLE_1198308 tptp.nat) (BOUND_VARIABLE_1198309 tptp.nat)) (= (ho_4288 (ho_4287 k_6559 BOUND_VARIABLE_1198308) BOUND_VARIABLE_1198309) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198309)) (ho_4290 k_4289 BOUND_VARIABLE_1198308)))))) (let ((_let_3935 (forall ((BOUND_VARIABLE_1198296 tptp.nat) (BOUND_VARIABLE_1198297 tptp.nat)) (= (ho_5196 (ho_6561 k_6560 BOUND_VARIABLE_1198296) BOUND_VARIABLE_1198297) (ho_4560 (ho_4564 k_4630 (ho_5196 (ho_6564 k_6563 (ho_4560 k_4559 (ho_4562 k_4561 tptp.one))) BOUND_VARIABLE_1198297)) (ho_5196 k_6562 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198296) BOUND_VARIABLE_1198297))))))) (let ((_let_3936 (forall ((BOUND_VARIABLE_1198286 tptp.nat) (BOUND_VARIABLE_1198287 tptp.nat)) (= (ho_4288 (ho_4287 k_6565 BOUND_VARIABLE_1198286) BOUND_VARIABLE_1198287) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198287)) (ho_4290 k_4289 BOUND_VARIABLE_1198286)))))) (let ((_let_3937 (forall ((BOUND_VARIABLE_1198268 tptp.nat) (BOUND_VARIABLE_1198269 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (= (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 _let_2) BOUND_VARIABLE_1198269)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198268) BOUND_VARIABLE_1198269)) (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (ho_4767 (ho_4779 k_6566 BOUND_VARIABLE_1198268) BOUND_VARIABLE_1198269))))))) (let ((_let_3938 (forall ((BOUND_VARIABLE_1198258 tptp.nat) (BOUND_VARIABLE_1198259 tptp.nat)) (= (ho_4288 (ho_4287 k_6567 BOUND_VARIABLE_1198258) BOUND_VARIABLE_1198259) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198259)) (ho_4290 k_4289 BOUND_VARIABLE_1198258)))))) (let ((_let_3939 (forall ((BOUND_VARIABLE_1198234 tptp.nat) (BOUND_VARIABLE_1198235 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1198235) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1198234) BOUND_VARIABLE_1198235)) _let_2))) (ho_4216 (ho_4215 k_6568 BOUND_VARIABLE_1198234) BOUND_VARIABLE_1198235)))))))) (let ((_let_3940 (forall ((BOUND_VARIABLE_1198224 tptp.nat) (BOUND_VARIABLE_1198225 tptp.nat)) (= (ho_4288 (ho_4287 k_6569 BOUND_VARIABLE_1198224) BOUND_VARIABLE_1198225) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198225)) (ho_4290 k_4289 BOUND_VARIABLE_1198224)))))) (let ((_let_3941 (forall ((BOUND_VARIABLE_1198214 tptp.nat) (BOUND_VARIABLE_1198215 tptp.nat)) (= (ho_4288 (ho_4287 k_6570 BOUND_VARIABLE_1198214) BOUND_VARIABLE_1198215) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198215)) (ho_4290 k_4289 BOUND_VARIABLE_1198214)))))) (let ((_let_3942 (forall ((BOUND_VARIABLE_1316298 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1198199 tptp.real) (BOUND_VARIABLE_1198200 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1316298 BOUND_VARIABLE_1198200)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1198199) BOUND_VARIABLE_1198200)) (ho_4245 (ho_4244 (ho_4512 k_6571 BOUND_VARIABLE_1316298) BOUND_VARIABLE_1198199) BOUND_VARIABLE_1198200))))) (let ((_let_3943 (forall ((BOUND_VARIABLE_1316314 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1198183 tptp.real) (BOUND_VARIABLE_1198184 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1316314 BOUND_VARIABLE_1198184)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1198183) BOUND_VARIABLE_1198184)) (ho_4245 (ho_4244 (ho_4512 k_6572 BOUND_VARIABLE_1316314) BOUND_VARIABLE_1198183) BOUND_VARIABLE_1198184))))) (let ((_let_3944 (forall ((BOUND_VARIABLE_1198172 tptp.nat) (BOUND_VARIABLE_1198173 tptp.nat)) (= (ho_4288 (ho_4287 k_6573 BOUND_VARIABLE_1198172) BOUND_VARIABLE_1198173) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198173)) (ho_4290 k_4289 BOUND_VARIABLE_1198172)))))) (let ((_let_3945 (forall ((BOUND_VARIABLE_1316342 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1198090 tptp.real) (BOUND_VARIABLE_1198091 tptp.real) (BOUND_VARIABLE_1198092 tptp.nat) (BOUND_VARIABLE_1198093 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4740 (ho_4782 (ho_4807 k_4806 BOUND_VARIABLE_1316342) BOUND_VARIABLE_1198090) BOUND_VARIABLE_1198091) BOUND_VARIABLE_1198093)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4808 BOUND_VARIABLE_1198092) BOUND_VARIABLE_1198093))) (ho_4245 (ho_4487 (ho_4740 (ho_4782 (ho_4807 k_6574 BOUND_VARIABLE_1316342) BOUND_VARIABLE_1198090) BOUND_VARIABLE_1198091) BOUND_VARIABLE_1198092) BOUND_VARIABLE_1198093))))) (let ((_let_3946 (forall ((BOUND_VARIABLE_1198079 tptp.nat) (BOUND_VARIABLE_1198080 tptp.nat)) (= (ho_4288 (ho_4287 k_6575 BOUND_VARIABLE_1198079) BOUND_VARIABLE_1198080) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1198080)) (ho_4290 k_4289 BOUND_VARIABLE_1198079)))))) (let ((_let_3947 (forall ((BOUND_VARIABLE_1316377 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1198068 tptp.int) (BOUND_VARIABLE_1198069 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6576 BOUND_VARIABLE_1316377) BOUND_VARIABLE_1198068) BOUND_VARIABLE_1198069) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1316377 BOUND_VARIABLE_1198069)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1198068) BOUND_VARIABLE_1198069)))))) (let ((_let_3948 (forall ((BOUND_VARIABLE_1316393 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1198056 tptp.int) (BOUND_VARIABLE_1198057 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6577 BOUND_VARIABLE_1316393) BOUND_VARIABLE_1198056) BOUND_VARIABLE_1198057) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1316393 BOUND_VARIABLE_1198057)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1198056) BOUND_VARIABLE_1198057)))))) (let ((_let_3949 (forall ((BOUND_VARIABLE_1198045 tptp.nat) (BOUND_VARIABLE_1198046 tptp.nat)) (= (ho_4288 (ho_4287 k_6578 BOUND_VARIABLE_1198045) BOUND_VARIABLE_1198046) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1198046)) (ho_4290 k_4289 BOUND_VARIABLE_1198045)))))) (let ((_let_3950 (forall ((BOUND_VARIABLE_1316420 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1197963 tptp.int) (BOUND_VARIABLE_1197964 tptp.int) (BOUND_VARIABLE_1197965 tptp.nat) (BOUND_VARIABLE_1197966 tptp.nat)) (= (ho_6080 (ho_6079 k_6526 (ho_4726 (ho_4725 (ho_4811 (ho_4810 k_4809 BOUND_VARIABLE_1316420) BOUND_VARIABLE_1197963) BOUND_VARIABLE_1197964) BOUND_VARIABLE_1197966)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4812 BOUND_VARIABLE_1197965) BOUND_VARIABLE_1197966))) (ho_4335 (ho_4726 (ho_4725 (ho_4811 (ho_4810 k_6579 BOUND_VARIABLE_1316420) BOUND_VARIABLE_1197963) BOUND_VARIABLE_1197964) BOUND_VARIABLE_1197965) BOUND_VARIABLE_1197966))))) (let ((_let_3951 (forall ((BOUND_VARIABLE_1197952 tptp.nat) (BOUND_VARIABLE_1197953 tptp.nat)) (= (ho_4288 (ho_4287 k_6580 BOUND_VARIABLE_1197952) BOUND_VARIABLE_1197953) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197953)) (ho_4290 k_4289 BOUND_VARIABLE_1197952)))))) (let ((_let_3952 (forall ((BOUND_VARIABLE_1316454 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1197937 tptp.rat) (BOUND_VARIABLE_1197938 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1316454 BOUND_VARIABLE_1197938)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1197937) BOUND_VARIABLE_1197938)) (ho_4316 (ho_4799 (ho_6533 k_6581 BOUND_VARIABLE_1316454) BOUND_VARIABLE_1197937) BOUND_VARIABLE_1197938))))) (let ((_let_3953 (forall ((BOUND_VARIABLE_1316470 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1197921 tptp.rat) (BOUND_VARIABLE_1197922 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1316470 BOUND_VARIABLE_1197922)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1197921) BOUND_VARIABLE_1197922)) (ho_4316 (ho_4799 (ho_6533 k_6582 BOUND_VARIABLE_1316470) BOUND_VARIABLE_1197921) BOUND_VARIABLE_1197922))))) (let ((_let_3954 (forall ((BOUND_VARIABLE_1197910 tptp.nat) (BOUND_VARIABLE_1197911 tptp.nat)) (= (ho_4288 (ho_4287 k_6583 BOUND_VARIABLE_1197910) BOUND_VARIABLE_1197911) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197911)) (ho_4290 k_4289 BOUND_VARIABLE_1197910)))))) (let ((_let_3955 (forall ((BOUND_VARIABLE_1316498 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1197828 tptp.rat) (BOUND_VARIABLE_1197829 tptp.rat) (BOUND_VARIABLE_1197830 tptp.nat) (BOUND_VARIABLE_1197831 tptp.nat)) (= (ho_6089 (ho_6088 k_6536 (ho_4338 (ho_4736 (ho_4815 (ho_4814 k_4813 BOUND_VARIABLE_1316498) BOUND_VARIABLE_1197828) BOUND_VARIABLE_1197829) BOUND_VARIABLE_1197831)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4816 BOUND_VARIABLE_1197830) BOUND_VARIABLE_1197831))) (ho_4316 (ho_4338 (ho_4736 (ho_4815 (ho_4814 k_6584 BOUND_VARIABLE_1316498) BOUND_VARIABLE_1197828) BOUND_VARIABLE_1197829) BOUND_VARIABLE_1197830) BOUND_VARIABLE_1197831))))) (let ((_let_3956 (forall ((BOUND_VARIABLE_1197817 tptp.nat) (BOUND_VARIABLE_1197818 tptp.nat)) (= (ho_4288 (ho_4287 k_6585 BOUND_VARIABLE_1197817) BOUND_VARIABLE_1197818) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197818)) (ho_4290 k_4289 BOUND_VARIABLE_1197817)))))) (let ((_let_3957 (forall ((BOUND_VARIABLE_1316533 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1197806 tptp.complex) (BOUND_VARIABLE_1197807 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6586 BOUND_VARIABLE_1316533) BOUND_VARIABLE_1197806) BOUND_VARIABLE_1197807) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1316533 BOUND_VARIABLE_1197807)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1197806) BOUND_VARIABLE_1197807)))))) (let ((_let_3958 (forall ((BOUND_VARIABLE_1316549 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1197794 tptp.complex) (BOUND_VARIABLE_1197795 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6587 BOUND_VARIABLE_1316549) BOUND_VARIABLE_1197794) BOUND_VARIABLE_1197795) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1316549 BOUND_VARIABLE_1197795)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1197794) BOUND_VARIABLE_1197795)))))) (let ((_let_3959 (forall ((BOUND_VARIABLE_1197783 tptp.nat) (BOUND_VARIABLE_1197784 tptp.nat)) (= (ho_4288 (ho_4287 k_6588 BOUND_VARIABLE_1197783) BOUND_VARIABLE_1197784) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197784)) (ho_4290 k_4289 BOUND_VARIABLE_1197783)))))) (let ((_let_3960 (forall ((BOUND_VARIABLE_1316576 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1197701 tptp.complex) (BOUND_VARIABLE_1197702 tptp.complex) (BOUND_VARIABLE_1197703 tptp.nat) (BOUND_VARIABLE_1197704 tptp.nat)) (= (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4778 (ho_4777 (ho_4818 k_4817 BOUND_VARIABLE_1316576) BOUND_VARIABLE_1197701) BOUND_VARIABLE_1197702) BOUND_VARIABLE_1197704)) (ho_4516 k_4515 (ho_4287 (ho_4303 k_4819 BOUND_VARIABLE_1197703) BOUND_VARIABLE_1197704))) (ho_4767 (ho_4779 (ho_4778 (ho_4777 (ho_4818 k_6589 BOUND_VARIABLE_1316576) BOUND_VARIABLE_1197701) BOUND_VARIABLE_1197702) BOUND_VARIABLE_1197703) BOUND_VARIABLE_1197704))))) (let ((_let_3961 (forall ((BOUND_VARIABLE_1197690 tptp.nat) (BOUND_VARIABLE_1197691 tptp.nat)) (= (ho_4288 (ho_4287 k_6590 BOUND_VARIABLE_1197690) BOUND_VARIABLE_1197691) (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197691)) (ho_4290 k_4289 BOUND_VARIABLE_1197690)))))) (let ((_let_3962 (forall ((BOUND_VARIABLE_1197662 tptp.nat) (BOUND_VARIABLE_1197663 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4258 (ho_4257 _let_2 k_4248) _let_1))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) _let_3))) (let ((_let_6 (ho_4272 k_4271 k_4270))) (let ((_let_7 (ho_4264 _let_4 k_4275))) (= (ho_4258 (ho_4265 _let_7 (ho_4258 (ho_4265 _let_7 (ho_4245 (ho_4244 k_4243 _let_3) BOUND_VARIABLE_1197663)) (ho_4258 (ho_4273 _let_6 BOUND_VARIABLE_1197663) _let_5))) (ho_4258 (ho_4273 _let_6 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1197662) BOUND_VARIABLE_1197663)) _let_5)) (ho_4245 (ho_4487 k_6591 BOUND_VARIABLE_1197662) BOUND_VARIABLE_1197663)))))))))))) (let ((_let_3963 (forall ((BOUND_VARIABLE_1197652 tptp.nat) (BOUND_VARIABLE_1197653 tptp.nat)) (= (ho_4288 (ho_4287 k_6592 BOUND_VARIABLE_1197652) BOUND_VARIABLE_1197653) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197653)) (ho_4290 k_4289 BOUND_VARIABLE_1197652)))))) (let ((_let_3964 (forall ((BOUND_VARIABLE_1197624 tptp.nat) (BOUND_VARIABLE_1197625 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4442 (ho_4441 _let_4 k_4435) _let_3))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) _let_5))) (let ((_let_8 (ho_4457 k_4456 k_4455))) (let ((_let_9 (ho_4447 _let_6 k_4697))) (= (ho_4442 (ho_4448 _let_9 (ho_4442 (ho_4448 _let_9 (ho_4316 (ho_4799 k_4798 _let_5) BOUND_VARIABLE_1197625)) (ho_4442 (ho_4458 _let_8 BOUND_VARIABLE_1197625) _let_7))) (ho_4442 (ho_4458 _let_8 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1197624) BOUND_VARIABLE_1197625)) _let_7)) (ho_4316 (ho_4338 k_6593 BOUND_VARIABLE_1197624) BOUND_VARIABLE_1197625)))))))))))))) (let ((_let_3965 (forall ((BOUND_VARIABLE_1197614 tptp.nat) (BOUND_VARIABLE_1197615 tptp.nat)) (= (ho_4288 (ho_4287 k_6594 BOUND_VARIABLE_1197614) BOUND_VARIABLE_1197615) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197615)) (ho_4290 k_4289 BOUND_VARIABLE_1197614)))))) (let ((_let_3966 (forall ((BOUND_VARIABLE_1197586 tptp.nat) (BOUND_VARIABLE_1197587 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) _let_2))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4222 (ho_4335 (ho_4334 k_4333 _let_2) BOUND_VARIABLE_1197587)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1197587) _let_3))) (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1197586) BOUND_VARIABLE_1197587)) _let_3)) (ho_4335 (ho_4726 k_6595 BOUND_VARIABLE_1197586) BOUND_VARIABLE_1197587))))))))) (let ((_let_3967 (forall ((BOUND_VARIABLE_1197576 tptp.nat) (BOUND_VARIABLE_1197577 tptp.nat)) (= (ho_4288 (ho_4287 k_6596 BOUND_VARIABLE_1197576) BOUND_VARIABLE_1197577) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197577)) (ho_4290 k_4289 BOUND_VARIABLE_1197576)))))) (let ((_let_3968 (forall ((BOUND_VARIABLE_1197561 tptp.nat) (BOUND_VARIABLE_1197562 tptp.nat)) (= (ho_5196 (ho_6561 k_6597 BOUND_VARIABLE_1197561) BOUND_VARIABLE_1197562) (ho_4560 (ho_4564 k_4630 (ho_4560 (ho_4564 k_4630 (ho_5196 (ho_6564 k_6563 (ho_4560 k_4559 (ho_4562 k_4561 tptp.one))) BOUND_VARIABLE_1197562)) (ho_5196 k_6562 BOUND_VARIABLE_1197562))) (ho_5196 k_6562 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1197561) BOUND_VARIABLE_1197562))))))) (let ((_let_3969 (forall ((BOUND_VARIABLE_1197551 tptp.nat) (BOUND_VARIABLE_1197552 tptp.nat)) (= (ho_4288 (ho_4287 k_6598 BOUND_VARIABLE_1197551) BOUND_VARIABLE_1197552) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197552)) (ho_4290 k_4289 BOUND_VARIABLE_1197551)))))) (let ((_let_3970 (forall ((BOUND_VARIABLE_1197525 tptp.nat) (BOUND_VARIABLE_1197526 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 k_4702 _let_1))) (let ((_let_3 (ho_4703 (ho_4705 k_4704 _let_1) _let_2))) (let ((_let_4 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4767 (ho_4766 k_4765 _let_2) BOUND_VARIABLE_1197526)) (ho_4703 (ho_4709 _let_4 BOUND_VARIABLE_1197526) _let_3))) (ho_4703 (ho_4709 _let_4 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1197525) BOUND_VARIABLE_1197526)) _let_3)) (ho_4767 (ho_4779 k_6599 BOUND_VARIABLE_1197525) BOUND_VARIABLE_1197526))))))))) (let ((_let_3971 (forall ((BOUND_VARIABLE_1197515 tptp.nat) (BOUND_VARIABLE_1197516 tptp.nat)) (= (ho_4288 (ho_4287 k_6600 BOUND_VARIABLE_1197515) BOUND_VARIABLE_1197516) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197516)) (ho_4290 k_4289 BOUND_VARIABLE_1197515)))))) (let ((_let_3972 (forall ((BOUND_VARIABLE_1197505 tptp.nat) (BOUND_VARIABLE_1197506 tptp.nat)) (= (ho_4288 (ho_4287 k_6601 BOUND_VARIABLE_1197505) BOUND_VARIABLE_1197506) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197506)) (ho_4290 k_4289 BOUND_VARIABLE_1197505)))))) (let ((_let_3973 (forall ((BOUND_VARIABLE_1197495 tptp.nat) (BOUND_VARIABLE_1197496 tptp.nat)) (= (ho_4288 (ho_4287 k_6602 BOUND_VARIABLE_1197495) BOUND_VARIABLE_1197496) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197496)) (ho_4290 k_4289 BOUND_VARIABLE_1197495)))))) (let ((_let_3974 (forall ((BOUND_VARIABLE_1197485 tptp.nat) (BOUND_VARIABLE_1197486 tptp.nat)) (= (ho_4288 (ho_4287 k_6603 BOUND_VARIABLE_1197485) BOUND_VARIABLE_1197486) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197486)) (ho_4290 k_4289 BOUND_VARIABLE_1197485)))))) (let ((_let_3975 (forall ((BOUND_VARIABLE_1197475 tptp.nat) (BOUND_VARIABLE_1197476 tptp.nat)) (= (ho_4288 (ho_4287 k_6604 BOUND_VARIABLE_1197475) BOUND_VARIABLE_1197476) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197476)) (ho_4290 k_4289 BOUND_VARIABLE_1197475)))))) (let ((_let_3976 (forall ((BOUND_VARIABLE_1197465 tptp.nat) (BOUND_VARIABLE_1197466 tptp.nat)) (= (ho_4288 (ho_4287 k_6605 BOUND_VARIABLE_1197465) BOUND_VARIABLE_1197466) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197466)) (ho_4290 k_4289 BOUND_VARIABLE_1197465)))))) (let ((_let_3977 (forall ((BOUND_VARIABLE_1197455 tptp.nat) (BOUND_VARIABLE_1197456 tptp.nat)) (= (ho_4288 (ho_4287 k_6606 BOUND_VARIABLE_1197455) BOUND_VARIABLE_1197456) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197456)) (ho_4290 k_4289 BOUND_VARIABLE_1197455)))))) (let ((_let_3978 (forall ((BOUND_VARIABLE_1197426 tptp.real) (BOUND_VARIABLE_1197427 tptp.nat) (BOUND_VARIABLE_1197428 tptp.real) (BOUND_VARIABLE_1197429 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (= (ho_4245 (ho_4244 (ho_4492 (ho_6521 k_6607 BOUND_VARIABLE_1197426) BOUND_VARIABLE_1197427) BOUND_VARIABLE_1197428) BOUND_VARIABLE_1197429) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1197429 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4258 _let_3 BOUND_VARIABLE_1197426)) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1197427 BOUND_VARIABLE_1197429)) _let_1) (ho_4258 (ho_4265 (ho_4264 _let_4 k_4259) _let_1) (ho_4258 _let_3 _let_1))))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1197428) BOUND_VARIABLE_1197429)))))))))) (let ((_let_3979 (forall ((BOUND_VARIABLE_1197416 tptp.nat) (BOUND_VARIABLE_1197417 tptp.nat)) (= (ho_4288 (ho_4287 k_6608 BOUND_VARIABLE_1197416) BOUND_VARIABLE_1197417) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197417)) (ho_4290 k_4289 BOUND_VARIABLE_1197416)))))) (let ((_let_3980 (forall ((BOUND_VARIABLE_1197386 tptp.rat) (BOUND_VARIABLE_1197387 tptp.nat) (BOUND_VARIABLE_1197388 tptp.rat) (BOUND_VARIABLE_1197389 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (= (ho_4316 (ho_4799 (ho_6540 (ho_6539 k_6609 BOUND_VARIABLE_1197386) BOUND_VARIABLE_1197387) BOUND_VARIABLE_1197388) BOUND_VARIABLE_1197389) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1197389 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4442 _let_5 BOUND_VARIABLE_1197386)) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1197387 BOUND_VARIABLE_1197389)) _let_3) (ho_4442 (ho_4448 (ho_4447 _let_6 k_4443) _let_3) (ho_4442 _let_5 _let_3))))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1197388) BOUND_VARIABLE_1197389)))))))))))) (let ((_let_3981 (forall ((BOUND_VARIABLE_1197376 tptp.nat) (BOUND_VARIABLE_1197377 tptp.nat)) (= (ho_4288 (ho_4287 k_6610 BOUND_VARIABLE_1197376) BOUND_VARIABLE_1197377) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197377)) (ho_4290 k_4289 BOUND_VARIABLE_1197376)))))) (let ((_let_3982 (forall ((BOUND_VARIABLE_1197355 tptp.code_integer) (BOUND_VARIABLE_1197356 tptp.nat) (BOUND_VARIABLE_1197357 tptp.code_integer) (BOUND_VARIABLE_1197358 tptp.nat)) (let ((_let_1 (ho_4562 k_4561 tptp.one))) (= (ho_5196 (ho_6564 (ho_6613 (ho_6612 k_6611 BOUND_VARIABLE_1197355) BOUND_VARIABLE_1197356) BOUND_VARIABLE_1197357) BOUND_VARIABLE_1197358) (ho_4560 (ho_4564 k_4630 (ho_4560 (ho_4564 (ho_4569 k_4568 (= BOUND_VARIABLE_1197358 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4560 k_4559 BOUND_VARIABLE_1197355)) (ho_4560 (ho_4564 (ho_4569 k_4568 (= BOUND_VARIABLE_1197356 BOUND_VARIABLE_1197358)) _let_1) (ho_4560 (ho_4564 k_4563 _let_1) (ho_4560 k_4559 _let_1))))) (ho_5196 (ho_6564 k_6563 BOUND_VARIABLE_1197357) BOUND_VARIABLE_1197358))))))) (let ((_let_3983 (forall ((BOUND_VARIABLE_1197345 tptp.nat) (BOUND_VARIABLE_1197346 tptp.nat)) (= (ho_4288 (ho_4287 k_6614 BOUND_VARIABLE_1197345) BOUND_VARIABLE_1197346) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197346)) (ho_4290 k_4289 BOUND_VARIABLE_1197345)))))) (let ((_let_3984 (forall ((BOUND_VARIABLE_1197324 tptp.complex) (BOUND_VARIABLE_1197325 tptp.nat) (BOUND_VARIABLE_1197326 tptp.complex) (BOUND_VARIABLE_1197327 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4767 (ho_4766 (ho_6548 (ho_6547 k_6615 BOUND_VARIABLE_1197324) BOUND_VARIABLE_1197325) BOUND_VARIABLE_1197326) BOUND_VARIABLE_1197327) (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1197327 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4703 k_4702 BOUND_VARIABLE_1197324)) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1197325 BOUND_VARIABLE_1197327)) _let_1) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1197326) BOUND_VARIABLE_1197327))))))) (let ((_let_3985 (forall ((BOUND_VARIABLE_1197314 tptp.nat) (BOUND_VARIABLE_1197315 tptp.nat)) (= (ho_4288 (ho_4287 k_6616 BOUND_VARIABLE_1197314) BOUND_VARIABLE_1197315) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197315)) (ho_4290 k_4289 BOUND_VARIABLE_1197314)))))) (let ((_let_3986 (forall ((BOUND_VARIABLE_1197285 tptp.int) (BOUND_VARIABLE_1197286 tptp.nat) (BOUND_VARIABLE_1197287 tptp.int) (BOUND_VARIABLE_1197288 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4335 (ho_4334 (ho_6530 (ho_6529 k_6617 BOUND_VARIABLE_1197285) BOUND_VARIABLE_1197286) BOUND_VARIABLE_1197287) BOUND_VARIABLE_1197288) (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1197288 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (ho_4209 _let_2 BOUND_VARIABLE_1197285)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1197286 BOUND_VARIABLE_1197288)) _let_1) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1))))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1197287) BOUND_VARIABLE_1197288)))))))) (let ((_let_3987 (forall ((BOUND_VARIABLE_1197275 tptp.nat) (BOUND_VARIABLE_1197276 tptp.nat)) (= (ho_4288 (ho_4287 k_6618 BOUND_VARIABLE_1197275) BOUND_VARIABLE_1197276) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197276)) (ho_4290 k_4289 BOUND_VARIABLE_1197275)))))) (let ((_let_3988 (forall ((BOUND_VARIABLE_1197258 tptp.nat) (BOUND_VARIABLE_1316998 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1316997 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1197261 tptp.nat)) (= (ho_4245 (ho_4473 (ho_5457 (ho_6620 k_6619 BOUND_VARIABLE_1197258) BOUND_VARIABLE_1316998) BOUND_VARIABLE_1316997) BOUND_VARIABLE_1197261) (ho_4258 (ho_4265 (ho_4277 k_4276 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197261)) (ho_4290 k_4289 BOUND_VARIABLE_1197258))) (ho_4245 BOUND_VARIABLE_1316998 BOUND_VARIABLE_1197261)) (ho_4245 BOUND_VARIABLE_1316997 BOUND_VARIABLE_1197261)))))) (let ((_let_3989 (forall ((BOUND_VARIABLE_1197241 tptp.nat) (BOUND_VARIABLE_1197242 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197242)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197241) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6621 BOUND_VARIABLE_1197241) BOUND_VARIABLE_1197242))))))))) (let ((_let_3990 (forall ((BOUND_VARIABLE_1317040 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1197212 tptp.nat) (BOUND_VARIABLE_1317035 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1197214 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (let ((_let_6 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197214)) (ho_4290 k_4289 BOUND_VARIABLE_1197212))) (ho_4245 BOUND_VARIABLE_1317040 BOUND_VARIABLE_1197214)) (ho_4258 (ho_4265 (ho_4277 k_4276 (= BOUND_VARIABLE_1197212 BOUND_VARIABLE_1197214)) (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_6) k_4259) _let_5) (ho_4258 (ho_4257 _let_6 k_4248) _let_5))) (ho_4245 BOUND_VARIABLE_1317035 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197214) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4245 (ho_4473 (ho_5084 (ho_5083 k_6622 BOUND_VARIABLE_1317040) BOUND_VARIABLE_1197212) BOUND_VARIABLE_1317035) BOUND_VARIABLE_1197214))))))))))) (let ((_let_3991 (forall ((BOUND_VARIABLE_1197201 tptp.nat) (BOUND_VARIABLE_1197202 tptp.nat)) (= (ho_4288 (ho_4287 k_6623 BOUND_VARIABLE_1197201) BOUND_VARIABLE_1197202) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197202)) (ho_4290 k_4289 BOUND_VARIABLE_1197201)))))) (let ((_let_3992 (forall ((BOUND_VARIABLE_1197184 tptp.nat) (BOUND_VARIABLE_1317077 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1317076 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1197187 tptp.nat)) (= (ho_4216 (ho_5088 (ho_5820 (ho_6001 k_6624 BOUND_VARIABLE_1197184) BOUND_VARIABLE_1317077) BOUND_VARIABLE_1317076) BOUND_VARIABLE_1197187) (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197187)) (ho_4290 k_4289 BOUND_VARIABLE_1197184))) (ho_4216 BOUND_VARIABLE_1317077 BOUND_VARIABLE_1197187)) (ho_4216 BOUND_VARIABLE_1317076 BOUND_VARIABLE_1197187)))))) (let ((_let_3993 (forall ((BOUND_VARIABLE_1197167 tptp.nat) (BOUND_VARIABLE_1197168 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197168)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197167) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6625 BOUND_VARIABLE_1197167) BOUND_VARIABLE_1197168))))))))) (let ((_let_3994 (forall ((BOUND_VARIABLE_1317115 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1197139 tptp.nat) (BOUND_VARIABLE_1317110 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1197141 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) (= (ho_4216 (ho_4215 (ho_4613 k_4612 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197141)) (ho_4290 k_4289 BOUND_VARIABLE_1197139))) (ho_4216 BOUND_VARIABLE_1317115 BOUND_VARIABLE_1197141)) (ho_4216 (ho_4215 (ho_4613 k_4612 (= BOUND_VARIABLE_1197139 BOUND_VARIABLE_1197141)) _let_5) (ho_4216 BOUND_VARIABLE_1317110 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197141) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 _let_5) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4216 (ho_5088 (ho_5087 (ho_5086 k_6626 BOUND_VARIABLE_1317115) BOUND_VARIABLE_1197139) BOUND_VARIABLE_1317110) BOUND_VARIABLE_1197141)))))))))) (let ((_let_3995 (forall ((BOUND_VARIABLE_1197128 tptp.nat) (BOUND_VARIABLE_1197129 tptp.nat)) (= (ho_4288 (ho_4287 k_6627 BOUND_VARIABLE_1197128) BOUND_VARIABLE_1197129) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197129)) (ho_4290 k_4289 BOUND_VARIABLE_1197128)))))) (let ((_let_3996 (forall ((BOUND_VARIABLE_1197111 tptp.nat) (BOUND_VARIABLE_1317152 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1317151 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1197114 tptp.nat)) (= (ho_4335 (ho_5994 (ho_5993 (ho_5992 k_6628 BOUND_VARIABLE_1197111) BOUND_VARIABLE_1317152) BOUND_VARIABLE_1317151) BOUND_VARIABLE_1197114) (ho_4209 (ho_4211 (ho_4593 k_4592 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197114)) (ho_4290 k_4289 BOUND_VARIABLE_1197111))) (ho_4335 BOUND_VARIABLE_1317152 BOUND_VARIABLE_1197114)) (ho_4335 BOUND_VARIABLE_1317151 BOUND_VARIABLE_1197114)))))) (let ((_let_3997 (forall ((BOUND_VARIABLE_1197094 tptp.nat) (BOUND_VARIABLE_1197095 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197095)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197094) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6629 BOUND_VARIABLE_1197094) BOUND_VARIABLE_1197095))))))))) (let ((_let_3998 (forall ((BOUND_VARIABLE_1317190 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1197065 tptp.nat) (BOUND_VARIABLE_1317185 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1197067 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 (ho_4593 k_4592 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197067)) (ho_4290 k_4289 BOUND_VARIABLE_1197065))) (ho_4335 BOUND_VARIABLE_1317190 BOUND_VARIABLE_1197067)) (ho_4209 (ho_4211 (ho_4593 k_4592 (= BOUND_VARIABLE_1197065 BOUND_VARIABLE_1197067)) _let_2) (ho_4335 BOUND_VARIABLE_1317185 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197067) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4335 (ho_5994 (ho_5998 (ho_5997 k_6630 BOUND_VARIABLE_1317190) BOUND_VARIABLE_1197065) BOUND_VARIABLE_1317185) BOUND_VARIABLE_1197067))))))))) (let ((_let_3999 (forall ((BOUND_VARIABLE_1197054 tptp.nat) (BOUND_VARIABLE_1197055 tptp.nat)) (= (ho_4288 (ho_4287 k_6631 BOUND_VARIABLE_1197054) BOUND_VARIABLE_1197055) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197055)) (ho_4290 k_4289 BOUND_VARIABLE_1197054)))))) (let ((_let_4000 (forall ((BOUND_VARIABLE_1197037 tptp.nat) (BOUND_VARIABLE_1317227 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1317226 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1197040 tptp.nat)) (= (ho_4316 (ho_4249 (ho_4260 (ho_6633 k_6632 BOUND_VARIABLE_1197037) BOUND_VARIABLE_1317227) BOUND_VARIABLE_1317226) BOUND_VARIABLE_1197040) (ho_4442 (ho_4448 (ho_5050 k_5049 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1197040)) (ho_4290 k_4289 BOUND_VARIABLE_1197037))) (ho_4316 BOUND_VARIABLE_1317227 BOUND_VARIABLE_1197040)) (ho_4316 BOUND_VARIABLE_1317226 BOUND_VARIABLE_1197040)))))) (let ((_let_4001 (forall ((BOUND_VARIABLE_1197020 tptp.nat) (BOUND_VARIABLE_1197021 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1197021)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1197020) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6634 BOUND_VARIABLE_1197020) BOUND_VARIABLE_1197021))))))))) (let ((_let_4002 (forall ((BOUND_VARIABLE_1317269 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1196991 tptp.nat) (BOUND_VARIABLE_1317264 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1196993 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_6 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (= (ho_4442 (ho_4448 (ho_5050 k_5049 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1196993)) (ho_4290 k_4289 BOUND_VARIABLE_1196991))) (ho_4316 BOUND_VARIABLE_1317269 BOUND_VARIABLE_1196993)) (ho_4442 (ho_4448 (ho_5050 k_5049 (= BOUND_VARIABLE_1196991 BOUND_VARIABLE_1196993)) (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) _let_6) k_4443) _let_5) (ho_4442 (ho_4441 _let_6 k_4435) _let_5))) (ho_4316 BOUND_VARIABLE_1317264 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1196993) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4316 (ho_4249 (ho_6637 (ho_6636 k_6635 BOUND_VARIABLE_1317269) BOUND_VARIABLE_1196991) BOUND_VARIABLE_1317264) BOUND_VARIABLE_1196993))))))))))) (let ((_let_4003 (forall ((BOUND_VARIABLE_1196980 tptp.nat) (BOUND_VARIABLE_1196981 tptp.nat)) (= (ho_4288 (ho_4287 k_6638 BOUND_VARIABLE_1196980) BOUND_VARIABLE_1196981) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196981)) (ho_4290 k_4289 BOUND_VARIABLE_1196980)))))) (let ((_let_4004 (forall ((BOUND_VARIABLE_1196963 tptp.nat) (BOUND_VARIABLE_1317314 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1317313 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196966 tptp.nat)) (= (ho_4767 (ho_6642 (ho_6641 (ho_6640 k_6639 BOUND_VARIABLE_1196963) BOUND_VARIABLE_1317314) BOUND_VARIABLE_1317313) BOUND_VARIABLE_1196966) (ho_4703 (ho_4705 (ho_4775 k_4774 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1196966)) (ho_4290 k_4289 BOUND_VARIABLE_1196963))) (ho_4767 BOUND_VARIABLE_1317314 BOUND_VARIABLE_1196966)) (ho_4767 BOUND_VARIABLE_1317313 BOUND_VARIABLE_1196966)))))) (let ((_let_4005 (forall ((BOUND_VARIABLE_1196946 tptp.nat) (BOUND_VARIABLE_1196947 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196947)) (ho_4290 k_4289 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1196946) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (ho_4288 (ho_4287 k_6643 BOUND_VARIABLE_1196946) BOUND_VARIABLE_1196947))))))))) (let ((_let_4006 (forall ((BOUND_VARIABLE_1317363 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196918 tptp.nat) (BOUND_VARIABLE_1317358 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196920 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 (ho_4775 k_4774 (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 BOUND_VARIABLE_1196920)) (ho_4290 k_4289 BOUND_VARIABLE_1196918))) (ho_4767 BOUND_VARIABLE_1317363 BOUND_VARIABLE_1196920)) (ho_4703 (ho_4705 (ho_4775 k_4774 (= BOUND_VARIABLE_1196918 BOUND_VARIABLE_1196920)) (ho_4703 (ho_4705 k_4704 _let_5) (ho_4703 k_4702 _let_5))) (ho_4767 BOUND_VARIABLE_1317358 (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1196920) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 (ho_4216 (ho_4215 k_4221 _let_3) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2))))))) (ho_4767 (ho_6642 (ho_6646 (ho_6645 k_6644 BOUND_VARIABLE_1317363) BOUND_VARIABLE_1196918) BOUND_VARIABLE_1317358) BOUND_VARIABLE_1196920)))))))))) (let ((_let_4007 (forall ((BOUND_VARIABLE_1196907 tptp.nat) (BOUND_VARIABLE_1196908 tptp.nat)) (= (ho_4288 (ho_4287 k_6647 BOUND_VARIABLE_1196907) BOUND_VARIABLE_1196908) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196908)) (ho_4290 k_4289 BOUND_VARIABLE_1196907)))))) (let ((_let_4008 (forall ((BOUND_VARIABLE_1317405 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1196900 tptp.nat)) (= (ho_4245 (ho_4473 k_6648 BOUND_VARIABLE_1317405) BOUND_VARIABLE_1196900) (ho_4258 k_6167 (ho_4245 BOUND_VARIABLE_1317405 BOUND_VARIABLE_1196900)))))) (let ((_let_4009 (forall ((BOUND_VARIABLE_1317416 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1196892 tptp.nat)) (= (ho_4245 (ho_4473 k_6649 BOUND_VARIABLE_1317416) BOUND_VARIABLE_1196892) (ho_4258 k_6167 (ho_4245 BOUND_VARIABLE_1317416 BOUND_VARIABLE_1196892)))))) (let ((_let_4010 (forall ((BOUND_VARIABLE_1317428 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1317427 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1196846 tptp.nat)) (= (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4486 (ho_4821 k_4820 BOUND_VARIABLE_1317428) BOUND_VARIABLE_1317427) BOUND_VARIABLE_1196846)) (ho_4516 k_4515 (ho_4287 k_4822 BOUND_VARIABLE_1196846))) (ho_4245 (ho_4473 (ho_5457 k_6650 BOUND_VARIABLE_1317428) BOUND_VARIABLE_1317427) BOUND_VARIABLE_1196846))))) (let ((_let_4011 (forall ((BOUND_VARIABLE_1317444 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196822 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4767 BOUND_VARIABLE_1317444 BOUND_VARIABLE_1196822))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_4245 (ho_6166 k_6651 BOUND_VARIABLE_1317444) BOUND_VARIABLE_1196822)))))))))) (let ((_let_4012 (forall ((BOUND_VARIABLE_1317464 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196799 tptp.nat)) (let ((_let_1 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one))))) (let ((_let_2 (ho_4767 BOUND_VARIABLE_1317464 BOUND_VARIABLE_1196799))) (let ((_let_3 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_4 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) _let_3) k_4259))) (let ((_let_5 (ho_4247 k_4246 tptp.one))) (= (ho_4258 (ho_4265 (ho_4277 k_4276 (= _let_1 (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 (ho_4196 k_4195 tptp.one))) _let_1))) (ho_4258 (ho_4265 _let_4 _let_5) (ho_4258 (ho_4257 _let_3 k_4248) _let_5))) (ho_4258 (ho_4946 (ho_4945 k_4944 tptp.top_top_set_real) k_4943) (ho_4258 (ho_4265 _let_4 (ho_4245 (ho_4244 k_4243 (ho_4769 k_4773 _let_2)) _let_1)) (ho_4245 (ho_4244 k_4243 (ho_4769 k_4768 _let_2)) _let_1)))) (ho_4245 (ho_6166 k_6652 BOUND_VARIABLE_1317464) BOUND_VARIABLE_1196799)))))))))) (let ((_let_4013 (forall ((BOUND_VARIABLE_1317487 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1317486 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1196753 tptp.nat)) (= (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4825 (ho_4824 k_4823 BOUND_VARIABLE_1317487) BOUND_VARIABLE_1317486) BOUND_VARIABLE_1196753)) (ho_4516 k_4515 (ho_4287 k_4826 BOUND_VARIABLE_1196753))) (ho_4767 (ho_6642 (ho_6641 k_6653 BOUND_VARIABLE_1317487) BOUND_VARIABLE_1317486) BOUND_VARIABLE_1196753))))) (let ((_let_4014 (forall ((BOUND_VARIABLE_1196741 tptp.nat) (BOUND_VARIABLE_1196742 tptp.nat)) (= (ho_4216 (ho_4215 k_6654 BOUND_VARIABLE_1196741) BOUND_VARIABLE_1196742) (ho_4216 (ho_4215 k_4214 (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1196741) BOUND_VARIABLE_1196742)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))))) (let ((_let_4015 (forall ((BOUND_VARIABLE_1196731 tptp.nat) (BOUND_VARIABLE_1196732 tptp.nat)) (= (ho_4288 (ho_4287 k_6655 BOUND_VARIABLE_1196731) BOUND_VARIABLE_1196732) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196732)) (ho_4290 k_4289 BOUND_VARIABLE_1196731)))))) (let ((_let_4016 (forall ((BOUND_VARIABLE_1317529 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1196706 tptp.nat) (BOUND_VARIABLE_1196707 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1317529 BOUND_VARIABLE_1196707)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1196706) BOUND_VARIABLE_1196707)) _let_2))) (ho_4216 (ho_4215 (ho_4730 k_6656 BOUND_VARIABLE_1317529) BOUND_VARIABLE_1196706) BOUND_VARIABLE_1196707)))))))) (let ((_let_4017 (forall ((BOUND_VARIABLE_1196695 tptp.nat) (BOUND_VARIABLE_1196696 tptp.nat)) (= (ho_4288 (ho_4287 k_6657 BOUND_VARIABLE_1196695) BOUND_VARIABLE_1196696) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196696)) (ho_4290 k_4289 BOUND_VARIABLE_1196695)))))) (let ((_let_4018 (forall ((BOUND_VARIABLE_1317561 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1196670 tptp.nat) (BOUND_VARIABLE_1196671 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 BOUND_VARIABLE_1317561 BOUND_VARIABLE_1196671)) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1196670) BOUND_VARIABLE_1196671)) _let_2))) (ho_4216 (ho_4215 (ho_4730 k_6658 BOUND_VARIABLE_1317561) BOUND_VARIABLE_1196670) BOUND_VARIABLE_1196671)))))))) (let ((_let_4019 (forall ((BOUND_VARIABLE_1196659 tptp.nat) (BOUND_VARIABLE_1196660 tptp.nat)) (= (ho_4288 (ho_4287 k_6659 BOUND_VARIABLE_1196659) BOUND_VARIABLE_1196660) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196660)) (ho_4290 k_4289 BOUND_VARIABLE_1196659)))))) (let ((_let_4020 (forall ((BOUND_VARIABLE_1317596 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1317595 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1196587 tptp.nat) (BOUND_VARIABLE_1196588 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_5346 (ho_6084 k_6660 (ho_4215 (ho_4730 (ho_4828 k_4827 BOUND_VARIABLE_1317596) BOUND_VARIABLE_1317595) BOUND_VARIABLE_1196588)) (ho_4516 k_4515 (ho_4287 k_4829 BOUND_VARIABLE_1196588)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1196587) BOUND_VARIABLE_1196588)) _let_2))) (ho_4216 (ho_4215 (ho_4730 (ho_4828 k_6661 BOUND_VARIABLE_1317596) BOUND_VARIABLE_1317595) BOUND_VARIABLE_1196587) BOUND_VARIABLE_1196588)))))))) (let ((_let_4021 (forall ((BOUND_VARIABLE_1196556 tptp.nat) (BOUND_VARIABLE_1196557 tptp.nat) (BOUND_VARIABLE_1196558 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196558)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1196556) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1196557) _let_2))))) (ho_4288 (ho_4287 (ho_4303 k_6662 BOUND_VARIABLE_1196556) BOUND_VARIABLE_1196557) BOUND_VARIABLE_1196558)))))))) (let ((_let_4022 (forall ((BOUND_VARIABLE_1196533 tptp.rat) (BOUND_VARIABLE_1196534 tptp.nat) (BOUND_VARIABLE_1196535 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1196533)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1196534) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1196535) (ho_4442 (ho_4458 (ho_4699 k_6663 BOUND_VARIABLE_1196533) BOUND_VARIABLE_1196534) BOUND_VARIABLE_1196535)))))))))))) (let ((_let_4023 (forall ((BOUND_VARIABLE_1196497 tptp.rat) (BOUND_VARIABLE_1196498 tptp.nat) (BOUND_VARIABLE_1196499 tptp.nat) (BOUND_VARIABLE_1196500 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1196497) (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1196498) _let_8)))) _let_3)) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1196499) _let_8))) BOUND_VARIABLE_1196500) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_6664 BOUND_VARIABLE_1196497) BOUND_VARIABLE_1196498) BOUND_VARIABLE_1196499) BOUND_VARIABLE_1196500)))))))))))))) (let ((_let_4024 (forall ((BOUND_VARIABLE_1196474 tptp.real) (BOUND_VARIABLE_1196475 tptp.nat) (BOUND_VARIABLE_1196476 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1196474)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1196475) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1196476) (ho_4258 (ho_4273 (ho_4696 k_6665 BOUND_VARIABLE_1196474) BOUND_VARIABLE_1196475) BOUND_VARIABLE_1196476)))))))))) (let ((_let_4025 (forall ((BOUND_VARIABLE_1196438 tptp.real) (BOUND_VARIABLE_1196439 tptp.nat) (BOUND_VARIABLE_1196440 tptp.nat) (BOUND_VARIABLE_1196441 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1196438) (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1196439) _let_6)))) _let_1)) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1196440) _let_6))) BOUND_VARIABLE_1196441) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_6666 BOUND_VARIABLE_1196438) BOUND_VARIABLE_1196439) BOUND_VARIABLE_1196440) BOUND_VARIABLE_1196441)))))))))))) (let ((_let_4026 (forall ((BOUND_VARIABLE_1196415 tptp.int) (BOUND_VARIABLE_1196416 tptp.nat) (BOUND_VARIABLE_1196417 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 BOUND_VARIABLE_1196415)) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1196416) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1))))) BOUND_VARIABLE_1196417) (ho_4209 (ho_4220 (ho_4723 k_6667 BOUND_VARIABLE_1196415) BOUND_VARIABLE_1196416) BOUND_VARIABLE_1196417))))))) (let ((_let_4027 (forall ((BOUND_VARIABLE_1196380 tptp.int) (BOUND_VARIABLE_1196381 tptp.nat) (BOUND_VARIABLE_1196382 tptp.nat) (BOUND_VARIABLE_1196383 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1196380) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1196381) _let_3)))) _let_1)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1196382) _let_3))) BOUND_VARIABLE_1196383) (ho_4209 (ho_4220 (ho_6076 (ho_6669 k_6668 BOUND_VARIABLE_1196380) BOUND_VARIABLE_1196381) BOUND_VARIABLE_1196382) BOUND_VARIABLE_1196383))))))))) (let ((_let_4028 (forall ((BOUND_VARIABLE_1196359 tptp.complex) (BOUND_VARIABLE_1196360 tptp.nat) (BOUND_VARIABLE_1196361 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1196359)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1196360) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1196361) (ho_4703 (ho_4709 (ho_4712 k_6670 BOUND_VARIABLE_1196359) BOUND_VARIABLE_1196360) BOUND_VARIABLE_1196361)))))) (let ((_let_4029 (forall ((BOUND_VARIABLE_1196324 tptp.complex) (BOUND_VARIABLE_1196325 tptp.nat) (BOUND_VARIABLE_1196326 tptp.nat) (BOUND_VARIABLE_1196327 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (let ((_let_3 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1196324) (ho_4703 k_4702 (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1196325) _let_2)))) _let_1)) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1196326) _let_2))) BOUND_VARIABLE_1196327) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_6671 BOUND_VARIABLE_1196324) BOUND_VARIABLE_1196325) BOUND_VARIABLE_1196326) BOUND_VARIABLE_1196327)))))))) (let ((_let_4030 (forall ((BOUND_VARIABLE_1196288 tptp.rat) (BOUND_VARIABLE_1196289 tptp.nat) (BOUND_VARIABLE_1196290 tptp.nat) (BOUND_VARIABLE_1196291 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (let ((_let_8 (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3)))) (let ((_let_9 (ho_4457 k_4456 k_4455))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 (ho_4442 (ho_4448 _let_7 BOUND_VARIABLE_1196288) (ho_4442 _let_5 (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1196289) _let_8)))) _let_3)) (ho_4442 (ho_4458 _let_9 BOUND_VARIABLE_1196290) _let_8))) BOUND_VARIABLE_1196291) (ho_4442 (ho_4458 (ho_4718 (ho_4717 k_6672 BOUND_VARIABLE_1196288) BOUND_VARIABLE_1196289) BOUND_VARIABLE_1196290) BOUND_VARIABLE_1196291)))))))))))))) (let ((_let_4031 (forall ((BOUND_VARIABLE_1196265 tptp.rat) (BOUND_VARIABLE_1196266 tptp.nat) (BOUND_VARIABLE_1196267 tptp.rat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4441 _let_4 k_4435))) (let ((_let_6 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_7 (ho_4447 _let_6 k_4443))) (= (ho_4442 (ho_4448 (ho_4447 _let_6 k_4697) (ho_4442 (ho_4448 _let_7 (ho_4442 _let_5 BOUND_VARIABLE_1196265)) (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) BOUND_VARIABLE_1196266) (ho_4442 (ho_4448 _let_7 _let_3) (ho_4442 _let_5 _let_3))))) BOUND_VARIABLE_1196267) (ho_4442 (ho_4458 (ho_4699 k_6673 BOUND_VARIABLE_1196265) BOUND_VARIABLE_1196266) BOUND_VARIABLE_1196267)))))))))))) (let ((_let_4032 (forall ((BOUND_VARIABLE_1196229 tptp.real) (BOUND_VARIABLE_1196230 tptp.nat) (BOUND_VARIABLE_1196231 tptp.nat) (BOUND_VARIABLE_1196232 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (let ((_let_6 (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1)))) (let ((_let_7 (ho_4272 k_4271 k_4270))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 (ho_4258 (ho_4265 _let_5 BOUND_VARIABLE_1196229) (ho_4258 _let_3 (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1196230) _let_6)))) _let_1)) (ho_4258 (ho_4273 _let_7 BOUND_VARIABLE_1196231) _let_6))) BOUND_VARIABLE_1196232) (ho_4258 (ho_4273 (ho_4715 (ho_4714 k_6674 BOUND_VARIABLE_1196229) BOUND_VARIABLE_1196230) BOUND_VARIABLE_1196231) BOUND_VARIABLE_1196232)))))))))))) (let ((_let_4033 (forall ((BOUND_VARIABLE_1196206 tptp.real) (BOUND_VARIABLE_1196207 tptp.nat) (BOUND_VARIABLE_1196208 tptp.real)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4257 _let_2 k_4248))) (let ((_let_4 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_5 (ho_4264 _let_4 k_4259))) (= (ho_4258 (ho_4265 (ho_4264 _let_4 k_4275) (ho_4258 (ho_4265 _let_5 (ho_4258 _let_3 BOUND_VARIABLE_1196206)) (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) BOUND_VARIABLE_1196207) (ho_4258 (ho_4265 _let_5 _let_1) (ho_4258 _let_3 _let_1))))) BOUND_VARIABLE_1196208) (ho_4258 (ho_4273 (ho_4696 k_6675 BOUND_VARIABLE_1196206) BOUND_VARIABLE_1196207) BOUND_VARIABLE_1196208)))))))))) (let ((_let_4034 (forall ((BOUND_VARIABLE_1196171 tptp.int) (BOUND_VARIABLE_1196172 tptp.nat) (BOUND_VARIABLE_1196173 tptp.nat) (BOUND_VARIABLE_1196174 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (let ((_let_3 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1)))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4211 k_4210 BOUND_VARIABLE_1196171) (ho_4209 _let_2 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1196172) _let_3)))) _let_1)) (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1196173) _let_3))) BOUND_VARIABLE_1196174) (ho_4209 (ho_4220 (ho_6076 (ho_6669 k_6676 BOUND_VARIABLE_1196171) BOUND_VARIABLE_1196172) BOUND_VARIABLE_1196173) BOUND_VARIABLE_1196174))))))))) (let ((_let_4035 (forall ((BOUND_VARIABLE_1196148 tptp.int) (BOUND_VARIABLE_1196149 tptp.nat) (BOUND_VARIABLE_1196150 tptp.int)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4210 (ho_4209 _let_2 BOUND_VARIABLE_1196148)) (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) BOUND_VARIABLE_1196149) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 _let_2 _let_1))))) BOUND_VARIABLE_1196150) (ho_4209 (ho_4220 (ho_4723 k_6677 BOUND_VARIABLE_1196148) BOUND_VARIABLE_1196149) BOUND_VARIABLE_1196150))))))) (let ((_let_4036 (forall ((BOUND_VARIABLE_1196113 tptp.complex) (BOUND_VARIABLE_1196114 tptp.nat) (BOUND_VARIABLE_1196115 tptp.nat) (BOUND_VARIABLE_1196116 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (let ((_let_2 (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (let ((_let_3 (ho_4708 k_4707 k_4706))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 (ho_4703 (ho_4705 k_4704 BOUND_VARIABLE_1196113) (ho_4703 k_4702 (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1196114) _let_2)))) _let_1)) (ho_4703 (ho_4709 _let_3 BOUND_VARIABLE_1196115) _let_2))) BOUND_VARIABLE_1196116) (ho_4703 (ho_4709 (ho_4721 (ho_4720 k_6678 BOUND_VARIABLE_1196113) BOUND_VARIABLE_1196114) BOUND_VARIABLE_1196115) BOUND_VARIABLE_1196116)))))))) (let ((_let_4037 (forall ((BOUND_VARIABLE_1196092 tptp.complex) (BOUND_VARIABLE_1196093 tptp.nat) (BOUND_VARIABLE_1196094 tptp.complex)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4704 (ho_4703 k_4702 BOUND_VARIABLE_1196092)) (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) BOUND_VARIABLE_1196093) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1))))) BOUND_VARIABLE_1196094) (ho_4703 (ho_4709 (ho_4712 k_6679 BOUND_VARIABLE_1196092) BOUND_VARIABLE_1196093) BOUND_VARIABLE_1196094)))))) (let ((_let_4038 (forall ((BOUND_VARIABLE_1196062 tptp.real) (BOUND_VARIABLE_1196063 tptp.real) (BOUND_VARIABLE_1196064 tptp.nat) (BOUND_VARIABLE_1196065 tptp.nat)) (let ((_let_1 (ho_4247 k_4246 tptp.one))) (let ((_let_2 (ho_4256 (ho_4255 k_4254 k_4252) k_4250))) (let ((_let_3 (ho_4263 (ho_4262 k_4261 k_4252) _let_2))) (let ((_let_4 (ho_4264 _let_3 k_4275))) (= (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4265 _let_4 (ho_4258 (ho_4273 (ho_4272 k_4271 k_4270) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1196064) BOUND_VARIABLE_1196065)) (ho_4258 (ho_4265 (ho_4264 _let_3 k_4259) _let_1) (ho_4258 (ho_4257 _let_2 k_4248) _let_1)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1196062) BOUND_VARIABLE_1196065))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1196063) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1196064) BOUND_VARIABLE_1196065))) (ho_4245 (ho_4487 (ho_4740 (ho_4782 k_6680 BOUND_VARIABLE_1196062) BOUND_VARIABLE_1196063) BOUND_VARIABLE_1196064) BOUND_VARIABLE_1196065))))))))) (let ((_let_4039 (forall ((BOUND_VARIABLE_1196052 tptp.nat) (BOUND_VARIABLE_1196053 tptp.nat)) (= (ho_4288 (ho_4287 k_6681 BOUND_VARIABLE_1196052) BOUND_VARIABLE_1196053) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1196053)) (ho_4290 k_4289 BOUND_VARIABLE_1196052)))))) (let ((_let_4040 (forall ((BOUND_VARIABLE_1196002 tptp.nat) (BOUND_VARIABLE_1196003 tptp.nat) (BOUND_VARIABLE_1196004 tptp.nat) (BOUND_VARIABLE_1196005 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 (ho_4730 k_4729 k_4728) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1196004) BOUND_VARIABLE_1196005)) (ho_4216 (ho_4215 k_4221 (ho_4213 k_4212 _let_1)) (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1196002) BOUND_VARIABLE_1196005)) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4216 (ho_4215 k_4214 BOUND_VARIABLE_1196003) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1196004) BOUND_VARIABLE_1196005))) _let_2))) (ho_4216 (ho_4215 (ho_4269 (ho_6683 k_6682 BOUND_VARIABLE_1196002) BOUND_VARIABLE_1196003) BOUND_VARIABLE_1196004) BOUND_VARIABLE_1196005)))))))) (let ((_let_4041 (forall ((BOUND_VARIABLE_1195992 tptp.nat) (BOUND_VARIABLE_1195993 tptp.nat)) (= (ho_4288 (ho_4287 k_6684 BOUND_VARIABLE_1195992) BOUND_VARIABLE_1195993) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195993)) (ho_4290 k_4289 BOUND_VARIABLE_1195992)))))) (let ((_let_4042 (forall ((BOUND_VARIABLE_1195962 tptp.rat) (BOUND_VARIABLE_1195963 tptp.rat) (BOUND_VARIABLE_1195964 tptp.nat) (BOUND_VARIABLE_1195965 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4434 k_4433 (ho_4432 (ho_4431 (ho_4430 k_4429 (= _let_1 _let_2)) (ho_4428 (ho_4427 k_4426 _let_2) _let_1)) (ho_4428 (ho_4427 k_4426 _let_1) _let_1))))) (let ((_let_4 (ho_4440 (ho_4439 k_4438 k_4436) k_4433))) (let ((_let_5 (ho_4446 (ho_4445 k_4444 k_4436) _let_4))) (let ((_let_6 (ho_4447 _let_5 k_4697))) (= (ho_4442 (ho_4448 _let_6 (ho_4442 (ho_4448 _let_6 (ho_4442 (ho_4458 (ho_4457 k_4456 k_4455) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1195964) BOUND_VARIABLE_1195965)) (ho_4442 (ho_4448 (ho_4447 _let_5 k_4443) _let_3) (ho_4442 (ho_4441 _let_4 k_4435) _let_3)))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1195962) BOUND_VARIABLE_1195965))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1195963) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1195964) BOUND_VARIABLE_1195965))) (ho_4316 (ho_4338 (ho_4736 (ho_4815 k_6685 BOUND_VARIABLE_1195962) BOUND_VARIABLE_1195963) BOUND_VARIABLE_1195964) BOUND_VARIABLE_1195965))))))))))) (let ((_let_4043 (forall ((BOUND_VARIABLE_1195952 tptp.nat) (BOUND_VARIABLE_1195953 tptp.nat)) (= (ho_4288 (ho_4287 k_6686 BOUND_VARIABLE_1195952) BOUND_VARIABLE_1195953) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195953)) (ho_4290 k_4289 BOUND_VARIABLE_1195952)))))) (let ((_let_4044 (forall ((BOUND_VARIABLE_1195922 tptp.int) (BOUND_VARIABLE_1195923 tptp.int) (BOUND_VARIABLE_1195924 tptp.nat) (BOUND_VARIABLE_1195925 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (= (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 (ho_4219 k_4218 k_4217) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1195924) BOUND_VARIABLE_1195925)) (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1195922) BOUND_VARIABLE_1195925))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1195923) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1195924) BOUND_VARIABLE_1195925))) (ho_4335 (ho_4726 (ho_4725 (ho_4811 k_6687 BOUND_VARIABLE_1195922) BOUND_VARIABLE_1195923) BOUND_VARIABLE_1195924) BOUND_VARIABLE_1195925)))))) (let ((_let_4045 (forall ((BOUND_VARIABLE_1195912 tptp.nat) (BOUND_VARIABLE_1195913 tptp.nat)) (= (ho_4288 (ho_4287 k_6688 BOUND_VARIABLE_1195912) BOUND_VARIABLE_1195913) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195913)) (ho_4290 k_4289 BOUND_VARIABLE_1195912)))))) (let ((_let_4046 (forall ((BOUND_VARIABLE_1195882 tptp.complex) (BOUND_VARIABLE_1195883 tptp.complex) (BOUND_VARIABLE_1195884 tptp.nat) (BOUND_VARIABLE_1195885 tptp.nat)) (let ((_let_1 (ho_4701 k_4700 tptp.one))) (= (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4705 k_4710 (ho_4703 (ho_4709 (ho_4708 k_4707 k_4706) (ho_4216 (ho_4215 k_4332 BOUND_VARIABLE_1195884) BOUND_VARIABLE_1195885)) (ho_4703 (ho_4705 k_4704 _let_1) (ho_4703 k_4702 _let_1)))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195882) BOUND_VARIABLE_1195885))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195883) (ho_4216 (ho_4215 k_4223 BOUND_VARIABLE_1195884) BOUND_VARIABLE_1195885))) (ho_4767 (ho_4779 (ho_4778 (ho_4777 k_6689 BOUND_VARIABLE_1195882) BOUND_VARIABLE_1195883) BOUND_VARIABLE_1195884) BOUND_VARIABLE_1195885)))))) (let ((_let_4047 (forall ((BOUND_VARIABLE_1195872 tptp.nat) (BOUND_VARIABLE_1195873 tptp.nat)) (= (ho_4288 (ho_4287 k_6690 BOUND_VARIABLE_1195872) BOUND_VARIABLE_1195873) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195873)) (ho_4290 k_4289 BOUND_VARIABLE_1195872)))))) (let ((_let_4048 (forall ((BOUND_VARIABLE_1195830 tptp.nat) (BOUND_VARIABLE_1195831 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1195830) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1195831 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6691 BOUND_VARIABLE_1195830) BOUND_VARIABLE_1195831))))) (let ((_let_4049 (forall ((BOUND_VARIABLE_1318182 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1195815 tptp.real) (BOUND_VARIABLE_1195816 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1318182 BOUND_VARIABLE_1195816)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1195815) BOUND_VARIABLE_1195816)) (ho_4245 (ho_4244 (ho_4512 k_6692 BOUND_VARIABLE_1318182) BOUND_VARIABLE_1195815) BOUND_VARIABLE_1195816))))) (let ((_let_4050 (forall ((BOUND_VARIABLE_1195804 tptp.nat) (BOUND_VARIABLE_1195805 tptp.nat)) (= (ho_4288 (ho_4287 k_6693 BOUND_VARIABLE_1195804) BOUND_VARIABLE_1195805) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195805)) (ho_4290 k_4289 BOUND_VARIABLE_1195804)))))) (let ((_let_4051 (forall ((BOUND_VARIABLE_1318210 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1195793 tptp.complex) (BOUND_VARIABLE_1195794 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6694 BOUND_VARIABLE_1318210) BOUND_VARIABLE_1195793) BOUND_VARIABLE_1195794) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1318210 BOUND_VARIABLE_1195794)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195793) BOUND_VARIABLE_1195794)))))) (let ((_let_4052 (forall ((BOUND_VARIABLE_1195782 tptp.nat) (BOUND_VARIABLE_1195783 tptp.nat)) (= (ho_4288 (ho_4287 k_6695 BOUND_VARIABLE_1195782) BOUND_VARIABLE_1195783) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195783)) (ho_4290 k_4289 BOUND_VARIABLE_1195782)))))) (let ((_let_4053 (forall ((BOUND_VARIABLE_1195740 tptp.nat) (BOUND_VARIABLE_1195741 tptp.nat)) (= (not (forall ((I3 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4213 k_4212 _let_1))) (let ((_let_4 (ho_4219 k_4218 k_4217))) (let ((_let_5 (ho_4464 (ho_4463 k_4462 _let_3) (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_4 BOUND_VARIABLE_1195740) _let_2)) (ho_4209 (ho_4220 _let_4 _let_3) _let_2)))))) (or (not (= BOUND_VARIABLE_1195741 (ho_4216 (ho_4468 k_4467 _let_5) I3))) (not (ho_4293 (ho_4292 k_4291 (ho_4290 k_4289 I3)) (ho_4290 k_4289 (ho_4466 k_4465 _let_5)))))))))))) (ho_4288 (ho_4287 k_6696 BOUND_VARIABLE_1195740) BOUND_VARIABLE_1195741))))) (let ((_let_4054 (forall ((BOUND_VARIABLE_1318260 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1195725 tptp.real) (BOUND_VARIABLE_1195726 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1318260 BOUND_VARIABLE_1195726)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1195725) BOUND_VARIABLE_1195726)) (ho_4245 (ho_4244 (ho_4512 k_6697 BOUND_VARIABLE_1318260) BOUND_VARIABLE_1195725) BOUND_VARIABLE_1195726))))) (let ((_let_4055 (forall ((BOUND_VARIABLE_1195714 tptp.nat) (BOUND_VARIABLE_1195715 tptp.nat)) (= (ho_4288 (ho_4287 k_6698 BOUND_VARIABLE_1195714) BOUND_VARIABLE_1195715) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195715)) (ho_4290 k_4289 BOUND_VARIABLE_1195714)))))) (let ((_let_4056 (forall ((BOUND_VARIABLE_1318287 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1195699 tptp.real) (BOUND_VARIABLE_1195700 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4245 BOUND_VARIABLE_1318287 BOUND_VARIABLE_1195700)) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1195699) BOUND_VARIABLE_1195700)) (ho_4245 (ho_4244 (ho_4512 k_6699 BOUND_VARIABLE_1318287) BOUND_VARIABLE_1195699) BOUND_VARIABLE_1195700))))) (let ((_let_4057 (forall ((BOUND_VARIABLE_1195688 tptp.nat) (BOUND_VARIABLE_1195689 tptp.nat)) (= (ho_4288 (ho_4287 k_6700 BOUND_VARIABLE_1195688) BOUND_VARIABLE_1195689) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195689)) (ho_4290 k_4289 BOUND_VARIABLE_1195688)))))) (let ((_let_4058 (forall ((BOUND_VARIABLE_1318317 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1318316 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1195636 tptp.real) (BOUND_VARIABLE_1195637 tptp.nat)) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4275) (ho_4519 (ho_4518 k_4517 (ho_4487 (ho_4486 (ho_4821 k_4830 BOUND_VARIABLE_1318317) BOUND_VARIABLE_1318316) BOUND_VARIABLE_1195637)) (ho_4516 k_4515 (ho_4287 k_4831 BOUND_VARIABLE_1195637)))) (ho_4245 (ho_4244 k_4243 BOUND_VARIABLE_1195636) BOUND_VARIABLE_1195637)) (ho_4245 (ho_4244 (ho_4512 (ho_6702 k_6701 BOUND_VARIABLE_1318317) BOUND_VARIABLE_1318316) BOUND_VARIABLE_1195636) BOUND_VARIABLE_1195637))))) (let ((_let_4059 (forall ((BOUND_VARIABLE_1195605 tptp.nat) (BOUND_VARIABLE_1195606 tptp.nat) (BOUND_VARIABLE_1195607 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195607)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195605) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195606) _let_2))))) (ho_4288 (ho_4287 (ho_4303 k_6703 BOUND_VARIABLE_1195605) BOUND_VARIABLE_1195606) BOUND_VARIABLE_1195607)))))))) (let ((_let_4060 (forall ((BOUND_VARIABLE_1318364 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1195594 tptp.int) (BOUND_VARIABLE_1195595 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6704 BOUND_VARIABLE_1318364) BOUND_VARIABLE_1195594) BOUND_VARIABLE_1195595) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1318364 BOUND_VARIABLE_1195595)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1195594) BOUND_VARIABLE_1195595)))))) (let ((_let_4061 (forall ((BOUND_VARIABLE_1195583 tptp.nat) (BOUND_VARIABLE_1195584 tptp.nat)) (= (ho_4288 (ho_4287 k_6705 BOUND_VARIABLE_1195583) BOUND_VARIABLE_1195584) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195584)) (ho_4290 k_4289 BOUND_VARIABLE_1195583)))))) (let ((_let_4062 (forall ((BOUND_VARIABLE_1318391 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1195572 tptp.int) (BOUND_VARIABLE_1195573 tptp.nat)) (= (ho_4335 (ho_4334 (ho_6427 k_6706 BOUND_VARIABLE_1318391) BOUND_VARIABLE_1195572) BOUND_VARIABLE_1195573) (ho_4209 (ho_4211 k_4222 (ho_4335 BOUND_VARIABLE_1318391 BOUND_VARIABLE_1195573)) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1195572) BOUND_VARIABLE_1195573)))))) (let ((_let_4063 (forall ((BOUND_VARIABLE_1195561 tptp.nat) (BOUND_VARIABLE_1195562 tptp.nat)) (= (ho_4288 (ho_4287 k_6707 BOUND_VARIABLE_1195561) BOUND_VARIABLE_1195562) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195562)) (ho_4290 k_4289 BOUND_VARIABLE_1195561)))))) (let ((_let_4064 (forall ((BOUND_VARIABLE_1318420 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1318419 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1195508 tptp.int) (BOUND_VARIABLE_1195509 tptp.nat)) (= (ho_4209 (ho_4211 k_4222 (ho_6080 (ho_6079 k_6526 (ho_4726 (ho_4834 (ho_4833 k_4832 BOUND_VARIABLE_1318420) BOUND_VARIABLE_1318419) BOUND_VARIABLE_1195509)) (ho_4516 k_4515 (ho_4287 k_4835 BOUND_VARIABLE_1195509)))) (ho_4335 (ho_4334 k_4333 BOUND_VARIABLE_1195508) BOUND_VARIABLE_1195509)) (ho_4335 (ho_4334 (ho_6427 (ho_6709 k_6708 BOUND_VARIABLE_1318420) BOUND_VARIABLE_1318419) BOUND_VARIABLE_1195508) BOUND_VARIABLE_1195509))))) (let ((_let_4065 (forall ((BOUND_VARIABLE_1195477 tptp.nat) (BOUND_VARIABLE_1195478 tptp.nat) (BOUND_VARIABLE_1195479 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195479)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195477) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195478) _let_2))))) (ho_4288 (ho_4287 (ho_4303 k_6710 BOUND_VARIABLE_1195477) BOUND_VARIABLE_1195478) BOUND_VARIABLE_1195479)))))))) (let ((_let_4066 (forall ((BOUND_VARIABLE_1318466 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1195462 tptp.rat) (BOUND_VARIABLE_1195463 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1318466 BOUND_VARIABLE_1195463)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1195462) BOUND_VARIABLE_1195463)) (ho_4316 (ho_4799 (ho_6533 k_6711 BOUND_VARIABLE_1318466) BOUND_VARIABLE_1195462) BOUND_VARIABLE_1195463))))) (let ((_let_4067 (forall ((BOUND_VARIABLE_1195451 tptp.nat) (BOUND_VARIABLE_1195452 tptp.nat)) (= (ho_4288 (ho_4287 k_6712 BOUND_VARIABLE_1195451) BOUND_VARIABLE_1195452) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195452)) (ho_4290 k_4289 BOUND_VARIABLE_1195451)))))) (let ((_let_4068 (forall ((BOUND_VARIABLE_1318493 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1195436 tptp.rat) (BOUND_VARIABLE_1195437 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_4316 BOUND_VARIABLE_1318493 BOUND_VARIABLE_1195437)) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1195436) BOUND_VARIABLE_1195437)) (ho_4316 (ho_4799 (ho_6533 k_6713 BOUND_VARIABLE_1318493) BOUND_VARIABLE_1195436) BOUND_VARIABLE_1195437))))) (let ((_let_4069 (forall ((BOUND_VARIABLE_1195425 tptp.nat) (BOUND_VARIABLE_1195426 tptp.nat)) (= (ho_4288 (ho_4287 k_6714 BOUND_VARIABLE_1195425) BOUND_VARIABLE_1195426) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195426)) (ho_4290 k_4289 BOUND_VARIABLE_1195425)))))) (let ((_let_4070 (forall ((BOUND_VARIABLE_1318523 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1318522 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1195372 tptp.rat) (BOUND_VARIABLE_1195373 tptp.nat)) (= (ho_4442 (ho_4448 (ho_4447 (ho_4446 (ho_4445 k_4444 k_4436) (ho_4440 (ho_4439 k_4438 k_4436) k_4433)) k_4697) (ho_6089 (ho_6088 k_6536 (ho_4338 (ho_4838 (ho_4837 k_4836 BOUND_VARIABLE_1318523) BOUND_VARIABLE_1318522) BOUND_VARIABLE_1195373)) (ho_4516 k_4515 (ho_4287 k_4839 BOUND_VARIABLE_1195373)))) (ho_4316 (ho_4799 k_4798 BOUND_VARIABLE_1195372) BOUND_VARIABLE_1195373)) (ho_4316 (ho_4799 (ho_6533 (ho_6716 k_6715 BOUND_VARIABLE_1318523) BOUND_VARIABLE_1318522) BOUND_VARIABLE_1195372) BOUND_VARIABLE_1195373))))) (let ((_let_4071 (forall ((BOUND_VARIABLE_1195341 tptp.nat) (BOUND_VARIABLE_1195342 tptp.nat) (BOUND_VARIABLE_1195343 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195343)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195341) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195342) _let_2))))) (ho_4288 (ho_4287 (ho_4303 k_6717 BOUND_VARIABLE_1195341) BOUND_VARIABLE_1195342) BOUND_VARIABLE_1195343)))))))) (let ((_let_4072 (forall ((BOUND_VARIABLE_1318570 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1195330 tptp.complex) (BOUND_VARIABLE_1195331 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6718 BOUND_VARIABLE_1318570) BOUND_VARIABLE_1195330) BOUND_VARIABLE_1195331) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1318570 BOUND_VARIABLE_1195331)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195330) BOUND_VARIABLE_1195331)))))) (let ((_let_4073 (forall ((BOUND_VARIABLE_1195319 tptp.nat) (BOUND_VARIABLE_1195320 tptp.nat)) (= (ho_4288 (ho_4287 k_6719 BOUND_VARIABLE_1195319) BOUND_VARIABLE_1195320) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195320)) (ho_4290 k_4289 BOUND_VARIABLE_1195319)))))) (let ((_let_4074 (forall ((BOUND_VARIABLE_1318597 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1195308 tptp.complex) (BOUND_VARIABLE_1195309 tptp.nat)) (= (ho_4767 (ho_4766 (ho_4858 k_6720 BOUND_VARIABLE_1318597) BOUND_VARIABLE_1195308) BOUND_VARIABLE_1195309) (ho_4703 (ho_4705 k_4710 (ho_4767 BOUND_VARIABLE_1318597 BOUND_VARIABLE_1195309)) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195308) BOUND_VARIABLE_1195309)))))) (let ((_let_4075 (forall ((BOUND_VARIABLE_1195297 tptp.nat) (BOUND_VARIABLE_1195298 tptp.nat)) (= (ho_4288 (ho_4287 k_6721 BOUND_VARIABLE_1195297) BOUND_VARIABLE_1195298) (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195298)) (ho_4290 k_4289 BOUND_VARIABLE_1195297)))))) (let ((_let_4076 (forall ((BOUND_VARIABLE_1318626 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1318625 |u_(-> tptp.nat tptp.complex)|) (BOUND_VARIABLE_1195245 tptp.complex) (BOUND_VARIABLE_1195246 tptp.nat)) (= (ho_4703 (ho_4705 k_4710 (ho_6495 (ho_6494 k_6493 (ho_4779 (ho_4825 (ho_4824 k_4840 BOUND_VARIABLE_1318626) BOUND_VARIABLE_1318625) BOUND_VARIABLE_1195246)) (ho_4516 k_4515 (ho_4287 k_4841 BOUND_VARIABLE_1195246)))) (ho_4767 (ho_4766 k_4765 BOUND_VARIABLE_1195245) BOUND_VARIABLE_1195246)) (ho_4767 (ho_4766 (ho_4858 (ho_6723 k_6722 BOUND_VARIABLE_1318626) BOUND_VARIABLE_1318625) BOUND_VARIABLE_1195245) BOUND_VARIABLE_1195246))))) (let ((_let_4077 (forall ((BOUND_VARIABLE_1195214 tptp.nat) (BOUND_VARIABLE_1195215 tptp.nat) (BOUND_VARIABLE_1195216 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195216)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195214) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195215) _let_2))))) (ho_4288 (ho_4287 (ho_4303 k_6724 BOUND_VARIABLE_1195214) BOUND_VARIABLE_1195215) BOUND_VARIABLE_1195216)))))))) (let ((_let_4078 (forall ((BOUND_VARIABLE_1195182 tptp.nat) (BOUND_VARIABLE_1195183 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (= (ho_4293 (ho_4292 k_4304 (ho_4290 k_4289 BOUND_VARIABLE_1195183)) (ho_4290 k_4289 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195182) _let_2)))) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4288 (ho_4287 k_6725 BOUND_VARIABLE_1195182) BOUND_VARIABLE_1195183)))))))) (let ((_let_4079 (forall ((BOUND_VARIABLE_1318699 |u_(-> tptp.nat tptp.real)|) (BOUND_VARIABLE_1195149 tptp.nat)) (let ((_let_1 (ho_4196 k_4195 tptp.one))) (let ((_let_2 (ho_4209 (ho_4211 k_4210 _let_1) (ho_4209 (ho_4208 (ho_4207 (ho_4206 k_4205 k_4203) k_4201) (ho_4200 k_4199 k_4197)) _let_1)))) (let ((_let_3 (ho_4219 k_4218 k_4217))) (let ((_let_4 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4222 (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 (ho_4196 k_4195 (ho_4193 k_4192 tptp.one)))) _let_2)) (ho_4209 (ho_4220 _let_3 BOUND_VARIABLE_1195149) _let_2))))) (= (ho_4258 (ho_4265 (ho_4264 (ho_4263 (ho_4262 k_4261 k_4252) (ho_4256 (ho_4255 k_4254 k_4252) k_4250)) k_4259) (ho_4245 BOUND_VARIABLE_1318699 _let_4)) (ho_4245 BOUND_VARIABLE_1318699 (ho_4213 k_4212 (ho_4209 (ho_4211 k_4210 (ho_4209 (ho_4220 _let_3 _let_4) _let_2)) (ho_4209 (ho_4220 _let_3 (ho_4213 k_4212 _let_1)) _let_2))))) (ho_4245 (ho_4473 k_6726 BOUND_VARIABLE_1318699) BOUND_VARIABLE_1195149))))))))) (let ((_let_4080 (forall ((BOUND_VARIABLE_1195138 tptp.nat) (BOUND_VARIABLE_1195139 tptp.nat)) (= (ho_4288 (ho_4287 k_6727 BOUND_VARIABLE_1195138) BOUND_VARI